I should start with a confession: almost every interesting result in this project showed up first as a bug.

The value function looked wrong before it looked right, the defensive zones came out more valuable than the penalty box, which is the kind of thing that should make you stop and distrust everything downstream of it. The headline policy comparison flipped sign between two runs of the same code with a different random seed, which meant the number I nearly wrote down as “the effect” was, for a while, just noise wearing a confidence interval as a costume. None of this is a special property of football, or of me being particularly careless. It’s what happens whenever you try to build something quantitative that continuously simulates itself: every layer you add is a new place for a plausible-looking number to be wrong in a way that doesn’t announce itself.

Here’s the idea underneath all of that. Basketball analytics figured out years ago that a possession isn’t one event, it’s a sequence: a chain of decisions, each one changing the odds of what happens next. Once you accept that, a possession stops being a row in a spreadsheet and starts looking like something with real mathematical structure: a Markov decision process (MDP), the same framework used for robot navigation, inventory management, and, since Cervone, D’Amour, Bornn, and Goldsberry’s 2016 paper, a full NBA possession, using the shot clock as the variable that makes the whole thing nonstationary: what happens next depends not just on where the ball is, but on how much time is left to do something with it.

Football doesn’t have a shot clock. But it has something close enough to steal the idea from: the amount of time a team has actually had the ball since winning it. I call it the possession clock, and it does not behave the way the shot-clock analogy predicts.

I spent an ongoing season’s worth of Ecuadorian Liga Pro data (136 matches, 16 teams, 37,075 possessions, full Opta/Stats Perform event data , building this out end to end: fitting the model, solving it, simulating with it, and repeatedly catching myself believing something that turned out to be a mistake in my own code rather than a finding about football.

Table of contents

1. The Possession as a Markov Decision Process

2. Bayesian Hierarchical Parametrization

3. Possession-Clock Nonstationary

4. The Value Function

5. Policy Simulation and the Paired-Design Correction

6. Game-Theoretic Limitations

7. Where this fits

8. Conclusion

9. Sources

The Possession as a Markov Decision Process

Picture a single possession as a chain of small bets. The team on the ball is somewhere on the pitch, has held it for some amount of time, and has to decide: push forward, go sideways, play it back, whip in a cross, or shoot. Whatever they choose changes where the ball ends up and how much time is left before the whole thing resolves in a goal, a stopped shot, or a turnover.

That’s the whole model, stripped down. Mathematicians call this a Markov decision process: states, actions, and the odds of moving from one to the next.

Break it into pieces. A possession starts the instant a team wins the ball and ends the moment it’s lost, shot, or the whistle blows. While it’s alive, the “state” is just two numbers which of 24 zones on the pitch the ball occupies (a 6-by-4 grid over the attacking half) and which of five time windows the clock has ticked into: 0–5 seconds, 5–10, 10–15, 15–25, or 25-plus. From any of those states, a team picks one of five actions — advance, sideways, back, cross, or shoot — and the model doesn’t care whether the action actually works. A completed pass, an intercepted cross, a foul won: all of that gets absorbed into what happens next, not into the label of what was attempted. It’s the same trick basketball analytics uses to keep “attempt a three-pointer” separate from “make it or miss it.”

Those start and end aren’t left to intuition. A possession begins the instant ball control changes hands, a completed pass, a successful take-on, a won aerial duel, or a loose-ball recovery—and it ends in exactly one of a fixed set of ways: a goal, a shot that doesn’t score, a failed pass or take-on, a defensive interception, tackle, or clearance, a foul conceded, or the whistle at the end of a half. Every one of the 37,075 possessions in the dataset was carved out of the raw Opta event stream by applying that rule automatically, match by match.

A possession starts on any change of ball control and ends in a goal, a shot, a turnover, or the whistle , applied automatically across the full event stream.

The part that actually does the work is how the odds of the next state shift depending on how long the ball’s already been on a team’s foot. Five extra seconds of possession and the odds genuinely change, that’s what makes this nonstationary, rather than one fixed set of odds applied blindly regardless of the clock.

One deliberate shortcut sits underneath all of it: the model has no memory. A pass from the final third is treated identically whether the team arrived there through a slow 25-pass build-up or a single long ball forward. That’s not a claim that build-up style is irrelevant to how football actually works—it’s what makes fitting a full season of matches computationally possible at all. The cost is that things like fatigue or the scoreline, which plainly do shape decisions on a pitch, aren’t in the model.

None of the specific numbers here, five actions, a 6-by-4 zone grid, five clock windows—come from theory. They’re a deliberate coarseness tradeoff: fine enough that zone and clock still carry real information and coarse enough that a single season of matches still leaves enough real possessions in each cell to fit reliably, especially once lineups start splitting the data further, which is the whole subject of the next chapter. A finer grid would look more precise on paper and emptier in practice.

Once a season of possessions is written this way, two questions open up that a stats sheet can’t answer on its own: from any position on the pitch, what’s the chance this possession ends in a goal? And what happens to a team’s numbers across a whole season if it played differently? Answering either means modelling the possession as a whole, not just how it ended.

The possession as a Markov decision process: state, attempted action, transition, and the terminal outcomes.

Bayesian Hierarchical Parametrization

Here’s the problem nobody warns you about before trying this in football: there isn’t enough football. An NBA team runs through dozens of shot-clock possessions in a single game. Slice a football season down by which eleven players were actually on the pitch, and most situations, a given zone, a given clock window, a given lineup, get visited a handful of times, or never. Lineups don’t even hold still long enough to help; they turn over constantly through substitutions and rotation across more than 30 matches.

The fix borrows a trick statisticians have used since the 1970s, when Bradley Efron and Carl Morris showed that a baseball player’s early-season batting average is a poor guess of his true ability, and that nudging every player’s number toward the league average—harder for players with less data behind them—produces a better one. Do the same thing here, but in three layers instead of one: pull a lineup’s estimate toward its team’s overall tendency, and pull each team’s estimate toward the league baseline, in both cases only as hard as the data demands. A settled first-choice XI with hundreds of possessions in a given zone barely gets touched. A makeshift back line that showed up for eleven minutes in one match gets pulled hard toward “how this team normally plays.” Recent matches also count for more than early-season ones, decaying by about 2% in weight per week, so current estimates track a team’s present identity rather than freezing it in August.

That solves sparsity. It doesn’t solve a second problem: a team uses many different lineups across a season, and each one technically has its own fitted model. Simulating a season faithfully would mean carrying every lineup’s version forward in parallel — accurate, but a computational headache once uncertainty and thousands of simulated seasons get layered on top. So all those lineup-specific models get folded into one team-average version, weighted by how much each lineup actually played rather than by how often it happened to touch a given part of the pitch. There’s a proof in the full paper showing the weighting behaves exactly as it should mathematically, but the plain version is: the model doesn’t let a fringe substitute’s ten minutes quietly distort what “the team” is assumed to do.

The three-level shrinkage cascade: a fringe lineup is pulled hard toward its team, a settled lineup is dominated by its own data.

Possession-Clock Nonstationarity

Borrow the shot-clock intuition and the obvious bet is that turnovers pile up as the clock runs down — the defense gets organised, options narrow. That bet loses.

Turnover risk peaks in the first five seconds after a team wins the ball back , 22.9% of actions in that window end in a turnover, league-wide, and then drops to a steadier 16–17% for the rest of the possession. The danger zone isn’t the end of a possession. It’s the beginning.

The likely explanation: the moment right after winning the ball back is chaotic, the first touch is contested, the ball is loose, nobody’s organised yet. Once a possession survives that opening scramble, the team settles and the risk falls. It’s the exact opposite shape basketball’s shot clock would predict, a reminder that the analogy is a starting point, not an answer, and the real behavior has to be measured rather than assumed.

Not every team behaves the same way here, either. Break the same numbers down by club and most sides share that early spike, but differ a lot in how steady they get afterward, some stay fragile deep into a possession, others settle down hard and fast. That’s a genuinely useful scouting signal: whether an opponent is easiest to dispossess in the first five seconds after winning the ball, or whether the pressure has to be sustained because their risk never really drops.

League-wide possession outcome by possession-clock bucket. Turnover risk peaks in the first five seconds, not at the end.

Per-team breakdown: most sides share the early spike, but differ sharply in how much risk falls afterward.

The same per-team lens works across a different axis too, not the clock within a possession but the calendar across a season. Track a five-match rolling average of how often a team’s possessions end in a shot, and the trends aren’t uniform: Independiente del Valle opens the season at the league’s highest rate, around 21%, and drifts down to roughly 15% by its end, while Liga Deportiva Universitaria de Quito does the opposite, climbing from the bottom of the league, near 6%, up to among the highest, around 15%, by the same point in the season. A single-season average, the kind reported everywhere else in this piece, can quietly average over two teams that arrived at the same number by opposite routes.

Five-match rolling average of shot-ending rate per possession, all 16 teams, ranked by current form. Faint points are single-match values.

The Value Function

Once the model is fitted, it can answer a sharper question than “what happens next”: from anywhere on the pitch, at any point in a possession, what’s the probability this ends in a goal? Solve that for every position and the result is a value function, computed here the standard way, value iteration, where an initial guess of zero gets updated repeatedly from neighboring states until the numbers stop moving. It settles quickly, well under 150 passes through the data.

For Independiente del Valle, the resulting map does exactly what you’d hope: value climbs smoothly the closer the ball gets to the opponent’s goal, in every single time window, from under 1% deep in their own third to 12–19% inside the box. That’s not a shocking finding by itself. What’s worth admitting is that it wasn’t the first result this exact chart produced.

The first version showed defensive-third zones as more dangerous than the penalty area, obviously wrong, and a useful kind of wrong, because a model that violates common sense this badly is telling you to go check your code, not your football theory. Two separate bugs turned up. Own goals were being credited to the wrong team as a converted shot of their own, inflating how valuable defensive zones looked. And a plotting-library quirk was quietly printing the right numbers on the wrong squares of the heatmap, a coordinate flip that had nothing to do with football and everything to do with how a plotting library orients a vertical pitch. Fix both, and the map snaps into the shape it should always have had. The lesson survives the specific bugs: if a model says defending your own goal is safer than attacking the opponent’s, don’t write a paragraph explaining why that might secretly be true. Go find the bug.

The solved value function for Independiente del Valle: probability a possession ends in a goal, by zone and clock bucket.

That gradient isn’t only a property of the fitted model, it shows up directly in the raw data, before any Bellman equation gets involved. Shot-attempt rate and goal-conversion rate both concentrate in the same zones: shots cluster almost entirely in the attacking third, peaking at 46–50% of visits to the central zones right in front of goal, and conversion given a shot climbs from roughly 4–5% out wide to 13–14% centrally inside the box (zones with fewer than 15 shots are masked rather than reported, since a raw rate off a handful of attempts would be noise). The value function and the raw shot data are telling the same story independently.

League-wide shot-attempt rate and goal-conversion rate by pitch zone. Zones with fewer than 15 shots are masked rather than reported.

Policy Simulation and the Paired-Design Correction

Different teams already play differently, and the model can show that directly before any counterfactual enters the picture. Rank every team’s real, observed mix of forward, sideways, and backward passing, and the league spreads out across a genuine range rather than clustering in one corner, forward shares run 35–47%, sideways 43–52%, backward 11–18% across the 16 clubs. Marker size below encodes each team’s simulated on-policy goal rate, and Independiente del Valle sits at the league’s highest despite an unremarkable build-up-style position: their attacking output looks like it comes from execution quality more than from an unusual style.

Forward/sideways/backward share of every non-shot action attempted, by team; marker size is simulated on-policy goal rate per possession.

The simulator’s job is to play out entire possessions from the fitted model while staying honest about how uncertain the underlying numbers still are: for every decision point, it draws one plausible version of “how the world behaves” from the model’s uncertainty, plays out hundreds of possessions against that version, and repeats the whole thing across many separately-drawn versions of the world. Because the model keeps a team’s decision-making — how often it chooses to cross versus play safe, separate from the outcomes those decisions produce, it supports a real counterfactual: what if this team played more directly, more advancing and crossing, less sideways and backward passing, while everything else about how defenses respond stays the same?

Here’s what that shift actually looks like for one real, well-populated situation, a wide attacking position for Independiente del Valle. The altered policy moves probability mass away from sideways and backward passes and toward advancing and crossing, while the fitted execution quality, what happens once a decision is attempted, stays exactly the same on both sides of the comparison.

On-policy vs. altered-policy action-choice probabilities for one real fitted state. Only the decision mix moves; the fitted dynamics are identical under both policies.

This is where the project nearly went wrong. The first version of this comparison ran the on-policy simulation once, the altered-policy simulation once, independently, and subtracted the two. For Independiente del Valle, that produced a headline number: playing more directly was worth +0.15 percentage points of goal rate. Running the identical comparison again, with nothing changed except the random seed, produced −0.39 percentage points. The sign flipped. Nothing about the team’s tactics had changed between those two runs, only the dice.

The reason is that goals are rare, roughly 1–2% of possessions even for a good team, and each of those two simulation runs was independently guessing at the underlying odds of how the world behaves. The comparison wasn’t measuring the effect of the policy change. It was measuring the policy change plus two separate, uncorrelated guesses about the world, and the guessing noise was bigger than the effect being hunted for.

The fix: within each simulated version of the world, run both the real policy and the altered policy against the exact same draw of “how the world behaves,” instead of two separately-guessed worlds. The only thing that can differ between the two outcomes is then the policy itself. Do that across enough simulated worlds, and report the confidence interval around the average difference, not the spread of individual outcomes, which answers a different question, and the sign stops flipping.

Run properly, the finding is more modest than the original headline, and more honest for it. Across all 16 Liga Pro teams, only three show a directness effect that clears the bar of statistical confidence: Independiente del Valle (+0.73 percentage points), Universidad Católica del Ecuador (+0.48pp), and Orense SC (+0.43pp). For the other 13, the data simply doesn’t support a confident answer either way. That’s not the simulator failing, given how rare goals are and how small the tactical nudge was, “we can’t tell” is often the honest answer, and a model willing to say so is more trustworthy than one that finds a headline every time you ask it a question.

On-policy vs. altered-policy simulated possession outcomes for Independiente del Valle, with 95% predictive intervals.

Before looking at how much directness could move each team, here’s where every team already stands: simulated on-policy goal rate per possession, all 16 clubs, with 95% predictive intervals.

Simulated on-policy goal rate per possession, all 16 teams, with 95% predictive intervals.

The corrected, paired-design estimate of the directness effect for all 16 Liga Pro teams. Only three clear the bar of statistical confidence.

Game-Theoretic Limitations

There’s a limit to how far any of this should be trusted, and it’s worth stating plainly. The odds this model learned were produced by real defenses reacting to what teams actually do. If a team almost never crosses from deep, opposing full-backs don’t have to respect that threat and can tuck inside, which is baked into the data the model learned from. Simulate a version of that team that suddenly crosses a lot more, while keeping those same learned odds fixed, and the simulation is quietly assuming the opposition doesn’t notice or adjust.

For a small, occasional change, that’s a fine approximation. For a big, sustained one, it breaks down in a predictable direction, a defense that’s paying attention should specifically shut down whatever the new approach is trying to exploit. So the directness numbers above are best read as an upper bound on the surprise value of a change, not a promise of what happens once opponents have seen enough tape to adjust. The honest way to think about “what’s the right way to play” isn’t one team optimizing against a defense that stands still, it’s two teams’ game plans responding to each other, a genuinely harder problem this version of the model doesn’t attempt to solve. Teaching the simulator to play both sides against each other, adjusting back and forth, is the obvious next step.

What this project computes today (a single fixed-dynamics pass) against the opponent-adaptive loop described above as the natural extension.

Where This Fits

None of this happens in a vacuum, and it’s worth being explicit about the neighborhood. Football analytics already has a mature literature on valuing what happens with the ball. Decroos, Bransen, Van Haaren, and Davis’s VAEP framework values every on-the-ball action by the change in scoring and conceding probability it produces. Expected Threat (xT) models do something similar with a simpler zone-to-zone Markov chain. Fernández, Bornn, and Cervone’s Expected Possession Value framework uses player-tracking data to value an entire possession moment by moment through a deep-learning model of pitch control — the closest existing relative to what this project is doing, just with continuous tracking coordinates in place of a discretized zone-and-clock grid. The single closest relative is more recent still: Le Coz, Boustila, and Imbach published a semi-Markov framework for football possessions in 2026, modeling event timing as a continuous sojourn time rather than discretizing it into buckets — a more principled treatment of exactly the nonstationarity this project handles with five clock windows, at the cost of a heavier model.

Two other threads get borrowed rather than extended. Constantinou and Fenton’s pi-rating system and the Dixon-Coles bivariate-Poisson model both established, well before this project, that shrinkage and structured pooling matter for football’s comparatively sparse per-team data, just applied to match scorelines rather than to transition probabilities. And the statistical machinery underneath the hierarchy itself — hierarchical Bayes, value iteration, empirical-Bayes shrinkage, isn’t new either; it’s standard material from Gelman and Hill’s multilevel-modeling text, Puterman’s Markov decision process text, and Efron and Morris’s original shrinkage result, redirected at a football-specific problem.

A rough, editorial landscape of related work by scope (single action vs. whole possession) and time-treatment (stationary vs. explicit clock).

What’s different here isn’t any single piece of machinery. It’s fitting a clock-nonstationary MDP at team-and-lineup granularity from event data alone, and then using it to run a paired-design policy simulation rather than stopping at a static value function. Most existing football work does one of those things well. This project’s contribution, such as it is, is doing all of them together on a dataset this size.

Conclusion

Basketball figured out years ago that a possession is a chain of decisions worth modeling as one, not a single row in a spreadsheet. This project asks whether that idea survives the trip to football, where there’s no shot clock, far less data per team, and, as it turned out more than once during the build, far more places for a plausible-looking number to be quietly wrong. It does survive, with the right substitutions: an endogenous possession clock standing in for the shot clock, a three-level statistical hierarchy standing in for basketball’s relative data abundance, and a paired-simulation fix standing in for the assumption that comparing two random simulations is safe when it isn’t.

None of the individual tools here are new, shrinkage estimators, value iteration, and Monte Carlo simulation are all decades old. What’s worth taking from this isn’t the machinery, it’s the discipline the machinery forces on you: distrust a value function that violates basic geometry until you’ve gone and found the bug, and never trust a policy comparison built on two independently-noisy simulations, in any sport, for any question shaped like “what if we played differently.” Both of those turned out to matter more than any single finding about Ecuadorian football.

Sources

Possession- and sequence-value modeling

1. Cervone, D., D’Amour, A., Bornn, L., & Goldsberry, K. (2016). A multiresolution stochastic process model for predicting basketball possession outcomes. Journal of the American Statistical Association, 111(514). https://doi.org/10.1080/01621459.2016.1141685

2. Fernández, J., Bornn, L., & Cervone, D. (2019). Decomposing the immeasurable sport: A deep learning expected possession value framework for soccer. 13th MIT Sloan Sports Analytics Conference.

3. Fernández, J. & Bornn, L. (2018). Wide open spaces: A statistical technique for measuring space creation in professional soccer. 12th MIT Sloan Sports Analytics Conference.

4. Decroos, T., Bransen, L., Van Haaren, J., & Davis, J. (2019). Actions speak louder than goals: Valuing player actions in soccer. KDD ’19, 1851–1861. https://doi.org/10.1145/3292500.3330758

5. Le Coz, S., Boustila, F., & Imbach, F. (2026). A semi-Markov framework for modeling football possessions and temporal expected threat. Scientific Reports, 16. https://doi.org/10.1038/s41598-026-52938-1

6. van Arem, K., Söhl, J., Bruinsma, M., & Jongbloed, G. (2026). Model quality in football: Quantifying the quality of an Expected Threat model. arXiv:2604.21087.

Team and player rating, and style

7. Constantinou, A. C. & Fenton, N. E. (2013). Determining the level of ability of football teams by dynamic ratings based on the relative discrepancies in scores between adversaries. Journal of Quantitative Analysis in Sports, 9(1):37–50. https://doi.org/10.1515/jqas-2012-0036
8. Dixon, M. J. & Coles, S. G. (1997). Modelling association football scores and inefficiencies in the football betting market. JRSS: Series C (Applied Statistics), 46(2):265–280. https://doi.org/10.1111/1467-9876.00065
9. Clijmans, J., Van Roy, M., & Davis, J. (2023). Looking beyond the past: Analyzing the intrinsic playing style of soccer teams. MLSA 2022, 281–292. Springer. https://doi.org/10.1007/978-3-031-26422-1_23

Decision-making, game theory, and evaluation

10. Rahimian, P. & Toka, L. (2024). A data-driven approach to assist offensive and defensive players in optimal decision making. International Journal of Sports Science & Coaching, 19(1):245–256. https://doi.org/10.1177/17479541221149481
11. Chiappori, P.-A., Levitt, S., & Groseclose, T. (2002). Testing mixed-strategy equilibria when players are heterogeneous: The case of penalty kicks in soccer. American Economic Review, 92(4):1138–1151.
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Statistical and methodological foundations

14. Puterman, M. L. (1994). Markov Decision Processes: Discrete Stochastic Dynamic Programming. John Wiley & Sons.
15. Sutton, R. S. & Barto, A. G. (2018). Reinforcement Learning: An Introduction (2nd ed.). MIT Press.
16. Gelman, A. & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
17. Efron, B. & Morris, C. (1975). Data analysis using Stein’s estimator and its generalizations. Journal of the American Statistical Association, 70(350):311–319. https://doi.org/10.1080/01621459.1975.10479864

I have been looking at spreadsheets for football scouting for over a decade, and every now and then, my perception completely changes. The biggest change I have experienced is when I started to realise that we use data mostly to shape profiles and how they fit in the profile. Pure quality can be measured, but it often is so conflicted with different variables, that it is difficult to make a definitive contribution.

Lately, I’ve been creating more and more on a meta level, mostly in data engineering. In that light, I wanted to share something I have introduced in my day-to-day data scouting when working with aggregated data: scouting uncertainty.

The idea is to add an uncertainty score to the scouting score to add a level of trust towards the data. If the data is trustworthy and uncertainty is low, the quality of data scouting for that specific player will be higher.

Data

For this little research, I have had a look at Wyscout’s aggregated data of the J2-J3 league of 2026. Normally these are split into two different leagues, but for this anniversary year, things are a little bit different.

This data focuses only on strikers, so I’ve only looked at players with CF as a position and/or players with multiple positions, but CF as a dominant position in the games they have played.

The data has been collected in XLSX files from the Wyscout platform on June 15, 2026. Things will not have changed since the World Cup has been going on and the new season has to start, but for clarity’s sake, here it is.

vNot every striker is created equal. What I mean by this is that a striker is the position, but the profile is different. In other words, what kind of striker is the player?

I have categorised the strikers into five distinct profiles:

• Goalscoring Striker

• Target Striker

• Dynamic Striker

• Second Striker

• Complete forward

All these profiles are created from all the data we have available, but are created from weighted composite scores in z-scores, which are normalised from 0–100. This doesn’t say anything about the quality of the striker, but much more about the tendencies of said striker. A score of 67 means that this player scores 67% on the perfect striker profile scale.

We have 70 players that fit the filters, and if we look at the image above, we can state the following. The Target Striker leads the profiles with 31%, followed by the Goalscoring Striker with 23%, and the Second Striker with 23%. The Dynamic Striker has 20%, and finally, we end with a complete forward with only 3%. Note for the complete forward, they are only complete forwards if they score 65% or higher in each of the categories, which is a strict cutoff.

In the table above, you can see all 70 players and how they rank in the particular categories of striker profiles. This is more or less just information about each player and nothing definitive in terms of quality. What are the biggest relations are within two profiles, that is, between the Goalscoring Striker and the Target Striker?

In the visual above, you can see the five player per category who score the highest in their respective categories. Sagawa is the best fit for Target Striker, Mori for Dynamic Striker, Nishino for Goalscoring Striker and Anderson for Second Striker.

Calculating the uncertainty score

Every Scouting Score in this model comes paired with an Uncertainty Score, a 0 to 100 rating of how much to trust the number, where higher means less reliable. The idea is simple: a striker who has racked up 90 in a full, injury-free season means something very different from a striker who has hit the same number in half as many minutes off a hot streak of shooting luck. Rather than quietly averaging over that risk, the model surfaces it as its own figure, so a big Scouting Score can be read alongside a clear-eyed sense of how much of it is signal versus noise.

The Uncertainty Score is built from five factors, each scored 0 to 100 and blended into a weighted total:

• how much game time the player has actually logged relative to a settled 20-match sample (35% of the total, the single biggest driver);

• how many shots they have taken, since shooting and conversion numbers are notoriously unstable on small volumes (20%);

• how far outside a 24 to 29 prime age band they sit, since younger and older players’ underlying output tends to swing more from season to season (15%);

• how much of the underlying data was simply missing (15%);

• and whether their profile is genuinely well-rounded or propped up by one or two standout numbers rather than consistent performance across the board (15%). The result is a single confidence read, High, Medium, or Low, that sits next to every player’s Scouting Score, so a standout number always comes with an honest answer to the question of whether it can be trusted.

If we analyse our dataset, we can find that the mean uncertainty is 30,4 on a scale of 0–100. The median is almost the same, with 30, which is a pretty solid uncertainty score. If we look at the highest category, high-confidence players, who are the best in terms of the lowest uncertainty.

In the scatterplot above, you can see the scouting score compared to the uncertainty score. A high scouting score signifies the quality of the player according to the data, while a high uncertainty score signifies that we cannot fully trust the data. A lower score for uncertainty is better in this regard.

You can see that here as well, a high scouting score + a low uncertain score, makes for the best scouting options if we are looking purely at the data.

Okay, but what drives that uncertainty? We have looked at the calculations, but what drives it in our league, we are researching?

1. Minutes drive the most with 15.3 points on average. This is where we look at the minutes played throughout the season in comparison with the total.

2. Metric spread is followed by 7.6 points on average. This is where we look at the spread of quality throughout several metrics. If a player has an even distribution of metrics, that is better than performing exceptionally well in one and weak in the rest.

3. Shot-volume gap comes next with 5.8 points. This is where we look at the volume of shots for strikers. Yes, they can have a high shots per 90, but what’s the total volume of shots throughout the season? We want to limit the effect of an anomaly in a high-shots game.

4. Age volatility with 1.7 points. This is where we look at peak ages and give different meanings to very young or relatively old players.

5. Missing data. This is where we look at the data that is missing. Now here there is nothing, because the season has ended and nothing is missing. If you do this analysis during the season, this might be different due.

Results

In the visual above, you can see the final results for all strikers in the J2-J3 league 2026. Every player’s score shows the total uncertainty score, but also how that score is built up. This shows you what component drives the score.

If we look at the “worst” players in this regard, they are driven by multiple categories, and that shows that uncertainty is higher. When we look at the “best” players, we see that they have fewer metrics. What’s most significant is that age volatility hardly plays a role.

In the two tables above, you can see the two categories of Goalscoring Striker and Dynamic Striker in their profile. The scouting score is the fit for that particular profile, and the uncertainty score gives us an idea of how much to trust that data. In other words, how much do we trust the profile in relation to the individual data of the player?

For example, in the Goalscoring Striker, the best fit is also a player whose data we can trust. But in the Dynamic Striker profile, we could go with the second one on the list, because the uncertainty is lower.

Here we see the same kind of tables, but for other profiles. The thing I think is interesting is Patric from Zweigen Kanazawa. He scores relatively high on the Target Striker profile, but his uncertainty is really high compared to the rest. That would be a player you don’t trust in terms of data.

Final thoughts

What this exercise really produces is not a ranked list of “the best striker in Japan II and III,” it is a structured way of asking two questions at once: what kind of striker is this, and how much should we trust the number attached to his name. Seventy CF-listed players sorted cleanly into recognisable profiles, Target Strikers, Goalscoring Strikers, Second Strikers, Dynamic Strikers, and a rare pair of Complete Forwards who graded well across every dimension at once. That alone is useful for a recruitment department trying to fill a specific tactical need rather than simply chasing the highest overall score.

The Uncertainty Score is the part worth dwelling on, because it resists the instinct to treat a single number as gospel. A player putting up an elite Scouting Score on 700 minutes and a handful of shots is a different proposition than one doing it across a full season, even if the two numbers look identical on a spreadsheet. The efficient frontier on the risk map makes that trade-off visible: T. Nishino, D. Furukawa, and H. Iwabuchi all sit on it, meaning nobody in the pool beats them on both quality and reliability at once, while a name like Patric shows how a modest sample and an inconsistent underlying profile can inflate uncertainty even when the raw output looks tempting.

None of this replaces a scout with a laptop and a match to watch. It is a screening layer, a way to narrow seventy players down to the ten or so worth a longer look per role, and to walk into that look already knowing whether the data behind a name is thick or thin. Treat the shortlists as a starting point for video and in-person work, not a substitute for it, and treat a high Uncertainty Score not as a red flag to discard a player but as an honest instruction to watch more of him before deciding anything.

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If you are a goalkeeper scout or analyst, the aggregated data from different providers focuses mostly on shot-stopping. If you are fortunate, you may obtain some in-depth distribution figures, but that is broadly the limit of what is routinely available. Most clubs employ Wyscout on account of its integrated video and data offering, and in doing so, they tend to rely on exits per 90 minutes as the primary indicator of sweeping quality.

This is a methodological problem. A goalkeeper who rushes off his line constantly but misjudges half of his interventions is not an asset; he is a liability dressed up in an impressive counting statistic. Yet exits per 90 has become the default shorthand for the sweeper archetype, occupying the same position in goalkeeper discourse that goals do in striker evaluation: widely cited and rarely interrogated.

This article introduces an alternative framework. The Sweep Quality Score (SWP_Quality) is a composite metric that attempts to answer a fundamentally different question: not how much does this goalkeeper sweep, but how well does he do everything that a modern sweeping goalkeeper is asked to do? The metric is presented as a practical scouting tool, not a definitive model of goalkeeper quality, and its limitations are addressed explicitly in Section 6.

1.1 Data and scope

The analysis draws on Wyscout aggregated season data downloaded on 18 June 2026, spanning the 2025–26 season and the ongoing 2026 season. The latter is incomplete at the time of writing—the 2026 World Cup is currently in progress—but the application of a minimum-minutes filter (900 minutes; approximately ten full matches) renders the incomplete campaigns sufficiently representative for rate-based metrics.

The database encompasses 165 leagues across six competitive tiers, from continental elite competitions (Tier 1) to semi-professional and amateur competitions (Tier 6). Not every league, team, or player is of equivalent quality; this heterogeneity is addressed methodologically through league-tier stratification and, more importantly, through the percentile conversion procedure described in Section 3. The deliberate breadth of the database reflects a scouting philosophy that keeps the observational aperture as wide as possible in order to identify talent at all levels of the competitive pyramid.

2. Why the Sweeper Role Demands a Richer Lens

The compressed defensive lines associated with high-press tactical systems have fundamentally re-evaluated what goalkeepers are expected to contribute. Across European football’s top six leagues, the average defensive line sat approximately 3.2 meters higher in 2024 than it did in 2015 (Statsbomb, 2024). The space behind the defensive line, previously of minimal relevance to goalkeeping, is now actively contested territory. The goalkeeper has become the last line of structural defence against the through ball, the lofted diagonal, and the loose ball falling in the channel.

In this tactical context, a goalkeeper’s spatial authority constitutes a genuine performance dimension. The question is how to measure it rigorously and in a way that resists the perverse incentives created by volume-based statistics.

Three distinct competencies make a sweeping goalkeeper genuinely valuable to his team:

• The goalkeeper exits his line proactively to intercept before opposing attackers can reach the ball, reducing the probability of a direct attacking threat materialising.

• Sweeping activity is operationally worthless if the goalkeeper concedes goals he is expected to save. A GK who exits frequently but performs poorly in one-versus-one situations or against well-struck efforts negates the defensive benefit of his proactivity.

• A goalkeeper who wins the ball in space and immediately returns it to the opposition via an aimless clearance has captured the action but forfeited its value. Effective sweeping must be coupled with purposeful distribution to translate proactive defending into offensive continuity.

Any composite metric that omits one of these three dimensions will produce a ranking that flatters one archetype of goalkeeper at the expense of a complete and operationally relevant performance picture.

3. Building the Metric

3.1 Population and filtering

SWP_Quality is computed across a population of 2,663 goalkeepers satisfying a minimum threshold of 900 minutes played, drawn from 150 leagues across six competitive tiers. All component metrics are sourced directly from Wyscout event data. The 900-minute floor is calibrated to ensure that at least ten approximately full matches have been contested, providing sufficient sample volume for rate statistics to be meaningfully interpreted. The implications of this threshold are discussed in Section 6.

3.2 Stage one: percentile conversion

Each of the five component metrics is ranked within the full goalkeeper population and converted to a percentile score on a 0–100 scale, where higher values universally indicate superior performance. This normalisation procedure eliminates the problem of comparing raw values across leagues of heterogeneous quality and style: an exit rate of 2.1 per 90 minutes carries a different meaning in the Portuguese Primeira Liga than in the Austrian Regionalliga. After percentile conversion, both observations are expressed relative to the same reference distribution, enabling valid cross-league comparison.

For the goals saved above expected goals (GSaG) component, defined here as xG against per 90 minus goals conceded per 90, positive values indicate a goalkeeper saving shots beyond what their difficulty profile would predict, while negative values indicate underperformance relative to expectation. The percentile ranking therefore rewards goalkeepers who consistently outperform their expected concessions.

The distribution score is computed as the arithmetic mean of the short pass completion percentage (accurate passes, %) and long pass completion percentage (accurate long passes, %), providing a balanced measure of both recycling quality and ball-playing range.

3.3 Stage two: weighted aggregation

The five percentile scores are combined via a weighted average with the following component weights:

Table 1. SWP_Quality component weights and rationale. All weights sum to 1.00.

The resulting score runs from 0 to 100, where 50 represents the median goalkeeper in the reference population. A score above 75 places a goalkeeper in the top quartile, and a score below 30 in the bottom quartile. The score is not intended as an absolute measure of goalkeeper quality but as a relative positioning instrument for scouting and shortlisting purposes.

Figure 1. Left: SWP_Quality component weight breakdown (donut). Right: mean component percentile by goalkeeper archetype, illustrating how each style’s strengths and weaknesses contribute differentially to the composite score (dashed line = global median).

4. Methodological justification

Weight selection in composite metrics is the point at which most legitimate methodological criticism concentrates. Why 25% on exits per 90 and not 30%? Why not an equal distribution of 20% across all five components? These are fair questions that deserve explicit answers.

The assigned weights reflect a priority ordering of the role’s functional demands, not a causal claim about the relative contribution of each component to a team’s defensive output. That distinction matters: causal attribution would require controlled experimental data or at minimum a rigorous regression framework accounting for team-level and positional confounders. The present article does not make that claim.

The leading weight on exits per 90 (25%) follows directly from the metric’s purpose: if the objective is to identify goalkeepers with a demonstrated capacity to claim space proactively, then sweeping volume must hold the primary weight. The aerial duels component (20%) captures a distinct spatial dimension, command of the box in aerial contests, set pieces, and diagonal deliveries, which are conceptually separable from ground-level exits.

The combined weight of the stopping components (save rate and GSaG, 20% each) rests on a fundamental principle of the position: a goalkeeper is, first, a shot-stopper who also sweeps, not a sweeper who also stops shots. Without this structural constraint, the metric would systematically reward the Sweeper GK archetype at the expense of shot-stopping quality. In practice, this tension is empirically observable: the Sweeper GK cohort in this database posts a mean save rate of 68.1%, compared to 74.3% for Shot Stoppers. A pure exits-based ranking would promote goalkeepers who are measurably worse at the foundational requirement of the role.

The distribution weight (15%) is the most philosophically contentious. A legitimate counter-position holds that goalkeeper passing quality is downstream of the team system and cannot be reliably attributed to the individual. This is a defensible view. The counterargument embedded in this framework is that a goalkeeper who cannot reliably distribute, short or long, is systematically squandering the possession advantage that a successful sweeping action creates. The distributional benefit of a successful exit depends entirely on what happens next; a goalkeeper who cannot deliver a purposeful restart undermines his own sweeping value. The weight is set at 15% rather than 20% precisely to reflect this uncertainty: it is present and meaningful but subordinate to the core functional competencies.

5. Results and Distributional Analysis

5.1 Population distribution

Across the full population of 2,663 goalkeepers satisfying the minimum minutes threshold, SWP_Quality produces a distribution that is close to normal. Table 2 and Figures 2–3 present the key distributional statistics.

Table 2. SWP_Quality score distribution across 2,663 goalkeepers (900+ minutes, 150 leagues, 6 tiers).

Figure 2. IQR box plots for all five SWP_Quality component metrics. Box = interquartile range (25th–75th percentile); centre line = median; whiskers = 5th–95th percentile; open circles = outliers.

A mean of 51.2 sits within one point of the median (51.4), indicating a distribution with minimal skew. The standard deviation of approximately 15 makes z-score interpretation reliable: a goalkeeper at SWP_Quality 81.2 is exactly two standard deviations above the population mean, placing him at approximately the 97th percentile. Figure 3 illustrates the normal approximation and the z-score framework, which provides a standardised vocabulary for communicating goalkeeper quality in cross-league contexts.

Figure 3. Left: normal distribution approximation for SWP_Quality with z = 1.5 illustrated (top 7% of the population). Right: mean z-score by goalkeeper archetype relative to the global population mean, confirming Sweeper GKs hold the highest relative position.

5.2 Archetype comparison

Comparing the SWP_Quality distribution across the four goalkeeper archetypes identified in the Wyscout classification system surfaces a result that may initially appear counterintuitive. Table 3 and Figure 4 present the archetype-level means.

Table 3. Mean SWP_Quality and component metrics by goalkeeper archetype (900+ minutes). Row colours correspond to archetype identity.

Figure 4. Mean exits per 90, save rate, and SWP_Quality by goalkeeper archetype. Sweeper GKs lead on exits and composite score; Shot Stoppers lead on save rate by a substantial margin.

Sweeper GKs score highest overall, as expected given the metric’s sweeping-weighted structure. However, Shot Stoppers trail by only 5.7 SWP_Quality points despite exiting at less than two-thirds the rate of their Sweeper GK counterparts (1.40 versus 2.14 exits per 90). Their superior save rate (74.3% versus 68.1%) and positive mean goals-saved-above-xG (+0.11 versus -0.07) prevent the gap from widening further. This is the metric’s key structural feature: sweeping volume alone does not override stopping quality. A goalkeeper who sweeps prolifically but saves shots at a below-average rate will not lead this ranking.

Figure 5. Beeswarm plot of SWP_Quality by goalkeeper archetype. Each point represents one goalkeeper. Vertical bars indicate the median per archetype. Note the substantial overlap between archetypes, indicating that archetype classification alone is an insufficient predictor of composite sweeping quality.

Figure 6. Scatter plot of exits per 90 versus save rate, coloured by goalkeeper archetype. Dashed lines indicate the population medians. The upper-right quadrant identifies the “elite sweeper” profile—high exits combined with above-median save rates—which SWP_Quality is specifically designed to surface.

5.3 Top-ranked goalkeepers

Rather than presenting a single global ranking, the database is stratified by competitive tier to account for the structural differences in playing environment. Top 15 SWP_Quality performers per tier, drawn from pools of 84 (Tier 1), 235 (Tier 2), 550 (Tier 3), 1,344 (Tier 4), and 168 (Tier 5) goalkeepers, respectively.

Tier 1 is led by L. Gauer (Mainz 05 II, Germany, age 20, SWP_Quality 87.3) and A. Murić (Sassuolo, age 27, 86.0). The presence of Emiliano Martínez (Aston Villa, 79.7) — the highest-profile name in the global dataset — confirms the metric’s face validity at the elite level while also illustrating that established first-choice goalkeepers at major clubs do not automatically dominate a quality-adjusted sweeping ranking.

Tier 2 is headed by M. Koné (Charleroi, Belgium, age 24, 88.8)—the highest-scoring Tier 2 candidate and a genuine transfer target for Tier 1 clubs given his exit frequency (2.68/90) at a competitive Belgian Pro League standard. M. Miño (Barracas Central, Argentina, 85.3) and J. Heerkens (Ajax, Belgium, age 20, 84.3) complete a top three combining South American physicality with European technical development.

Tier 3 surfaces I. Brkić (Motor Lublin, Poland, 87.0) and W. Mannion (Charlton Athletic, England, 85.1) as the leading candidates—both sweeper GKs posting exit rates above 2.5 per 90 with save rates above 73%. The presence of South African (D. Msibi, L. Mathebula) and Egyptian (Ahmed Mayhoub, M. Saeed) goalkeepers in the top 15 is a direct consequence of the database’s geographic breadth.

Tier 4, the largest pool at 1,344 GKs, returns K. Vroman (Lierse Kempenzonen, 91.2) and D. Solsky (Wollongong Wolves, 88.7) at the summit—the two highest individual SWP_Quality scores in the entire database. This is not a data artifact: both are demonstrably performing at the top of the metric’s five component dimensions simultaneously, and both warrant video-led follow-up.

Tier 5 is led by M. Michaelis (Koninklijke HFC, Netherlands, age 32, 89.3), whose exit rate of 2.67 per 90 combined with a 78.1% save rate places him in elite company regardless of tier context.

6. Limitations

The following limitations are acknowledged explicitly, as they should inform the interpretation of any scouting decision based on SWP_Quality.

6.1 Off-ball positioning is unobserved

Wyscout event data logs exist when a goalkeeper leaves his line and contests the ball. Off-ball positioning that prevents an exit from being necessary, through anticipatory movement that closes down the threat before it materialises, is not captured in this framework. A goalkeeper who reads the game exceptionally well may score modestly on exits per 90 not because he sweeps poorly, but because his positioning makes the act of sweeping less frequently necessary. This represents a structural blind spot in all event-data approaches to measuring defensive proactivity.

6.2 Sample size variance near the minimum threshold

The 900-minute floor is a practical choice rather than a statistical guarantee. Goalkeepers near the minimum threshold (ten to eleven matches) will exhibit substantially greater variance in rate statistics than those with 2,500 or 3,000 minutes. Rankings among goalkeepers near the threshold should be treated with correspondingly greater caution, and scouts are advised to cross-reference SWP_Quality with observed match volume when assessing borderline candidates.

6.3 Absence of team-context controls

A goalkeeper playing behind a high defensive line at a structurally press-intensive club will encounter substantially more sweeping situations than one defending a deep block. The percentile method addresses cross-league volume differences at the population level but cannot isolate the goalkeeper’s individual contribution from his tactical system. Possession-adjusted variants, which normalise exits against the frequency of sweeping opportunities, represent the logical next development (see Section 7).

6.4 Incomplete league-tier matching

League-tier and country data populated for only a subset of the database. The matching procedure between the player data file and the team ratings reference relies on string-based club name matching, which is imperfect — particularly for clubs in lower-tier Eastern European, South American, and African competitions where naming conventions diverge between data sources. A future iteration of this framework would use unique club identifiers rather than string matching to eliminate this source of data loss.

7. Conclusions and Future Directions

SWP_Quality constitutes a scouting entry point, not a final verdict. Its function is to reduce a population of 2,663 goalkeepers to a manageable shortlist of candidates meriting detailed video analysis. The composite score identifies which goalkeepers warrant the time investment of observational review; it cannot determine whether a goalkeeper’s sweeping behaviour is driven by elite spatial reading, a tactically demanding high defensive line, or systematic over-aggression that occasionally leaves him exposed.

Two methodological extensions are identified as priorities for future work. First, a possession-adjusted variant that normalises exits and aerial duels against the frequency of sweeping opportunities created by a goalkeeper’s defensive system — analogous to the possession-adjusted PDI framework proposed by Griffis (2022) — would substantially improve the isolation of individual contribution from team structure. Second, a league-difficulty adjustment that weights component performances by the tier and competitive density of the context in which they were produced would allow more direct comparison between a goalkeeper in the Belgian Pro League and one in the Australian National Premier League.

Until those refinements are available, SWP_Quality offers something that conventional exits-based ranking does not: a disciplined, multi-dimensional reason to direct analytical attention toward a 22-year-old in Belgium and a 23-year-old in Wollongong, because the data — across 150 leagues and six tiers of competition — says they deserve it.

References

Griffis, B. (2022). Introducing the Passing Danger Index (PDI). Cafe Tactiques. Retrieved from

https://cafetactiques.com

StatsBomb (2024). StatsBomb Data Specification — Freeze Frames and Defensive Line Height. StatsBomb Services Ltd.

Wyscout (2026). Data export: Goalkeepers, season 2025–26 and 2026. Downloaded 18 June 2026. Wyscout S.p.A.

Data note: All visualisations are generated from Wyscout data (2025–26 and 2026 seasons). Minimum threshold: 900 minutes played. Population: n = 2,663 goalkeepers across 150 leagues in 6 competitive tiers. All percentile rankings are computed within the full GK population. Metric weights reflect the analytical judgement of the author and are not derived from a regression or causal estimation procedure.

If you ever wonder how I get to my ideas and think there’s a ridiculously academic process to it, let me kill that illusion. There isn’t. Sometimes I come across a set of ideas, and it will lead me to my own new concepts. Sometimes I just want to create something innovative. And sometimes I have created something for a club I work for and want to talk about the theory a bit more. This season, I became interested in one simple question: can short passes tell us something about build-up play that broader passing models miss?

Right now, in most models we quantify all passes in passing networks, in expected threat, in sequences etc. I want to go away from that and only look at short passes. I’m not sure this is a sound idea when I’m writing, and I think that’s the whole thing of it, I want to see whether something can be valuable. If the result is that it isn’t valuable, then that’s a result as well.

The article has two primary objectives:

• Can the value created by short passes be measured? To answer this, I introduce a Short Pass Value (SPV) model based on changes in Expected Threat.

• Can short-pass execution be predicted? To answer this, I develop an Expected Pass (xPass) model and derive Pass Completion Added (PCA).

Let’s start!

Data

There’s a plethora of data providers available, both paid and for free. For this research, I’m going to use Wyscout event data. This research uses only event data, meaning all analyses are based on on-ball actions and XY locations. Off-ball positioning, defensive pressure, player movement and spacing are therefore not observed directly, which is an important limitation of the study.

For this study, a short pass is defined as any completed pass shorter than 15 metres. This threshold was chosen because it captures the majority of circulation and combination play while excluding longer progression and switches of play.

The data is from the 2025–2026 Eredivisie season, which has now been concluded. When you read this at a later point, you might miss names such as FC Volendam, Heracles Almelo and NAC as being part of the Eredivisie 2026–2017, as they have been relegated, and Willem II, ADO Den Haag and SC Cambuur have been promoted.

Raw data were retrieved through the Wyscout API as JSON files before being converted into Apache Parquet format for faster processing and integration into a Streamlit application.

Theoretical framework

My model and calculations will feature a few interesting things, but what’s important to know here is which mathematical frameworks have been used to create hte more juicy stuff what we will use to analyse:

1. Markov Chains — Expected Threat: A Markov chain models the pitch as discrete zones where each zone has a fixed probability of transitioning to any other, regardless of how the ball got there — the “memoryless” property. Each zone’s value is solved iteratively by combining the direct shot threat from that zone with the expected value of all future zones the ball might reach via passing, repeating until the values converge. The result is a surface that maps every pitch coordinate to a single number representing how likely a goal eventually follows from possessing the ball there.

2. Reinforcement Learning: Temporal Difference learning is a Reinforcement Learning method where an agent receives a reward signal based purely on the change in state value caused by an action, without waiting for the episode to end. Applied here, each pass is the action and its reward is the difference in xT between where the ball landed and where it started — decomposing an entire match into pass-by-pass contributions. Only completed passes receive credit, so a turnover scores zero, consistent with the idea that lost possession eliminates all future threat.

3. Statistics/Machine Learning: Logistic regression estimates the probability of a binary outcome by learning a weighted combination of input features and squashing the result into a probability between zero and one using an S-shaped curve. The weights are found by Maximum Likelihood Estimation — choosing the values that make the observed completions and failures most probable under the model — with a regularisation penalty added to prevent overfitting rare pass types. Performance is measured by cross-validated ROC-AUC, which captures how reliably the model ranks a completed pass above a failed one across unseen data.

4. Econometrics/Sabermetrics: Pass Completion Added measures how much a player’s actual completion outcome deviates from what the difficulty model predicted, automatically isolating skill from situational context. Because the model is calibrated, the average PCA across all passes is zero by construction — a player must genuinely outperform expected difficulty to show a positive score. This is the same logic as goals-minus-xG in shooting, BABIP in baseball, and Jensen’s alpha in finance: observed outcome minus a difficulty-adjusted baseline.

5. Graph theory: Graph theory transforms the team into a communication network where players are nodes, passes are directed edges, and weights encode pass frequency or value. Betweenness Centrality identifies structural bottlenecks — players who sit on the most efficient routes between all pairs of teammates — while PageRank captures recursive influence, ranking a player highly if they receive passes from players who are themselves well-connected. Weighting both metrics by pass value rather than raw count shifts the question from who passes most to who passes most valuably.

Methodology

Short Pass Value measures the territorial gain of a pass by calculating the change in Expected Threat between where the ball started and where it ended. The pitch is divided into zones, each assigned an xT value representing how likely a goal eventually follows from possessing the ball there — so a pass that moves the ball from a low-threat zone into a high-threat zone produces a positive SPV. Only completed passes are credited, meaning turnovers score zero and do not artificially inflate a player’s contribution. Progressive short passes — those gaining at least 15 metres toward the opposition goal — are tracked separately to distinguish forward-threatening passes from safe sideways circulation. SPV therefore answers the question: how much dangerous territory did this player’s short passing actually generate? Aggregated across a season, it becomes a volume measure of a player’s territorial contribution through short passing.

Expected Pass Completion models the probability that any given pass will be completed, based on the characteristics of that pass at the moment it is played. A logistic regression is trained on 13 features — including pass length, angle, starting zone, whether the player was under pressure, and game minute — to learn which combinations of factors make a pass harder or easier to complete. The output is a single probability between zero and one for every pass, representing what a typical player would be expected to achieve in that exact situation. From this, Pass Completion Added is derived: the difference between whether the pass was actually completed and the model’s predicted probability. A positive PCA means the player completed a pass harder than expected; a negative PCA means they failed one that should have been routine. Aggregating PCA across all short passes isolates a player’s technical execution skill, stripped of the difficulty context they faced.

Short Pass Value

The short pass value is a metric that is modelled by looking at expected threat based on passing. The value measures the changes in expected threat via short passing. I will delve into this a little bit more:

In the image above, you can see which players create the most value per 90 with their short passing. Only players with 100 or more attempts are included. Verdonk, Hadj-Moussa and Ould-Chikh score the highest in the Eredivisie.

Obviously, we can also look at the most danger from a short pass with our SPV. What we see is the biggest positive change in xT per short pass. In doing so, Raul Moro scores highest, followed by Ould-Chikh and Hadj-Moussa.

In the image above, you see the total SPV across the whole Eredivisie season 2025–2026. PSV score highest and that isn’t too surprising as they are champions. They are followed by Twente and Feyenoord.

In the image above, you can see the passing networks based on short passes in the Eredivisie for four different teams. This shows the combination of short passes and which sides are being utilised. NEC is very symetrical, while Ajax is very mirrored.

Expected Pass and PCA

The next step what I wanted to do with this, is to measure the predictive nature of short passes and how we can find anomalies in the Eredivisie 2025–2026. Let us first start with Expected Pass.

In the image above you can see which players with at least 200 attempts, are considered to have the highest Expected Short Passes. Bouwman from Ajax scores highest, followed by GAE’s Nauber and Sparta’s Young.

In this boxplot visual, you can see how the xPass distribution is for each outplaying player (no goalkeepers). The xPass for defenders is highest with 0,884 median, followed with 0,842 median for midfielders and significantly lower with 0,779 median for attackers.

In the two graphs above, you see the best and worst player in PCA mean per attempt. This is the rate that they complete passes in relation to their xPass and in relation to the whole database. Ayew, Weghorst and Verdonk are the best overperformers. Noslin, Baeten and Kasius are the worst underperformers.

Now you can combine the xPass with PCA and get a complete image of how well they over/underperform with the scatterplot below.

As you can see the the quartile on the left, top side is what we want to analyse. And what’s interesting is that it’s occupied by mostply attackers and midfielders, indicating that defenders have the easiest passes, as you can see on the right.

But, more control?

Throughout football analysis, “control” is often used without a precise definition. In this article, I use the term to describe a team’s ability to advance territory while maintaining possession security. While short-pass metrics alone cannot fully capture control, they appear to capture one of its components: territorial advancement without sacrificing possession security. Teams such as PSV and NEC demonstrate that high progression through short passes can coexist with possession dominance, suggesting control is not simply about circulating the ball but about progressing it efficiently.

In the boxplot graph above, you can see how different positions on the pitch conduct their progressive passes in relation to all short passes. For the different thirds, we see that centre-backs score highest, followed by wide defenders and defensive midfielders.

When we look at the line-breaking and smart passing, we see that the more attacking profiles score higher: attacking midfielders, wide players and strikers.

In the scatterplot above, you see the pass context — how easy/hard is a pass?- compared to the progression rate of the short passes. It’s hard to quantify control in this way, but it does tell us that short passes lead mostly to low progression.

What’s interesting is that in general the lower placed teams (Heracles, Telstar, Excelior, Volendam) have high progression per pass, due to their direct style of play of counter-attacking football. But PSV and NEC are highly attacking teams with possession-based football, and still score high.

Final Thoughts

The original question behind this project was fairly simple: is there value in isolating short passes instead of treating all passes equally? After working through the models, the answer appears to be yes, although perhaps not in the way I initially expected.

Short passes are often dismissed as low-risk circulation actions. Traditional passing metrics frequently reward volume, progression, or direct chance creation, which means the vast majority of short combinations disappear into the background. Yet when we isolate them, a different picture emerges. Short passes are not merely maintenance actions; they are the mechanisms through which teams establish territorial control, manipulate defensive structures, and create the platform for future progression.

The Short Pass Value model shows that even seemingly simple actions can generate meaningful threat accumulation over time. Players such as Verdonk, Hadj-Moussa, Ould-Chikh and Moro demonstrate that value creation is not exclusively tied to spectacular line-breaking passes or assists. Repeatedly moving possession into more dangerous areas through short combinations can create substantial attacking value across a season.

The Expected Pass and PCA framework adds another layer. By separating pass difficulty from pass execution, we can identify players who genuinely outperform expectation rather than simply benefiting from easier passing environments. The positional differences are particularly revealing: defenders generally operate in safer contexts with higher completion probabilities, while attackers and advanced midfielders face a much steeper risk-reward trade-off. As a result, positive PCA among attacking players becomes especially noteworthy.

Perhaps the most interesting finding concerns control. Modern football discussions often use the term without clearly defining it. While this study does not claim to have solved the concept, short-pass analysis provides a useful lens. Teams with high short-pass progression rates are not necessarily the teams with the most possession, and teams with the most possession are not always the teams creating the most territorial value. Control appears to emerge from balancing security and progression rather than maximising either independently.

There are, of course, important limitations. The analysis relies entirely on event data and therefore ignores many crucial off-ball elements such as positioning, spacing, pressing pressure, passing lanes, and player movement. Tracking data would undoubtedly improve both the SPV and xPass models. Likewise, the choice of xT as the underlying value framework introduces assumptions about how threat accumulates that may not fully capture team-specific playing styles.

Still, I think the experiment was worthwhile. Even if short passes ultimately explain only a small part of football performance, they provide a unique perspective on how teams gain territory, retain structure, and create control. More importantly, they allow us to identify players who contribute value in ways that traditional progression or chance-creation metrics may overlook.

Sources

• Karun Singh (2019). Introducing Expected Threat (xT). Available at: https://karun.in/blog/expected-threat.html

• Sarah Rudd (2011). A Framework for Tactical Analysis and Individual Offensive Production Assessment in Soccer Using Markov Chains.

• David Sumpter (2016). Soccermatics: Mathematical Adventures in the Beautiful Game. Bloomsbury Publishing.

• Javier Fernández & Luke Bornn (2018). Wide Open Spaces: A Statistical Technique for Measuring Space Creation in Professional Soccer.

• StatsBomb Research. Expected Threat and Possession Value Models. Available at: https://statsbomb.com/articles/soccer/

• Wyscout. Event Data Documentation and API Reference. Available at:

https://support.wyscout.com

• Brin, S. & Page, L. (1998). The Anatomy of a Large-Scale Hypertextual Web Search Engine (PageRank methodology).

• Freeman, L.C. (1977). A Set of Measures of Centrality Based on Betweenness.

• Hastie, Tibshirani & Friedman (2009). The Elements of Statistical Learning. Springer.

• Sutton, R.S. & Barto, A.G. (2018). Reinforcement Learning: An Introduction (2nd Edition).

As I’m a product of the online data analysis sphere on Twitter (I refuse to call it X), I’m very well familiar with radar charts and pizza plots. In fact, I have been using them on social media, written articles and in club work as well. But recently, I’ve been very hesitant to use them because I genuinely don’t know whether they are good or bad. So that’s why I took the time to research their purpose and validity in football scouting.

I’m fairly confident that when I start writing about these, people from the established data providers will come for me, but I don’t actually care. One of the biggest threats to the data departments across football clubs, is the height of data illiteracy. That’s why understand radar charts are so important.

In this article, I will take a closer look at what radar charts are, which versions are typically used, and what the strengths and pitfalls are.

1. Radar charts

2. Different types of radar charts

3. Strengths

4. Lie Factor

5. Permutations Test

6. JND Testing

7. ANOVA

8. Final thoughts

Radar charts

A radar chart is a way of visualising multivariate data by arranging variables around a circle rather than along straight axes, like we do with bar charts. With multivariate data, we mean that we observe different types/categories of data at the same time. Each variable is given its own axis, radiating outward from a central point, and all axes are spaced evenly in angle. Values are plotted along these axes and then connected, producing a closed, often irregular polygon that represents a single observation.

What distinguishes the radar chart is not just its circular layout, but the way it translates a list of values into a shape. Each value extends outward and forms a geometric figure whose contours reflect the balance, imbalance, or distribution across dimensions.

In theoretical terms, the chart can be understood as mapping an n-dimensional vector onto a radial coordinate system: the identity of each variable is encoded by angle, while its magnitude is encoded by distance from the centre. The resulting polygon is therefore not just a collection of points, but a spatial expression of relationships within the data, where the overall form becomes a visual shorthand for comparison and pattern recognition.

Rather than reading values sequentially, as one might in a table or along linear axes, the viewer encounters the data as a configuration, a shape that can be scanned, compared, and interpreted at a glance.

Different types of radars

There are of course, different types of radars:

• Profile radar

• Comparitive Radar

• Normalised/percentile radar

• Stacked or layered radar

• Radial heatmap radar

• Bar-based radar

Let’s start with the profile radar. The profile radar shows a variety of metrics within the visualisation that form the profile of a specific player.

In this visualisation we can see M. Nzita from Charleroi in his profile radar. On the right we see the actual values per metric, but we have one standardised radar. This means that the values are all hold against a single value base. So in this sense, it looks like the player is really good in duels won % and bad at xA, but that isn’t necessarily true.

In the image above, you see a raw comparison chart. This shows the raw values for our chosen metrics in the same scale as the profile radar. It compares two specific players and gives the illustion that overal player A. Jungdal is better, but we cannot state since, we are comparing raw numbers on the same scale.

In the next step we want to level the data, so it’s more representative of our own database, because we want to see how our player compares to the whole. First we look at min-max radar charts:

In the min-max profile radar, we see a very different figure. We see that every metric has a new value, the min-max score. This normalises the values, so it’s easier to compare them in one specific data visualisation.

The min-max radar rescales each metric between the lowest and highest value in the dataset, converting everything to a 0–100 scale. A score of 0 means the player has the lowest value in the league for that metric, while 100 means they have the highest. Every other player is positioned proportionally between those two extremes. Unlike percentile radars, which show how many players a player outperforms, min-max radars show how close a player is to the absolute best and worst values in the dataset, which makes them more sensitive to extreme outliers.

Talking about percentile radars, those are the next ones:

Percentile radars rank a player relative to all other players in the dataset for each metric, converting performance into a 0–100 scale based on distribution rather than raw distance. A percentile score of 90 means the player performs better than 90% of players in that metric, while 50 represents league-average standing. Unlike min-max scaling, percentile radars are less affected by extreme outliers and provide a more stable view of how dominant or average a player is compared to the rest of the population, which is why they are commonly used in football analytics and scouting profiles.

The z-score radar standardizes each metric by measuring how far a player’s performance is from the dataset average in terms of standard deviations. A z-score of 0 represents league-average performance, positive values indicate above-average performance, and negative values indicate below-average performance. For example, a z-score of +2 means the player performs two standard deviations above the mean for that metric. Unlike percentile or min-max radars, z-score normalization preserves the statistical distance between players and highlights how exceptional or unusual a performance truly is relative to the overall distribution, making it especially useful for analytical comparisons across metrics with different scales.

I want to now continue with different forms of radar charts after scaling, but I will take the percentiles radar over min-max. Analytically speaking that is the better choice, since min-max are more aesthetically pleasing, but can showing a lot skewed data. For analytics and recruitment? I would take percentile or z-scores. For visual storytelling and presentations? I would go for min-max normalisations.

If we are going to split z-scores and percentiles, there are two distinct ways you can go. If you want to go for easy to ready, communicative radars, percentiles are the better choice. This is good for meetings in recruitment and analysis. However, if you want to go deeper in the pure statistical side and not only want to see how good a player is in relation to the rest, but also how much bettter than the most common value they are, z-scores are the way to go. But they are not as easy to read.

For the purpose of the rest, I will use percentile ranks as this a public post you can read and most likely is the thing we want to use in the public space.

In the visualisation above, you can see a stacked percentile radar. This shows the percentiles but in another light, you can see more clearly which slices fall in which categories. This approves the readability of the charts, which percentile already scores higher on in comparison to z-scores. In this case you can see that most of the percentiles fall in the 50–75 band.

We can take it in another direction with the radial heatmap radar. I haven’t seen this a lot, but it’s an interesting one to see nonetheless.

A radial heatmap radar combines the structure of a traditional radar chart with the visual intensity of a heatmap by representing each metric as a colored radial segment whose length and shading reflect the player’s percentile or normalized performance. Instead of relying solely on connected polygons, the chart emphasises magnitude through individual radial bars, making strengths and weaknesses easier to distinguish at a glance while reducing overlap and visual clutter. This approach improves readability, highlights metric-by-metric variation more clearly, and creates a modern analytical visualisation commonly used in advanced sports analytics dashboards and scouting presentations.

In the visual above, you can see a bar radar. For every metric there is a bar that represents a percentile value. Bar-based radar chart replaces the traditional connected polygon of a standard radar with independent radial bars extending outward from a circular center, where each bar represents the magnitude or percentile of a specific metric. Unlike classic radar charts that emphasize overall profile shape, bar radars prioritize metric separation, readability, and direct comparison by reducing overlap and visual distortion between categories.

Yes, they do look similar to pizza plots and we could say that pizza plots are a evolution from these bar based charts, but they are a distinct category. If you want to read more on those, I would suggest looking at this: https://mplsoccer.readthedocs.io/en/latest/gallery/pizza_plots/plot_pizza_basic.html

Strengths

Radar charts are effective multivariate visualisation tools because they allow multiple performance metrics to be displayed simultaneously within a single compact structure. By mapping variables onto a shared radial axis system, they provide an intuitive representation of a player’s overall statistical profile and facilitate rapid identification of relative strengths, weaknesses, and stylistic tendencies. The geometric structure of the chart makes it possible to evaluate how performance is distributed across dimensions rather than focusing on isolated variables, which is particularly valuable in football analytics where player evaluation is inherently multidimensional.

A further advantage of radar charts is their suitability for comparative analysis. Multiple player profiles can be overlaid within the same coordinate system, enabling efficient visual assessment of similarities, complementarities, and role-specific differences across a wide range of metrics. This makes radar charts especially useful in scouting, recruitment, and performance analysis contexts, where analysts seek to identify patterns, archetypes, and deviations from positional norms. In addition to their analytical utility, radar charts also provide a visually interpretable framework that supports communication of complex statistical information to both technical and non-technical audiences.

Lie Factor

Now, how can we statistically test whether the data we see, also reflects the data in our excel/csv/json files? One of these methods, is the lie factor. It shows how much cover of the area corresponds with the cover of data.

The lie factor analysis indicates that the radar chart substantially exaggerates the perceived statistical difference between T. Claes and Y. Khalifi. Although both players have very similar average percentile profiles (55.55 versus 54.71), the visual area of their radar polygons differs much more strongly, producing a graphic effect of 0.187 compared to an actual data effect of only 0.015. This results in a lie factor of 12.184, meaning the radar visualisation amplifies the underlying statistical difference by more than twelve times.

The result highlights one of the key criticisms of radar charts in statistical visualisation research: because viewers tend to perceive area rather than individual radial distances, relatively small differences across metrics can appear visually dramatic when converted into polygonal shapes.

Consequently, radar charts may be highly effective for visual storytelling and stylistic profiling, but they can also introduce substantial perceptual distortion if interpreted as precise representations of comparative performance.

Permutations Test

A permutation test is a non-parametric statistical method used to determine whether the observed difference between two players is statistically meaningful or could have occurred randomly. Instead of relying on assumptions about normal distributions, the test repeatedly shuffles the metric values between players thousands of times and recalculates the comparison statistic each iteration to build a null distribution. The observed difference is then compared against this randomized distribution to estimate a p-value, which represents the probability of obtaining a difference at least as extreme as the observed one under random chance.

The permutation test indicates that the statistical difference between T. Claes and Y. Khalifi is not particularly unusual relative to the broader distribution of player differences within the dataset. The observed profile difference between the two players was 42.62 percentile points across the selected metrics, compared to an average random player-pair difference of 32.42 with a standard deviation of 11.42. Although the observed difference is somewhat above the dataset average, its z-position of 0.89 suggests that it remains within the normal range of variation expected between randomly selected players. This is reinforced by the permutation p-value of 0.1883, meaning that approximately 18.8% of random player comparisons produced differences at least as large as the observed one. Consequently, the analysis suggests that the apparent separation between the two radar profiles is not statistically significant and may reflect ordinary variation rather than a uniquely distinct performance profile.

JND Testing

Just Noticeable Difference (JND) testing evaluates whether the visual difference between two charts is large enough for a human observer to reliably perceive. In the context of football radar charts, JND analysis is useful because radar visualisations can sometimes exaggerate or hide differences that may not actually be perceptually distinguishable to viewers. Rather than focusing purely on statistical significance, JND testing examines perceptual significance — whether the change in shape, area, or metric magnitude exceeds the threshold at which humans can visually detect a difference. This makes it particularly relevant for evaluating the interpretability and effectiveness of radar-based visualisations in scouting and analytical communication.

For your radar comparisons, a practical JND approach is to compare the observed difference between two percentile profiles against a perceptual threshold derived from the dataset, often using Euclidean distance or mean absolute percentile difference across metrics. If the observed difference exceeds the estimated JND threshold, the profiles are likely visually distinguishable; if not, viewers may perceive them as effectively similar despite measurable statistical variation. This allows you to study not only whether players are statistically different, but also whether those differences are likely to be meaningfully perceived in the visualisation itself.

The Just Noticeable Difference (JND) analysis suggests that the radar profiles of T. Claes and Y. Khalifi are perceptually distinguishable when viewed visually. The observed profile distance between the two players was 42.62 percentile points across the selected metrics, which substantially exceeds the estimated perceptual threshold of 24.08 derived from the lower quartile of random player-pair differences within the dataset. Unlike traditional significance testing, which evaluates whether a difference is statistically unlikely under random variation, the JND framework focuses on whether the difference is large enough to be meaningfully perceived by human observers when interpreting the visualisation. In this case, the analysis indicates that the separation between the two radar profiles is not only measurable statistically, but also sufficiently large to be visually noticeable in practical analytical or scouting contexts.

ANOVA

ANOVA (Analysis of Variance) is a statistical method used to evaluate whether differences between groups or profiles are larger than would be expected from natural variability within the data. In the context of football radar analytics, ANOVA can be applied to compare player profiles across multiple metrics by examining whether the overall differences between players are statistically meaningful relative to the variation within their individual performance distributions.

The ANOVA analysis suggests that the overall percentile radar profiles of T. Claes and Y. Khalifi are not statistically different when evaluated relative to the variability within their profiles. Although the two players exhibit slightly different average percentile values (55.55 versus 54.71), the extremely small F-statistic of 0.004 and very large p-value of 0.9487 indicate that these differences are negligible compared to the underlying variance across the selected metrics. In practical terms, the analysis suggests that the apparent visual differences between the two radar charts are not supported by strong statistical evidence and are likely consistent with ordinary variation in multidimensional player profiles rather than representing meaningfully distinct performance structures.

Final thoughts

Radar charts are neither inherently good nor inherently misleading; their value depends on how consciously they are constructed, interpreted, and contextualised. They remain powerful tools for summarising multidimensional football data into visually intuitive player profiles that support rapid comparison, stylistic identification, and communication across recruitment and analysis departments. However, as the statistical tests in this article demonstrate, the visual impact of a radar chart can diverge substantially from the underlying data structure. Differences that appear dramatic in polygonal form may not be statistically meaningful, while perceptually noticeable shapes may simply emerge from the geometry of the visualisation itself rather than from genuinely distinct player profiles. This does not make radar charts invalid, but it does require analysts to approach them critically rather than treating them as objective representations of truth.

The broader issue therefore is not the existence of radar charts, but the level of statistical literacy surrounding them. In modern football analysis, visualisations increasingly shape recruitment decisions, public narratives, and even player valuation, which makes understanding their strengths and limitations essential. Radar charts are most useful when they are treated as exploratory or communicative tools rather than definitive evaluative models. Combining them with contextual interpretation, statistical testing, and domain expertise allows them to remain highly valuable within the analytical workflow. Ultimately, the goal should not be to abandon radar charts, but to use them more responsibly, transparently, and critically in order to avoid mistaking visual impression for analytical certainty.

There was a time when I had the means and energy to write a new article every week, but with the appalling state of the world and genuinely being really busy, this isn’t the case anymore. It does give me time to ponder a few things, and one of these things is Expected Pass.

Expected pass is a weird statistic because it doesn’t signify the expectation of whether the pass is going to happen. It indicates what the likely completion of said pass is and could, in some instances, involve pass difficulty. We can look at different providers, and they all have done things differently.

My aim with this article is to create my own Expected Pass Model, but with a few things added. I would like to create a metric that includes Time-To-Execute. In other words, what does time on the ball have to do with pass completion probability?

Contents

1. Why this research?

2. Data representation and provider

3. Theoretical framework

4. Methodology

5. Results

6. Time-to-execute

7. Challenges

8. Final thoughts

9. Sources

1. Why this research?

The aim of this research is purely for my own purposes, because I want to create an xPass model myself. Different models out there look at expected passes. The model is focused on the probability of a pass being completed. I have looked at the models from Opta and Statsbomb. While they are incredibly useful and have a high degree of quality, I want to build my own. And I have three reasons for it:

1. I want to build my own model, so I will have total control of how the features and variables are being used.

2. I want to add time-to-execute: how quickly the ball is being passed, and what kind of effect it has on the expected probability

Whether I’m going to be successful or not depends on how I execute it correctly. I also think we need to be vigilant that data is always biased and that we can do innovative research, but it doesn’t mean that something useful comes out of it.

2. Data representation

I know these articles follow the same structure over and over again, but this might be one of the most important sections of our research. We need to understand that every data provider takes different actions in how they capture the data, what definitions they use, and how they make models and metrics. In being aware of this particular stuff, we can make higher-quality research with our own models.

I have the option to choose from different sources: Opta, Statsbomb, Wyscout and IMPECT. Because Opta is most accessible for most people who read this, I’ve chosen Opta. I am dealing with raw event data (X,Y) that focuses on on-ball actions rather than off-ball actions.

The data can be split in two databases. The first database is to train the model. I have selected 6 seasons of the Belgian Pro League from 2019–2020 until 2024–2025. These are in and around 1500 games we use to train the data. The next database is the current 2025–2026 season of the Belgian Pro League. I want to calculate the xPass numbers for the 2025–2026 using the model trained on all the other seasons.

The data was collected on March, 31st 2026, via the Opta API. The data was stored as JSON, which is now my preferred output to work with, but you can easily work with CSV/Excel files as well.

3. Theoretical framework

The model draws on four theories from statistics and mathematics. These underpin the calculations that follow, rather than forming part of them directly.

The first is the Bernoulli event framework. At its core, a pass is a binary event; it either succeeds or it doesn’t. In practice, this means every pass is assigned a value of 1 (completed) or 0 (incomplete), treating each one as a discrete decision with exactly two possible outcomes. The likelihood of success is governed by an underlying probability, though this is not fixed. It shifts depending on the contextual conditions surrounding each pass.

xPass represents the probability that any given pass will succeed, based on the conditions surrounding it. This grounds the metric in classical probability theory, the outcome is uncertain, but that uncertainty is structured by what we can observe. Framing pass completion this way gives the model a theoretically sound foundation, one that captures the inherent unpredictability of the action while still producing something meaningful and comparable across different types of passes.

The second theory is conditional modelling. The core idea here is straightforward: not all passes are created equal, and the likelihood of completing one depends heavily on the circumstances in which it is attempted. Rather than treating every pass the same, the model assumes that a set of contextual variables shapes the probability of success and that understanding those variables is key to understanding the outcome.

In this context, xPass is defined as the probability of a pass being completed given what we know about it at the moment it is played. The emphasis is on conditioning, isolating how individual factors influence the outcome while accounting for everything else. This makes it possible to compare passes that vary in difficulty and context in a meaningful way, effectively standardising performance across situations that would otherwise be hard to evaluate on the same terms.

The third theory is the statistical learning framework. This addresses a more fundamental question: how does the model actually learn the relationship between context and outcome? The honest answer is that the true mechanism is unknown. What the model does instead is approximate it, drawing on large samples of historical passes to identify patterns that associate particular combinations of features with higher or lower completion rates.

In practice, this means fitting a function that takes a set of input variables and returns a probability. Logistic regression is a natural fit here, given that the outcome is binary and the results are relatively easy to interpret. Regularisation is typically applied as well, acting as a check against overfitting, ensuring the model picks up on genuine patterns rather than quirks in the training data. The end result is an empirical estimate of how context and success relate to one another.

The fourth and final theory is the framework of generalisation. Training a model is only half the challenge; the other half is determining whether what it has learned actually holds up on new data. This framework asks whether the relationships identified during training remain valid when the model is applied to passes it has never seen before. The underlying assumption is that they do: that the connection between pass characteristics and outcomes is stable enough to transfer across different samples and situations.

In practice, xPass values assigned to new passes are treated as probability estimates grounded in historical evidence. How reliable those estimates are depends largely on how well the training data reflects the conditions the model will encounter going forward. If the game changes, tactically, personnel-wise, or even in how the data is collected, the model’s accuracy may deteriorate. This is why validation and out-of-sample testing are not optional extras but core parts of the framework.

4. Methodology

The modelling process begins with extracting pass data from match JSON files. Each file is parsed to identify pass events, in Opta’s data structure, a pass is recorded as typeId 1, with x and y coordinates capturing where on the pitch it took place. For each pass, a range of attributes are collected: the player and team involved, the match context, spatial coordinates, timing, and whether the pass was completed. The raw data is then cleaned, removing incomplete or invalid entries and organising what remains into a consistent tabular format.

From there, feature engineering transforms the raw event data into variables that are meaningful for the purposes of the model. Spatial features are derived from the start and end coordinates of each pass, capturing distance, direction, and how far the ball progresses up the pitch. Additional contextual variables are constructed to reflect tactical conditions — whether a pass is forward, long, or played late in the match, for instance. Categorical identifiers such as team and player are encoded numerically where possible, though using player names directly will produce non-numerical values. Missing data is addressed through a combination of imputation and indicator variables that flag absence rather than simply discarding it.

The dataset is then split into training and testing subsets to keep the evaluation clean. A logistic regression model with regularisation is fitted on the training data, learning how pass characteristics relate to completion outcomes. Once trained, the model generates probability estimates for both the training set and new, unseen passes — and it is these estimates that form the basis of the xPass metric.

Each pass is represented by a collection of features that are combined into a single score reflecting how favourable the conditions are. That score is converted into a value between zero and one, representing the estimated probability of completion. This is the xPass value.

Training the model involves optimising a loss function that measures how well predicted probabilities match observed outcomes. Log loss is used here, penalising confident predictions that turn out to be wrong most heavily. A regularisation component is included to limit the size of model coefficients, reducing the risk that the model latches onto noise in the training data rather than genuine patterns.

At the individual pass level, xPass gives an estimate of how likely each action was to succeed. These probabilities are then aggregated to produce player-level metrics. Summing probabilities across all of a player’s attempts gives expected completed passes, while actual completed passes come from the observed data. The gap between the two is a measure of performance relative to expectation. Supplementary metrics, average pass probability and overall completion rate, provide further context when evaluating players.

Model performance is assessed using a combination of probabilistic and ranking-based measures. Log loss evaluates how accurate the predicted probabilities are. The Brier score captures the average squared difference between predictions and outcomes. The area under the ROC curve tests how well the model separates successful passes from unsuccessful ones. Taken together, these metrics give a thorough picture of how reliable and accurate the model is.

5. Results

The model was trained on a dataset of 204,699 passes drawn from 224 matches, covering 16 teams and 446 unique players of whom 374 were retained after low-frequency players were grouped. The data was divided using a match-based split, producing a training set of 163,859 passes and a test set of 40,840. The overall pass completion rate across the full dataset was approximately 77.9%, with near-identical figures in both the training (78.0%) and test (77.5%) samples, suggesting the split is consistent, and neither subset is meaningfully skewed.

In terms of probabilistic accuracy, the model performs well. On the training set, it achieves a log loss of 0.396 and a Brier score of 0.127, both pointing to well-calibrated probability estimates. These figures hold up on the test set, where log loss rises modestly to 0.411 and the Brier score to 0.133. The limited deterioration between training and test performance is encouraging; it suggests the model is not simply memorising the training data, but has learned patterns that carry over to unseen passes.

The model is also effective at ranking pass outcomes. ROC AUC comes in at 0.835 on the training set and 0.822 on the test set, reflecting a strong capacity to distinguish between passes that succeed and those that do not. That these figures hold without access to tracking data or information about defensive pressure makes them particularly noteworthy — the model is extracting a meaningful signal about pass difficulty from contextual features alone.

At the pass level, the model’s predictions align with what we would intuitively expect. Low-risk passes; short, backward, or lateral, receive high xPass values, while longer and more progressive passes are assigned lower probabilities. This confirms that the model is picking up on the spatial and directional elements that drive passing difficulty in a way that makes footballing sense.

At the player level, aggregating xPass values across all attempts reveals variation in both volume and performance relative to expectation. High-involvement players naturally accumulate large expected completion totals, while the gap between actual and expected completions identifies those who are outperforming or underperforming their context. Equally telling is the variation in average xPass values across players. Those attempting more progressive or ambitious passes tend to operate at lower baseline probabilities, while players in deeper or less pressured roles show higher averages. This reflects genuine differences in passing profiles rather than differences in quality alone, which is precisely what the metric is designed to capture.

6. Adding time-to-execute

Having established the baseline xPass model, the next step is to introduce an innovation: time-to-execute.

The baseline model, as outlined above, was trained on 204,699 passes across 224 matches, with a pass completion rate of 77.9% that held consistently across both the training and test splits. The time-aware model uses the same dataset and the same split, but expands the feature space by adding temporal variables that capture the time elapsed since previous events, measured at the match, team, and player level. This allows the model to account for how quickly decisions are made and how possession tempo varies, layering a new dimension of context on top of the spatial characteristics already in use.

On the test set, the baseline model recorded a log loss of 0.411, a Brier score of 0.133, and an ROC AUC of 0.822. The time-aware model improves on each of these: log loss falls to 0.406, the Brier score to 0.131, and AUC rises to 0.828. The margins are modest — a reduction of 0.005 in log loss, 0.002 in Brier score, and a gain of 0.006 in AUC, but they are consistent across all three metrics, which matters. Taken together, they suggest that adding temporal features contributes a genuine predictive signal, improving both the calibration of the model’s probabilities and its ability to distinguish between successful and unsuccessful passes, without any sign of overfitting in the process.

At the pass level, both models produce probability estimates that make intuitive sense, assigning higher values to shorter and less progressive passes. The meaningful difference lies in how each model contextualises those passes. The baseline model evaluates difficulty purely through spatial and static features, while the time-aware model also accounts for how quickly a pass is played. A pass executed shortly after the previous team action, typically under greater pressure, receives a lower probability than a spatially identical pass played after a longer interval. That distinction is invisible to the baseline model.

At the player level, both models surface variation in passing volume and performance relative to expectation, but the time-aware model shifts the interpretation somewhat. Where the baseline primarily reflects spatial passing tendencies, the time-aware version also captures differences in tempo and the decision-making environment players operate in. Those involved in faster, high-pressure sequences tend to show slightly lower average xPass values than the baseline would suggest, while players who operate in slower, more controlled buildup phases appear with higher baseline probabilities. The result is a richer and more realistic picture of passing behaviour — one that combines where passes are played with the speed and pressure under which they are attempted.

7. Challenges

One of the model’s central limitations is that temporal features serve as proxies for decision-making under pressure rather than direct measurements of it. Variables like time since the previous event carry a useful signal, but they do not capture how long a player actually takes between receiving the ball and playing the pass. They may also reflect unrelated events in the data, introducing noise and limiting how faithfully they represent the pressure a player is operating under.

A related challenge is the absence of any defensive context. Because the model relies entirely on event data, it has no information about where opponents are positioned, how much pressure is being applied, or which passing lanes are available. Pass difficulty is therefore inferred indirectly from spatial and temporal patterns rather than observed directly, which means the model is on shakier ground when trying to explain outcomes in heavily contested situations.

The choice of logistic regression also brings structural constraints. The model assumes a linear relationship between features and the log-odds of pass success, which may not hold where variables interact in more complex ways, the combined effect of distance, angle, and tempo being one example. Feature engineering helps to an extent, but the underlying model remains limited in its ability to capture the non-linear dynamics that characterise football actions.

Player identity features introduce a further risk. Grouping low-frequency players reduces the danger of overfitting, but the model may still pick up on player-specific tendencies that do not generalise well. This can quietly erode both interpretability and the model’s usefulness when applied to players it has not encountered before.

Finally, the precision of event timestamps is not guaranteed. Timestamps are often recorded at a coarse level and may not perfectly reflect the true sequence of actions on the pitch. Since the time-based features depend on accurate ordering, even small inconsistencies in the data can introduce systematic errors into how the model represents the flow of the game.

9. Final thoughts

Time-to-execute fills a gap that conventional xPass models leave open. Where existing approaches evaluate passing difficulty through space, distance, direction, and field position, they say nothing about the speed at which a decision is made. This work demonstrates that temporal context carries a genuine predictive signal: the time-aware model improves consistently across log loss, Brier score, and ROC AUC on unseen data, and does so without overfitting. More importantly, those improvements make footballing sense. A pass played under immediate pressure is harder than a spatially identical pass played after a longer interval, and the model now reflects that.

What time-to-execute cannot do is equally important to state clearly. It is a proxy derived from event timestamps, not a direct observation of pressure or decision-making speed. It captures when something happened relative to surrounding events, not why a player chose to act at that moment or what defensive conditions forced his hand. The absence of tracking data means the model remains blind to positioning, pressing intensity, and passing lane availability, the very factors that make fast decisions genuinely difficult rather than simply fast. These are not flaws to be apologised for; they are honest boundaries that define what the metric is and is not.

The practical value of time-to-execute lies in what it adds to player profiling. Players operating in high-tempo, high-pressure sequences will carry systematically lower xPass values under this model than the baseline would assign them — a more accurate reflection of the environment they work in. That distinction matters for recruitment and performance analysis, where context-blind completion rates have always been a crude tool.

Future work should focus on two things: better measurement of decision time using tracking data, where the gap between ball receipt and release can be observed directly, and more flexible modelling approaches that can capture the interaction effects between tempo, space, and passing angle that logistic regression smooths over. The foundation is in place. The question of how time shapes passing success is now part of the model and it should stay there.

10. Sources

Bransen, L., & Van Haaren, J. (2019). Measuring football players’ on-the-ball contributions from a pass perspective. Machine Learning, 108(2), 349–369. https://doi.org/10.1007/s10994-018-5767-3

Decroos, T., Bransen, L., Van Haaren, J., & Davis, J. (2019). Actions speak louder than goals: Valuing player actions in soccer. Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, 1851–1861. https://doi.org/10.1145/3292500.3330758

Fernández, J., & Bornn, L. (2018). Wide open spaces: A statistical technique for measuring space creation in professional soccer. MIT Sloan Sports Analytics Conference.

Lucey, P., Bialkowski, A., Carr, P., Morgan, S., Matthews, I., & Sheikh, Y. (2015). Quality vs quantity: Improved shot prediction in soccer using strategic features from spatiotemporal data. MIT Sloan Sports Analytics Conference.

Power, P., Ruiz, H., Wei, X., & Lucey, P. (2017). Not all passes are created equal: Objectively measuring the risk and reward of passes in soccer from tracking data. Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 1605–1613. https://doi.org/10.1145/3097983.3098050

Spearman, W. (2018). Beyond expected goals. MIT Sloan Sports Analytics Conference.

StatsBomb. (n.d.). Expected pass (xPass) model. Retrieved from

https://statsbomb.com

Opta Sports. (n.d.). Opta event definitions. Retrieved from https://www.statsperform.com/opta-event-definitions/

Wyscout. (n.d.). Wyscout glossary and metrics definitions. Retrieved from

https://wyscout.com

Sumpter, D. (2016). Soccermatics: Mathematical adventures in the beautiful game. Bloomsbury Sigma.

Once in a while, I have this illusion that I’m well-equipped enough to write a more data-journalistic piece. Don’t worry, the urge will probably sink as soon as it came up, but I want to take advantage of the opportunity. So let’s talk about zone 14 and whether its relevance has changed in the last 5 seasons.

But let’s stop right there for a moment. I have been thinking a lot about writing about football analysis, whether that’s video, data or engineering, and I need to get a few things off my chest.

The first thing I think that needs addressing is that in the football sphere online, opinions are more and more presented in a way that they are stated to spark controversy. It’s either black or white, and in doing so, it sparks fuel to a very polarising view of football. We have seen this in how people say “this is the right way to play football” which also leads to remarks that there is something like “anti-football”. I think that’s very harmful because it portrays the idea that football should be played, viewed and analysed in a specific way, otherwise it isn’t valid.
Building on that, if we look at the analysis part of things, I came across a specific, well-written essay featured on Spielverlagerung:

One of my favourite writers at the moment, Hamzah Khalique-Loonat, alerted me to this piece, and I’m very happy he did, because it’s of vital importance in the way we see football. Personally, I think there is an issue with portraying rights and wrongs too in football, because in the end, they are all human constructs. And, I also agree with the notions that we can present our ideas as universal truths or paths to get somewhere. I have been guilty of this thing as well. You can read the essay here: https://spielverlagerung.com/2026/02/06/essay-escape-mx/

The next thing that worries me as well is more of a global trend in sports journalism. More and more cuts happen at qualitative newspapers and news outlets. This is a worrying state, because it feeds into the undermining of democracy in various nations all over the world. And it has the consequence that there are fewer journalists and more writers. There is a distinction and we can see this mostly in the fact that more and more writers launch medium or substack (yes, I can see the irony of me writing this) because they have to, to survive. The issue I have with that is that there is no feedback, no editor or pushback. You write and you publish what you ought to be good. I’m not a journalist in this industry and it’s not my priority in life, but the quality of football (data) journalism needs it.

So how does this tie in with me writing an article about the evolution of zone 14? I recognised a pattern in myself that I set out to have a research question and from that question I hoped to see a certain outcome. That outcome never came and I wanted to manipulate the question so I could find some meaningful change. But the reason I wanted to do that is rather selfish, because I wanted to feel the validation of many readers or engagement. But that in itself is a bit of a problematic view.

With this context, it will be easier to understand that sometimes a lack of result, is also a result and I want to go back to better research when writing this more data journalistic pieces.

What is zone 14?

We can divide the pitch into different zones away from the thirds (defensive, middle and attacking third) and create a pitch that has 18 zones. In that zone, we identify zone 14 as the zone in central area just before the penalty area, as you can see here:

Why have we identified this zone and used it frequently over the last few years? It was researched in 2002 that passes into the penalty area from this zone were 4 times more likely to lead to a goal, rather than coming from either the left or right flank.

Successful players and teams were more likely to use zone 14 to get the ball into the penalty area than they were from the flanks. There is a strong correlation between zone 14 usage and success. This research stems from 2002 and in this article I will attempt to answer a two distinct questions in 2026:

1. Does the ratio hold up in 2026?

2. Have we moved from a creating zone to a connector zone?

Data

I have used 5 season of Premier League football to analyse. The seasons are: 2021–2022, 2022–2023, 2023–2024, 2024–2025 and 2025–2026. This data was pulled from the Wyscout API on February 4th, and it’s event data. From that event data.

I focus on the Premier League, because I think it will be interesting to follow an elite league and the feeling that I have that zone 14 is used a lot. I’m saying a feeling, so this is just based on intuition.

Ratio anno 2026

So how does it hold up in 2026? Are we still talking about 4 times higher ratio from zone 14 into the penalty area? Or has something changed. A good indication would be to see what the percentages have been throughout the years.

As we can see above, the percentage of passes to the penalty area from zone 14 remains more or less the same. The percentage starts with 20,9% in 2021–2022 after COVID and is currently on 20,7%. This 0,2% less than a few seasons ago, but the change is almost nihil. What’s interesting though is that it’s being smaller since 2022–2023.

Something similar we can see in the percentages of going to the flanks. It was 40,3% at the beginning and dropped to 38,5% in 2023–2024 and is starting to climb again with currently 39,7%.

It shows us that there is a decline in zone 14 passes towards the penalty area and a slight growth in zone 14 passes to the flanks. This is obviously interesting, but now we want to see what it leads to: goals.

When we look at the percentage of goals from zone 14 into the penalty area, we see that 2024–2025 was the highest with 4,1% and the current season is the lowest with 3,5%. The flanks, however, had the highest percentage in 2023–2024 and are currently the lowest with 1,9%.

When we look at the graph above, we can see the ratio between zone 14-initiated goals and flanks-initiated goals. Nowhere in the last seasons has the ratio been four times higher from zone 14 than it is from the flanks. At it’s highest point, zone 14 has 1,85 times more success and it’s lowest point 1,32 times. Currently, the goal ratio is 1,82 times higher and that seems like zone 14 does deliver success.

From creation zone to connecting zone?

From watching games, I got the impression that zone 14 hasn’t been as much of a creation zone but more of a connecting zone. What I mean by this is that I think that fewer key passes come from this zone, but more passes that build the attacking in the latter phases of the sequences.

Looking at the last few Premier League seasons the connection from zone 14 is higher than the creation, meaning that there are less direct threat creation actions from passes. It started with 0,8 times and it’s now 0,7 times based on creation.

As you can see here, in the Premier League, 2022–2023 saw a spike in connecting through zone 14, but has also declined since and it’s 13,6% now. Creation has started at 10,8% but has just declined since and is at 8,8% now, which is -2%.

It would seem that in the Premier League over the last few seasons, zone 14 is more used a connection zone than a creation zone.

In the 2024–2025 season, the teams that created the highest percentage of shot-producing passes were Crystal Palace, Wolverhampton Wanderers and Everton. It meant that they were quite direct from the zone 14 and the shot that followed within 2 actions.

When we look at the connection zone 14 passes, we get to see different teams doing well.

Here we see some top teams scoring high who are high on the passing game such as Manchester City, Arsenal and Liverpool. But we also teams like Southampton, Leicester City and Ipswich Town who were all relegaeted at the end of the season.

Final thoughts

So, has zone 14 really evolved? The short answer is that it hasn’t changed in the way I initially expected or perhaps even hoped for. The usage of zone 14 in the Premier League has remained remarkably stable over the last five seasons, and the long-standing idea that actions from this zone are four times more effective than those from the flanks simply does not hold up here. There is still an advantage, but it is far more modest. In that sense, this analysis does not tell a story of tactical disruption, but rather one of continuity, and accepting that is already an important outcome.

What has changed is not the relevance of zone 14, but its role within attacking sequences. The data supports the idea that zone 14 functions increasingly as a connecting zone rather than a pure creation zone. Fewer actions from this space lead directly to shots, while more possessions flow through it as part of longer, more controlled attacking phases. This also explains why high zone-14 connectivity is not limited to successful teams: both dominant possession sides and relegated teams appear near the top. Accessing zone 14, on its own, is not a measure of quality — what matters is what teams are able to do after reaching it.

Finally, this piece forced me to confront something about research and writing itself. The absence of a strong, dramatic change does not mean the analysis failed, it simply means the game did not move in the direction I anticipated. Trying to reshape the question to force a “better” result would have said more about my own need for validation than about football. Sometimes, stability is the finding. And perhaps that is the more honest place to end: zone 14 has not disappeared, nor has it transformed completely: it has quietly adapted within a game that resists simple truths.

References

Horn, R., & Williams, M. (2002). A look ahead to World Cup 2002: What do the last 40 years tell us? Insight, 5(2), 26–29.

LeoChan Performance Analysis. (2013, August 18). What is “Zone 14” in football? Retrieved from https://leochanperformanceanalysis.blogspot.com/2013/08/what-is-zone-14-in-football.html

Spielverlagerung.com. (n.d.). Zone 14 [Glossary entry]. Retrieved February 6, 2026, from https://spielverlagerung.com/glossary/pitch-zones/zone-14

Goalkeeper data analysis is one of the hardest things I have experienced doing in this space. So why do I keep challenging myself to do it? The answer is two-fold. First of all, I really want to scout goalkeepers using data, because I think that’s possible. Secondly, the reasons I’m writing this article is that not many metrics exist for the purpose I want to data scout for goalkeepers. So that’s why I think: “if it doesn’t exist, you have to make it yourself.”

I embarked on this journey with my Goalkeeper Value Model, which I created in 2025. This model looks to add value to the goalkeeper’s actions on the pitch, so we can distinguish between different levels of goalkeepers in a specific database. If you want to read more about this, you can read my stuff here:

Building on that, I want to take the next step. Well, not sure whether next step is the right word, but I want to look at a different, more niche yet very important part of the game: how do goalkeepers make their saves and if they can’t catch it, what happens with the rebound? That’s why I created the Rebound Model, which measures the value of the rebound based on the offensive/defensive quality of the player AND the safe/danger parry of the goalkeeper.

Contents

1. The aim of my research and creation of the Rebound Model

2. Hidden Markov Model and Markov Decision

3. Data

4. Methodology and calculations

5. Results

6. Building the model with Logistic Regression

7. Goalkeeper results

8. Final Thoughts

The aim of the research: creation of the Rebound Model

My idea for this model came not from football but from Basketball. I remember the episode of The Last Dance that focused on Dennis Rodman and it intrigued me. The part that intrigued me is the way he studied every shot from a player and how the rebound would happen. Which spin, which side, what rotation and what speed? Based on that, he could get the rebound: being the first player to get to the ball after the shot was missed.

This sparked my interest and this was made bigger by the fact that we look at scores of basketball players and always include their rebound. This made me think, do we have a particular equilavent in football? And, if not — what value can we bring to it?

In this research, I want to measure rebounds after a goalkeeper save, measure the value of that save, measure the value of the rebound and how players react to it. This means that there will be two types of models, one for goalkeepers and one for players. I want to add value to rebounds because they are evidently of huge influence in an attacking and defensive role of the game.

Hidden Markov Model

A Hidden Markov Model (HMM) is a probabilistic model for time-ordered sequences where you assume there’s an underlying sequence of hidden states (things you can’t directly observe) generating a sequence of observations (things you do observe). The “Markov” part means the hidden state at time t depends only on the hidden state at time t−1 (not the full history). The “hidden” part means you never see the states directly — you only see the outputs they produce.

An HMM is defined by three sets of probabilities: initial state probabilities (how likely each hidden state is at the start), transition probabilities (how likely the model is to move from one hidden state to another), and emission probabilities (how likely each observation is given a particular hidden state). With those, you can answer three core questions: (1) Evaluation: how likely is an observation sequence under the model? (2) Decoding: what hidden-state path most likely produced the observations (often via Viterbi)? (3) Learning: how to fit the model parameters from data (often via EM / Baum–Welch).

Methodology: Modelling Post-Save Rebound Sequences with Hidden Markov Models

The way I approach this model comes from a simple idea: rebounds matter, but in football, we do not really treat them as something we can properly measure. In basketball, rebounds are a fundamental part of how we evaluate players and teams. In football, once a goalkeeper makes a save, the analysis often stops there. What happens next is usually reduced to whether a goal is conceded or not. This model is built on the belief that it misses a large and important part of the game.

Instead of treating a save as a single, isolated event, I treat it as the start of a short sequence. After a save, the ball is often still in play, players react, space opens or closes, and danger can either disappear or escalate very quickly. To capture this, every save becomes the anchor of a short time window in which all subsequent actions are observed. If the goalkeeper clearly collects the ball, the sequence ends immediately. If not, the rebound phase continues and becomes the object of analysis.

To make this tractable, I reduce the chaos of post-save play into a small number of meaningful event types: clearances, duels, shots, additional saves, and goals. These are the actions that actually decide whether a rebound turns into control or danger. Rather than trying to judge these moments with fixed rules, I use a Hidden Markov Model to learn recurring patterns in how rebounds evolve. The idea is that there are underlying “states” of play after a save — some calm and controlled, others chaotic and dangerous — that we cannot observe directly, but that reveal themselves through the sequence of actions that follows.

Once the model is trained, each rebound sequence can be described in terms of how long it stays “alive” and how quickly danger appears. A rebound that immediately leads to a duel or a shot looks very different from one that is resolved with a quick clearance or collection, even if neither results in a goal. This allows me to move away from binary thinking (goal vs. no goal) and toward a more continuous view of rebound control and rebound threat.

Importantly, this framework naturally leads to two perspectives. From the goalkeeper’s side, the question becomes: how well does a save turn into control? Does the goalkeeper consistently kill danger, or do their saves often lead to extended pressure? From the outfield player’s side, the question shifts to: who reacts best to rebounds? Which players consistently protect their own goalkeeper, and which players are best at exploiting rebounds against the opposition?

By modelling rebounds as sequences rather than moments, this methodology assigns explicit analytical value to something that is clearly influential in football but rarely measured directly. In that sense, the approach mirrors how rebounds are understood in basketball: not just as outcomes, but as repeatable, learnable patterns that separate good performers from great ones.

Calculations

Once rebounds are framed as short sequences rather than isolated events, the next challenge is deciding what to measure and how to measure it. The goal here is not to build a single “perfect” number, but to extract multiple signals that describe how a rebound develops: how dangerous it becomes, how quickly it is resolved, and which players are responsible for that outcome.

I approach this from two angles. First, I use probabilistic models to understand how rebound sequences typically evolve and end. Second, I compute a set of intuitive, football-driven metrics that describe space, time, and outcomes. Together, these form the basis for goalkeeper and player evaluation.

To establish a baseline understanding of rebound outcomes, I model the post-save phase as a simple absorbing Markov process. The idea is straightforward: once a save occurs, play either continues for a short period or eventually resolves into one of two terminal outcomes — safety or conceding a goal. By tracking how often rebound sequences transition from one action to the next before reaching one of these endpoints, I can estimate how dangerous a typical rebound situation is, independent of who the goalkeeper or players are.

From this model, two quantities are especially useful. The first is the probability that a rebound sequence ultimately results in a goal. The second is the expected number of actions before the rebound is resolved. Together, these tell us not only how risky rebounds are on average, but also how long pressure tends to last after a save.

While the Markov chain describes how rebounds end, it does not capture how they feel as they unfold. For that, I use a Hidden Markov Model. Here, the assumption is that there is an underlying rebound context, something like “controlled” or “chaotic”, that we cannot observe directly. What we do observe are the actions that follow the save: duels, clearances, shots, or goals.

The HMM learns these latent rebound states directly from data by looking at which actions tend to cluster together and how sequences move between them. After training, some states clearly correspond to calm situations that are quickly resolved, while others correspond to extended pressure with a high likelihood of shots or goals. Importantly, these states are not defined in advance; they emerge from the patterns in the data.

For each rebound sequence, I then calculate how much time it spends in the “live” state and whether the sequence is already live from the very first post-save action. These measures capture something that traditional metrics miss: two saves can both avoid a goal, but one can still leave the defense under far more pressure than the other.

Probability models alone are not enough, so I also calculate a set of direct, interpretable metrics based on where and when rebounds occur. Spatially, the location of the first meaningful post-save action is classified into danger zones based on proximity and angle to goal. A rebound that drops centrally and close to goal is treated very differently from one that spills wide or away from the box.

Temporally, I measure how quickly the first action occurs after the save and whether key events happen in an “immediate” window following the save. Fast reactions often indicate disorganization or poor control, while slower, delayed actions typically reflect better defensive structure or ball security.

Results

The first thing that stands out to me is that most saves do not immediately “kill” the situation, even when no goal follows. When you look at the episode summaries, a large proportion of saves lead to at least one additional meaningful action, and many lead to several. This confirms the original intuition behind the model: a save is often not the end of the defensive problem, it is simply the beginning of a new phase. The fact that average episode lengths regularly exceed two events suggests that rebounds are not rare edge cases, but a structural part of how attacking pressure is sustained.

What I find especially interesting is how clearly the Hidden Markov Model separates different rebound environments. One latent state is almost entirely driven by duels, which aligns very well with the idea of a “live” rebound — scrappy, contested, unstable situations where neither team has clear control. Another state is dominated by quiet moments, collections, and clearances, which fits the intuition of a rebound being effectively neutralized. Importantly, these states are learned from the data, not imposed. The model is effectively rediscovering, on its own, the difference between chaos and control after a save.

From a goalkeeper perspective, the Rebound Control Index reinforces this idea that not all non-goals are equal. Some goalkeepers show similar goal-concession rates, but very different rebound profiles. A higher RCI tends to be associated with quicker resolution, fewer dangerous parries, and rebounds that are pushed further away from high-value zones. In contrast, lower RCI values often come from goalkeepers whose saves consistently lead to extended sequences, second saves, or rebounds remaining centrally located. This is exactly the kind of separation that traditional save percentages fail to capture.

Another result I find revealing is how time and distance matter more than outcomes. Mean time to first meaningful action and rebound distance vary meaningfully across goalkeepers, even when goal rates do not. This suggests that some goalkeepers are systematically better at buying time for their defense or pushing the ball into less threatening areas, even if those actions do not show up directly as goals prevented. In that sense, rebound control looks much closer to positioning and anticipation — similar to Rodman’s approach in basketball — than to pure shot-stopping.

Finally, when the rebound sequences are attributed to players, the results underline that rebounds are a shared responsibility. Certain players consistently appear as first responders after saves, either clearing danger for their own goalkeeper or creating immediate threat against the opposition. These contributions are usually invisible in standard metrics, but here they show up as repeatable patterns. Some players specialize in stabilizing chaos; others specialize in exploiting it. That split feels both intuitive when watching matches and validating when it appears in the data.

Overall, the results support the core idea behind the model: rebounds are not random, and they are not just noise around saves. They follow patterns, they reflect skill and decision-making, and they have a measurable impact on both defensive solidity and attacking threat. By treating rebounds as sequences rather than moments, the model uncovers value that has been hiding in plain sight.

Building a goalkeeper model

After I have ran the calculations, I get a set of different csv files: Comprehensive player actions, Goalkeeper report, HMM State report and rebound analysis. From these reports/files, I get a lot of information about the hidden markov model as well as the rebounds, but I want to build a model that values these post-save sequences from a goalkeeper’s side. In other words, how good is a goalkeeper in:

1. Making a parried save that goes into a “Safe” zone?

2. Recovering after a parried save and positioning themselves for a second save?

And you know what? This is not a singular model; these are two different models. Both models were estimated using regularised logistic regression, which predicts the probability of a binary outcome as a smooth function of input features via the logistic link. Logistic regression is well suited to this setting because it produces calibrated probability estimates rather than arbitrary scores, allowing expected post-save risk to be interpreted directly and aggregated across episodes. An elastic-net penalty combining L1 and L2 regularisation was applied during estimation. The L1 component encourages sparsity by shrinking weak or redundant coefficients to zero, effectively performing feature selection in the presence of highly correlated predictors such as rebound geometry, danger flags, and recovery indicators. The L2 component stabilises coefficient estimates by shrinking large weights, reducing variance and preventing overfitting, which is particularly important given the rarity of post-save goals. Together, this combination yields models that are interpretable, robust to multicollinearity, and well calibrated out of sample.

Parry Quality Value (PQV). This measures the technique of a goalkeeper as it answers the question: How dangerous are the rebound situations a goalkeeper creates with their saves?

The first model estimates the probability of a rebound shot or goal using only features that describe the state created by the goalkeeper’s save itself. These inputs include the save outcome (e.g. hold, safe parry, dangerous parry), the spatial location of the save, and the geometry of the rebound such as distance, angle, and whether the ball is redirected into a high-danger zone. By excluding all subsequent recovery actions, timing variables, and defensive interventions, this model isolates the intrinsic risk associated with the goalkeeper’s parrying technique and ball control. The resulting predicted probability represents the expected level of danger immediately created by the save, independent of how the subsequent sequence unfolds. Aggregating these probabilities across a goalkeeper’s episodes forms the basis of the Parry Quality Value (PQV), a measure intended to capture how consistently a goalkeeper creates safe post-save situations.

The second model is the Post-Save Sequence Value. It extends the first model by incorporating information about what happens during the post-save sequence itself, including early recovery timing, opponent or defender first contact, secondary saves, clearances, duels, and contextual indicators derived from sequence or state models. This richer feature set allows the model to condition expected risk on how the rebound phase actually develops, rather than on the initial parry alone. The predicted probability from this model therefore, reflects the expected likelihood of a shot or goal given both the rebound state and the subsequent actions taken during the scramble. By comparing the observed outcome to this conditional expectation and aggregating the resulting residuals at the goalkeeper level, the model yields the Post-Save Sequence Value (PSSV), which quantifies whether a goalkeeper concedes more or fewer post-save shots or goals than would be expected given the situations they face.

Goalkeeper Results

For the first model, we want to measure the value of the goalkeepers’ parried saves. In other words, when the keeper has to parry, how “safe” are the zones where the balls end up. Using our model in Allsvenskan, we get the following results:

In the bargraph above, we see the Expected robund shots prevented per 100 saves. It shows the quality of the parried saves and the impact on the rebounds shots. As you can see F. Beckman scores highest, as he is expected to prevent 25,1 rebounds per 100 saves he makes. This rougly translate to 25% of the saves.

Now let’s have a look at the rebound goals in relation to the saves.

In this bargraph, you see the best goalkeepers per goal prevention from rebounds. It measures the Expected rebound goals prevented per 100 saves in the Allsvenskan. A. Csongvai does perform best in the expected metrics with 2,41 expected rebound goals prevented.

If we go ahead and look at the second model, we can make some interesting observations here as well. The first model focuses on expected prevention in rebounds on the moment of the save, but this second model focuses on the danger after the save. So what prevention of a rebound shot happens after the initial shot.

Here you see how many shots are allowed in rebounds. This might seem the same as in model I, but here we are not looking only at the first action after a save, but we are looking at a rebound sequence, meaning that the attacking team gets the rebound.

Beckman does really well, as he only seems to concede 14,76 rebounds shots per 100 saves. Pettersson and Rönning follow closely.

Final thoughts

This work shows that goalkeeper performance does not end at the save, but continues in the seconds that follow. By modelling rebounds as sequences rather than isolated events, the Rebound Model captures a phase of play that is structurally important yet largely ignored in traditional analysis. The Hidden Markov Model consistently separates controlled rebounds from chaotic ones, and the distinction between Parry Quality Value and Post-Save Sequence Value makes clear that creating a safe rebound and surviving the scramble that follows are two different skills. In doing so, the model moves goalkeeper evaluation away from binary outcomes and toward the management of space, time, and danger.

At the same time, the second model highlights the core challenge of sequence-based evaluation: context is no longer static. Once you condition on what happens after the save, the goalkeeper is no longer the sole driver of risk. Defensive reactions, attacker positioning, refereeing decisions, and even small random deflections all influence how a rebound sequence unfolds. This makes attribution inherently harder and increases variance, especially in small samples. The Post-Save Sequence Value therefore, has to balance richness against noise, capturing real goalkeeper skill without over-crediting or over-penalising them for events largely outside their control. That tension is not a flaw of the model, but a reflection of football itself — and it underlines why separating technique at the moment of the save from context in the sequence is both necessary and unavoidable.

Football metrics and models are also under the influence of trends within football. One of these trends is the use of set pieces to generate meaningful chances in the game. Another big recent trend or influence on the game is the use of long balls, specifically launches. In this article, I want to have a look a this trend, but also look ahead and why long balls are used. And, why are second balls vital

Aim

The aim of this research and, therefore, this article, is to have a look at how we shape long balls and how they interact with the teams. But, even more important, we are going to have a look at what second balls are from those passes. More and more we look at what’s happening at the middle of the park: transitions and pressing are good examples.

I also want to go further than just looking at aerial duels won %: these measure the first contact, but much more important is the retention of possession. With possessions, you can actually create sequences that are meaningful towards the attack. That’s where the second balls come in.

Second balls are defined later on, but we look for second balls, as the first contact is often an aerial duel. This duel is often 50/50 and even if the header is won, the possession isn’t determined. Therefore the second ball. If a team targets long balls and loses all aerial duels but wins the second balls, they are dominant. Even if their won aerial duels percentage is incredibly low. And that’s the POV of this research.

Data explainers

I’m using raw event data, which is positional XY data. The reason why I’m looking at positional data and especially raw data is that it allows me to fully build my own metrics and models. When I use things predesigned it either hasn’t the right definition or I don’t know how it is compiled.

This is data is collected from the Opta API, and the data I collected is from the 2025–2026 Eredivisie season. This was done on the 26th December of 2025. The model I create is meant to be for educational purposes; if I was to use it, I would actually load more files into the model.

The data can be used in different formats, but I’m using JSON files to load the data and convert to my database. You can also work with CSV and Excel, for example, but the latter isn’t ideal. If you were working with JSON, you have to make sure you normalise the date before you can properly work with it.

Programming languages

I mention this every time I write an article, and you will know by now that I predominantly use Python. But I’m also well-versed in R and Julia. A good exercise for me is to create things I make with data engineering in all of the programming languages I master. It really doesn’t matter as long as you get to the result you want. If you feel more comfortable at one language over the other, go for the one you like.

What’s important, regardless, is that you know the calculations and how to structure them. If you know that, it doesn’t really matter as much which programming language you use.

Personall,y I have used Python for this one, but I’ve also used SQL to structure the database after I got the results of my model. I want to add the values to my already existing database.

Part I: Long balls

What is a long ball?

Before we are going to anything with our raw data, we need to define what we see as a long ball. Every data provider has a different way of defining it and designing it.

• When we look at Wyscout, they define it as an aerial pass that exceeds 25 meters or as 45 45-meter for a ground pass

• Opta makes a difference between long balls, chipped passes and launches. The long ball is a pass that exceeds 32 meters. The difference between a chipped pass and a launch is the intention of the end location: designed for a teammate or designed to go into a position for a player to go to.

• Statsbomb has the same distance rules, but makes a difference between unpressured and pressured balls for the long balls.

I’m working with Opta data, so I’m going to use the distance definition of 32 meters, but then the question arises: what is a long ball telling us? And should it be both targeted and untargeted? I am going for launches because it sets up for 50/50 challenges in the air, and that’s what we need. A chipped pass is a pass that’s designed to avoid opposition involvement and therefore won’t help in the second part of this article.

Methodology

The methodology behind this is that we are going to look at the raw event data and, through Python code are going to design a metric that can be used for much more. We are going to take the launches from the defensive third that exceed 32 meters and end up in the final third.

The reason why I’m going to do that is that we are seeing long balls as a tactical instrument to force attacking options in the attacking third. So what we are going to do here is see what the long balls actually are, which you can see below:

In the image above, you can see the long balls by each team in Eredivisie 2025–2026. It features the counts of these passes as well as the locations where they are. At first glance, we can see that many of these particular passes have come from the middle and from the goalkeeper areas.

The last thing we do for these passes is to see where they most frequently end up for each team. We already have the right definition for our further calculation for our model, but let’s see where most of these long passes end for our teams.

In the heatmap above, you can see the end locations of all long passes and what it shows is where most passes end, but it also leads me to a new conclusion. I might have to readjust my intention of looking at final third receptions only, but I have to look at the attacking half/opposition half. That’s where most of the passes end, as you can see from the green above.

Part II: Second Ball Retention

What are second balls?

So now we are going up to the second part of the research, which is where we want to be. First, we have to define what second balls are. A second ball refers to the moment a ball becomes loose and contested immediately after an initial aerial duel or challenge. We have to look at it as a two-stage event:

1. The first ball: A long pass or clearance is played. Two players (usually an attacker and a defender) jump to head it or challenge for it.

2. The ball is not cleanly caught or controlled. It “drops” into a space near the original challenge. The player who reacts fastest to secure this loose ball has won the “second ball.”

What’s interesting about the second ball as well is the uncertainty. We can have end locations for passes and therefore the location of aerial duels, but we cannot really predict where the ball will drop before the second ball is regained. We speak of the drop zone, which is often 10–15 meters in radius from the pass end location. It focuses more on anticipation than raw skill.

Having concluded that, we need to conclude two different things going forward. There is a lot of uncertainty involved in second balls and that there needs to be ball recovery or a pass within 2–3 seconds after the initial aerial duel.

Challenge: no tracking data

I don’t have tracking data available for this model, which is a challenge. The challenge here is that with tracking data, I could see how packed an area was when the aerial duel was conducted, the distances of players and how quick the reaction time was.

I can only see/detect who won the ball, but not how they won it. Is it because of better access? Shorter distance? Being quicker? I can’t do that at this point.

Since we can’t see the off-ball movement, we focus on event proximity, which calculates the spatial distance between a long ball landing and the next recorded action. If a launch is followed within three seconds by a ball recovery, a tackle, or a foul in that same 15-meter “drop zone,” we can statistically infer a successful second-ball win.

Methodology

Above, we have seen how we can look at second balls and how we can see retention from a second ball. We need to look at a few variables before we can make the calculation. First of all, the long ball should be followed by a 50/50 aerial duel. The next step is to see whether the taker of the long ball (the team that is) also wins the second ball, regardless of the outcome of the aerial duel. We will measure this by looking at the next event, which is a ball recovery or a pass from the same team. If this happens, we can state that this is ball retention.

Results

So, how can we now see what this looks like? In other words, for every team in the Eredivisie, how often do they win the second ball and therefore keep possession via the second ball?

As you can see in the bar graph above, we can see how every team performs on this new metric. FC Utrecht scores the highest, followed by Sparta and Feyenoord. FC Groningen, PEC Zwolle and FC Volendam score lowest.

In the pitch map above, we can see the locations of where the second balls by the teams in the Eredivisie. This gives us a more clear idea of where they mostly happen and where. We have to concentrate in terms of long balls. What’s evident is that most the second balls happen in the attacking half, but more in the middle third than in the attacking third.

Lastly, we can also have a look at how the long balls line up against the second ball retention in this scatterplot below:

In the scatterplot above you can see how the teams perform in the long balls attempted vs the second ball retention in percentages. Heracles Almelo, Fortuna Sittard Excelsior, NEC Nijmegen and FC Twente have the highest volume of long ball.

In terms of winning second balls, FC Utrecht and Sparta Rotterdam are the clear leaders, followed by Feyenoord, FC Twente, Excelsior and NAC.

Part III: Expected Second Ball Retention (xSBR)

So, now we have defined the new metric of second ball retention. This, however, is based on historic data and actual event. What we want to achieve in the end is the Expected Second Ball Retention (xSBR). In other words, we want to add a xSBR value for every long ball from the defensive third.

To do so, we have to look at a few different things:

• Giving weights or rewards for certain zones: wide areas, half spaces, central areas, cutback zones, hot zone/zone 14/assist zone

• Giving weights or rewards for distances and angles

• Add a defensive proximity multiplier/score

• Add an entropy model for uncertainty -> without tracking data + the unpredictable nature of an aerial rebound, we need to add a factor for uncertainty

• Create the model in logistic regression or XGBoost

• Train the model 80/20 on historical data for more than just 1 season

First, we will look at giving rewards for certain zones. This seems quite straightforward by giving different weights, but we also need to make a distinction between the zones where the first contact is in (aerial duel) and the zones where the second ball is regained. The ratio for me is 3 times the importance for the second balls and 2 times the importance for the aerial duels.

Next what we will do is eaxtly the same, but for distances and angles. This will give different impacts. Distances will be the distance between the location of the aerial duel and the next event (second ball). For angle, we look at the angle from the second ball to the middle of the goal.

At this point we have this that is part of our calculations. The next part is to add a proximity score. This is needed to estimate the proximity of defenders as we don’t have any tracking data or off ball data, that will be helping us. We are going to infer proximity with our event data.

How we are going to do that? We are going to look at the second between the events. We want to look at the event of an aerial duel and see how much time it takes, before the second ball event happens in this particular sequence. If the second ball event happens in 1.5 seconds or less, we can assume that it’s a zone/situation with traffic. If the second ball event happens from 1.5 to 3 seconds, we can infere that there is room to breathe and that there is freedom. It’s about recovery speed and the window of opportunity it presents.

The last things we do before creating the model is to look at entropy. With entropy we measure the uncertainty of the outcome of the data: is it predictable yes or no, and adding randomness. We want to do this, because we don’t have the tracking data to ensure this. By adding this we help this challenge and offer a stroke of “luck” and uncertainty, which is vital.

We define low and high entropy for both the long ball start locations, as well as for the second ball recovery locations. We can develop a matrix with them. Important here is to stress that low entropy means a high predictability while high entropy mean a low predictability.

Creating the model

After running the calculation for the adjusted SBR scores, with all the weights and valuations for zones, angles, distance, proximity and entropy, we get this:

Now we have our adjusted-SBR impact. So we can establish the impact of the second ball won after a long ball and first-contact of aerial duel. This forms the basis of our expected model.

First of all we need much more data, so I will add three other seasons of Eredivisie data too: 2022–2023, 2023–2024 and 2024–2025 too. This data is needed to make the model more likely to be accurate. I will be using XGBoost over Logistic regression, because I’m working with many variables, especially weights and scores included as well.

XGBoost works through a process called Gradient Boosting. Unlike “Random Forest,” where trees are built independently in parallel, XGBoost builds trees sequentially.

• Tree 1: Makes a baseline prediction. It will likely have a high error rate.

• Tree 2: Specifically focuses on the mistakes (residuals) made by Tree 1.

• Tree 3: Focuses on the combined mistakes of Tree 1 and Tree 2.

This continues until the model minimises the error as much as possible. It is like a coach watching video footage: instead of telling the whole team to “get better,” the coach identifies the specific players who missed tackles and creates a drill just for them.

What does the model say when we load this first half of the 2025–2026 season?

The xSBR model achieved an AUC-ROC of 0.76, indicating a high degree of predictive reliability. The model successfully filters out ‘statistical noise,’ allowing us to isolate genuine tactical over-performance from random chance. 0.76 means that if we randomly picked one successful retention and one failed retention from our 100+ files, there is a 76% chance the model would correctly identify which one was which.

We also see in the calibration that the model doesn’t go beyond the predicted probability of 60%, which can be attributed to the fact that the model right now seems to rely on easy long balls, as most of the probabilities lie between 30 and 60%. We look at the second ball retention and now in many cases, it exceeds 60%.

We can do two things now: load more data to train the data and change our features a little. First let us see how it looks like when we load more seasons:

When we load the multiple seasons we can see that the AUC value has dropped to 0,64. The model has dropped from a good predictive model to a standard or even weaker model. How is this possible? This can be because of the calculations, but it can also happen because of factors within the league.

1. This can happen due to players moving and coming into the league that influences the model

2. The way teams press after an aerial duel has changed, so that results can have effect.

3. The influence of luck, randomness and individual duels

Let’s see how that looks, season per season:

With our new calculations, we see that the score is around 0,65/0,66 every season, which likely has to do with the difficulty of prediction events due to a set of variables we have not set as features. We can improve this by changing a few features regarding predictable independence on the angle (known before endlocation), launch entropy (chaos before the pass is being taken) and the aim of the kicker.

When we add these to the model we get a more accurate idea of the predictability.

It recognises that while we can predict some success, about 30% of second-ball retention is down to pure individual dueling and the “chaos” of the bounce. This is an improvement of 4–5% and can be a good way of identifying the expected second ball retention.

Results

Now we have saved the model and used that model to convert the data by the current season. This give us a different perspective on actuals and expected data, especially since we still have that chaos included in our results.

In this scatterplot, you can see all teams in the Eredivisie 2025–2026 and their results. You can see that in general, most teams stay around the right calibration, but there are some outliers in doing so. The chaos and unpredictable nature makes it so that we will stay away from higher predictability, but it still gives us an idea of the team’s indications.

What else we can create is to see a distribution plot, so we can see what the most common values are connected to our specific long balls:

Here you can see that the most percentage for the second ball retention are between the 20% and 25%. The average of the second ball retention % for long balls sits on 24,5%. This is interesting, because it gives us the indication that 1 in 4 long balls, has a second ball retention for the team taking the long ball..

How does this look for the expected side of it?

This looks a bit different too the second ball retention %. The average is 22,9% and that’s not very much difference to the actuals. The distribution however is concentrated between 21 and 24, with a maximum of 28%. This is a big difference with the actual have a maximum of 50%.

The significant delta between the maximum (50%) and Expected SBR (28%) indicates that Eredivisie teams in the 2025–2026 season are exhibiting high tactical efficiency and superior individual duel-winning capabilities. The model provides a physics baseline (28%), meaning that the remaining 22% of retentions are a direct result of coaching structure and player quality rather than the ease of the pass itself.

New metrics

1. SBR Efficiency Index (Retention Added)

SBR Efficiency Index measures the side’s relative strength to exceed the probability of the match. Subtracting the cumulative Expected Second Ball Retention (xSBR) from the total Actual Retentions helps filter the value created by the playing and coaching staff. In such a context, it shows that when the Efficiency Index is also positive, it states that their team is equipped with better aerial duel participants or that their structural pressing trap is highly disciplined in terms of “loose” ball recovery, exceeding the mean rate in their league.

2. Launch Difficulty Profile (Risk Appetite)

The Launch Difficulty Profile is a strategic signifier of a team’s distribution philosophy rather than a metric of success. It plots the average Expected Value of the passes being made. A lower Profile indicates a ‘High Risk’ approach, where there is a penchant to launch the ball into dense, high-entropy areas, often resulting in a physical contest. A higher Profile indicates a ‘Selective’ distributor, who makes use of long verticals only when structural angles indicate a high chance of successful, uncontested recovery.

3. Chaos Resistance Ratio (High-Entropy Dominance)

The Chaos Resistance Ratio in isolation performance in “Broken Play” scenarios specifically filters for events with an xSBR of less than 20%. In these high-entropy instances, the ball is objectively “50/50” or worse. Teams with a high Ratio in this category demonstrate systemic resilience to randomness, evidencing a team that thrives in the “scramble” phase of the game. This would be an essential metric for recruitment and scouting as it would identify squads that can maintain possession and territory in high-pressure match scripts where clean tactical structures have broken a vital trait for success in knockout competitions and high-intensity derbies.

Best players that lead to second ball recovery

Now we move one from teams to players. I want to know what the best players who start the long ball, as first.

In the bargraph above, you can see the players whose long ball lead to the highest value added in terms of second ball retention. What’s interesting is that most of these players who rank high are also from the goalkeepers’ rank, but M. van der Hoorn just stands out from the crowd.

So let’s look a step further, which players wins the most second balls?

Here we see the players who win the most second balls. Lauritsen is an exceptionally good second ball winner, followed by Van Hooijdonk and Brinkhorst.

What we can do with this data is anticipate in which areas second balls are most likely to be won, and have a look at which players we want to target. The second ball winners don’t necessarily have to be the ones with the aerial duels, but it’s important that we have them in and around that area. This makes this theoretical framework actionable for football coaches.

Expected goals. I don’t even know where to start with how I feel about this particular metric, but I’m going to try it anyway. I feel that expected goals is actually an exciting metric and concept, but it’s more complex than popular sports media often portrays. And, I think that’s primarily because we don’t fully grasp what it takes to create such a model. That’s exactly where it does pique my interest, but in a different way than you might expect.

Creating an expected goals model is something I’ve already done, and making such a model really makes you appreciate what complexity lies behind it. This article aims to show two different things:

1. What goes into creating a shot-based probability model?

2. In what way can we create an alternative to expected goals?

It’s important to stress, however, that this isn’t an expected goals model — but an alternative which can measure the same thing. This is called the Expected Shot Danger model.

Contents

1. Data explanation and justification

2. Concepts from the NHL

3. Theoretical framework: Probability models

4. Methodology: Python

5. Calculations

6. Model results

7. Applications

8. Challenges

9. Final thoughts

Data explanation and justification

The data used for the creation of this model is from Opta/StatsPerform. I have used raw event data — which is XY-positional data — to calculate it all. This gives me the freedom to do what I want. You can use other data providers of course, but be aware that this is a conscience decision and that a choice for a certain data provider, also comes with their own pros and cons. Also, it’s good to remember that while people talk about data being unbiased and objective, it never is. Every decision you make in terms of buidling/handling the data in this model, means that it is biased. Whether that’s good or bad, is a whole different question altogether.

Every model has to be created, but it also has to be trained. This means that enough data has to be imported and used. To just train it on a single season of a single league won’t paint a representative picture. That’s why I have trained in three different seasons for the following leagues:

• Eredivisie (NL)

• Eerste Divisie (NL2)

• Pro League (BEL)

• Premier League (ENG)

• Eliteserien (NOR)

• Allsvenskan (SWE)

This will be different from different leagues obviously, but in the end the result can be used across all the leagues. My own xG model has been trained on 500.000+ shots on a single league and is pretty accurate for other leagues too.

The data was collected on December, 10th 2025 via the Opta API. The model is an update from an older model I have already created. This actually is version 4.2.1 and is the evidence that it takes time and effort to create something you are comfortable with.

2. Concepts from the NHL

I learn a lot from data concepts from other sports and for this model, I look to Ice Hockey data, NHL in particular. They have a particular way of evaluating shot data with fenwick and corsi, which will be instrumental to my model. The definitions will follow here below.

2.1 Fenwick
Fenwick is an unblocked shot-attempt metric that counts shots on goal and missed shots while excluding blocked shots. By removing blocks, which often reflect defensive structure more than offensive intent, Fenwick isolates attempts that genuinely reach or approach the scoring area. This makes it a cleaner indicator of how frequently a team produces potentially dangerous opportunities.

Fenwick is used because unblocked attempts correlate more strongly with sustained offensive pressure and long-term scoring performance. Over larger samples, teams with higher Fenwick percentages typically demonstrate more consistent puck possession and shot-quality generation. As a result, the metric serves as a practical tool for evaluating underlying play beyond what the scoreboard or raw shot totals reveal

2.2 Corsi
Corsi is a shot-attempt metric that includes all attempts toward the net: shots on goal, missed shots, and blocked shots. It captures the total volume of offensive activity by tallying every attempt a team generates or allows, providing a broad measure of territorial control and play-driving ability.

Corsi is used because shot-attempt volume is strongly associated with puck possession and long-term team success. Although it weighs all attempts equally, its comprehensive nature makes it a stable predictor of future performance. Teams that routinely out-attempt their opponents tend to control the flow of the game, making Corsi a foundational metric for modern hockey analytics.

This distinction is very important to me as it forms the basis of my expected shot danger model. I include blocked shots and therefore we can assess more about shot danger.

3. Theoretical framework: Probability models

So why do I do this, and what’s my aim? My aim is to create a shot-based value model that is a hybrid between expected goals and expected threat that seeks to measure outcome danger whilst including blocked shots.

The model is designed to overcome a key limitation of existing football analytics models. It combines the strengths of two popular metrics:

• Expected Goals (xG): This model calculates the probability of a shot resulting in a goal based on factors like shot location, body part used, and play type. Its primary focus is on the final outcome: a goal. However, it assigns a value of zero to shots that are blocked, even if the shot was taken from a high-danger location.

• Expected Threat (xT): This model measures the change in a team’s probability of scoring when the ball moves from one location to another. It values passes and carries that move the ball into more dangerous areas, but it doesn’t directly value the shot itself.

What’s important to know about the theoretical framework, however, is that this a model that calculate probabilities based on historic data. After that we can use the model to calculate probabilities for more recent games and assign expected shot danger values to shots and players and teams.

4. Methodology: Python

In the past few years I have been developing expertise and interest in different programming languages to work with data. For the creation of the model I have chosen Python over other languages such as R and Julia. The reason for this is that I am simply better at writing Python code and that I know what to do for this kind of advance models. That’s not to say you can’t create this in other languages, but that’s simply what I’ve been using. But I will also list some of the key Python packages I’ve used to create the model and some of the visualisations (however I thing ggplot in R, also creates great data visualisations).

4.1 Matplotlib
Matplotlib is a widely used Python library for creating static, animated, and interactive data visualizations. It provides fine-grained control over plot elements, allowing researchers to customise figures to match academic or publication standards. The library supports a broad range of chart types, from simple line and bar plots to complex multi-panel figures. Because of its flexibility and stability, Matplotlib serves as the foundational plotting tool in the scientific Python ecosystem. Many other visualisation libraries build on top of it or integrate seamlessly with its framework.

4.2 Numpy
NumPy is the core library for numerical computing in Python, offering fast and memory-efficient operations on large multidimensional arrays and matrices. It provides a wide range of mathematical functions that operate at compiled speed, enabling efficient data manipulation and analysis. NumPy’s array structures form the backbone for many other scientific libraries, including pandas and scikit-learn. Its ability to vectorise computations allows researchers to avoid slow Python loops and write concise, high-performance code. As a result, it is essential for any workflow involving numerical data.

4.3 Pandas
Pandas is a data manipulation and analysis library built around flexible data structures such as Series and DataFrames. It offers powerful tools for cleaning, transforming, merging, and aggregating datasets, making it especially useful in data-heavy research workflows. With its intuitive syntax and built-in handling of missing values, pandas simplifies complex data operations that would otherwise require extensive coding. It also integrates smoothly with libraries like Matplotlib for quick visualization. Pandas has become a standard tool for organizing and preparing data prior to statistical analysis or modeling.

4.4 MPLsoccer
MPLsoccer is a plotting and analysis library designed specifically for soccer analytics, built on top of Matplotlib. It provides ready-made tools for creating pitch diagrams, tracking visualizations, passing networks, and other soccer-specific graphics. The library streamlines the production of publication-quality sports analytics figures that would otherwise require extensive custom plotting code. MPLsoccer also integrates well with pandas and NumPy, allowing analysts to move easily from data preparation to visualization. Its domain-specific functionality makes it a preferred toolkit for researchers and practitioners working in soccer data science.

5. Calculation

The first thing I do is look at my data. I have JSON files rather than CSV files, purely because it’s easier to work with and that’s how I save them. That means that we need to load them into our Python code and handle them as such, otherwise it will be difficult to make the right DF (=dataframe). I will filter for shot events only:

• typeId = 13 -> Missed shot

• typeId = 14 -> Shot on post

• typeId = 15 -> Shot on target

• typeId = 16 -> Goal

I filter for these events and they come with their own qualifiers and XY-coordinates, which will be proving important for actually buidling the model. Now I want to add a specific shot, which is the blocked shot. As I previously mentioned under the NHL data analytics part, I want to incorporate the danger of the blocked shot through this dataframe/model as well.

Then we look at shot context and mathematical physics-based features. Within the context we look at:

• body part used

• type of play (open play, counter, set piece, penalty)

• shot technique (volley, chip, overhead, etc.)

• assist type (cross, through ball, pullback, etc.)

• whether the shot was deflected

This gives us different qualifiers from the data. To add to the calculation is what I like to call distance and angle-based features: distance to centre of the goal, shooting angle and variations of the two.

Fenwick and Corsi are indications or strong attacking performance/weak defending performances as to the danger that comes forth from (un)blocked shots in our dataframe. This is important as to why it differs from typical xG.

The last part of the calculation is a two-staged structure of making this model. In stage 1, we predict the probability that a shot becomes on target. This isolates the ability to reach the goal. In stage 2, we predict the probability that an on-target attempt becomes a goal, based on shot quality.

Expected Shot Danger = P(on target) × P(goal | on target)

This mirrors how goals happen in reality:

1. A shot must first be directed well (accuracy)

2. Then it must beat the goalkeeper (finishing quality)

To do this all, I employ 4 different models:

1. Logistic stage 1 model

2. Logistic stage 2 model

3. LightGBM model: A highly efficient, modern gradient boosting framework that uses a novel technique called Gradient-based One-Side Sampling (GOSS) and Exclusive Feature Bundling (EFB) to train faster and consume less memory than traditional boosting models like XGBoost.

4. XGBoost model: A highly popular and powerful optimized distributed gradient boosting library designed to be extremely fast, flexible, and portable, known for its regularization techniques to prevent overfitting and its success in predictive modeling competitions.

And, out comes my model saved in PKL files.

6. Model Results

Okay, not the desired result is still a result, right? At this point, I first created a model solely focused on the Eredivisie 2025–2026, to give it a trial run. To assess my probability models, I use a ROC-AUC curve. This measures the ability to identify positive and negative rates of the model. Positive rate measures the ability of the model to identify positive rates, while negative rate measures when the model identifies negative rates as positive. It’s measured between 0–1 and the higher the number, the better the model performs. It’s an indication of ranking my probability quality.

So first run with only one season in one league:

In this visual above we can see how the AUC scores. The logit 2 stage model scores the highest with 0,80 which is an excellent score, logit 1 stage has 0,79 very good as well. LightGBM and XGBoost score lower with 0,70 and 0,73. However, this is just based on a single season in one specific league.

What happens if we load multiple leagues? How does the model change?

So as you can see, things are completely changing from loading all of our leagues. It’s evident that the AUC-scores will be lower, and what we see is that the differences between the scores are still closer to each other. I like this a lot better overall, I can go on and work with this.

I realised something midway through my next model: this is just an expected goal model with a slight modification. Yes, I want to create an alternative to expected goal model, but I primarily want to capture shot danger.

Instead of calculating the goal probability, I’m going to calculate the probability of a shot on target as a pre-shot danger model, and the probability of a shot on target being a goal with a post-shot danger model. Having done that, we get the following curve:

As you can see I switched from how I created the model, which focuses on pre-shot and post-shot danger. The AUC is lower on the pre-shot, but that also has the fact with much more variables and uncertainty. This is the model I’m using to go to the application of my work.

7. Applications

Now, we are going to use it. What can we do with it and what kind of visuals can we portray? First of all, we can look at the distribution of our new metric: Expected Danger in both models:

What we can analyse is that there are more lower danger score shots in post-shot model than there is in the post-shot. However, there are more high post-shot danger than in the pre-shot danger.

In the above shot map we can see how they compare to each other in terms of the models. Pre-shot danger averages higher, but we can also see where the average on target danger comes from, it’s much more concentrated closer to goal.

Another area of application which is interesting is the blocked shots vs unblocked shots.

Here we can see that there are fewer blocked shots and with lower values, but the majority of the blocked shots still have a consistent value. And some have a high value still, which indicates that block shots are concerned with danger. Something you wouldn’t see in traditional expected goals.

Here we can see that Liverpool has the greatest total danger of shots, but their post-shot danger value shows us that there is a big difference in how their dangerous shots actually become a threat. Manchester City, Arsenal and Brentford score the highest on their post-shot danger levels.

Let’s take a step closer towards player level as an example and look at a few players.

Final thoughts

The pre-shot and post-shot danger model offers a clearer, more decomposed view of finishing quality than traditional xG. By separating the likelihood that a shot becomes dangerous (reaching the target) from the likelihood that a dangerous shot becomes a goal, the model exposes two distinct skill sets: creating clean shooting conditions and executing decisive finishes. Even with event data alone, features such as location, open angles, technique, assist type, and team shot tendencies provide enough structure to produce stable patterns that align with football intuition. The resulting danger maps and distributions reveal meaningful differences in player profiles, team attacking styles, and defensive disruption effects that xG alone tends to compress.

At the same time, the model highlights the inherent limitations of event-only data: it lacks defender pressure, goalkeeper positioning, ball speed, and precise shot placement — factors that cap predictive performance compared to tracking-based models. Still, the framework’s biggest strength is its modularity. Each stage can be refined independently, swapped for more advanced models, or expanded with new features, making it a scalable foundation for future analytics. Whether used for scouting, shot selection analysis, player development, or tactical evaluation, this two-stage danger approach provides a flexible and interpretable lens through which to understand how chances are created, shaped, and ultimately finished.

I got to be honest with you, I have 37 projects which aren’t finished and are definitely in the midst of getting something tangible. And, a double truth here; I enjoy the process more than the finished product. Some finished products work and I will post them publicly, but most of them end up in a folder on my laptop with the idea that I might revisit them later (and sometimes I do!).

In this article, I want to acknowledge the process and look at an idea I had. How can we capture development or potential in aggregated data? In the end, my aim is to have an index value that gives an idea of how much a talent still can progress and whether talent turns into quality.

Data

The data is aggregated data and focuses on the Portuguese league of 2025-2026. The data was collected mid-November, so it might see any changes. However, this doesn’t matter for the research we are conducting.

I focus on CF/strikers only, which means each player that has played in that position. Further more I filter the data for a set of standard metrics: Age, Minutes played, Goals per 90, xG per 90, Shots per 90 and Shots on target, %. With this information we are going to start building.

I’m going to look at players with at least 300 minutes played, but I will also turn towards data per 30 minutes. The reason why? I can better compare players with fewer minutes played, which means they have the equivalent of 10 games when they have played 300 minutes. This gives a better idea in a smaller database or when we are working with youth/academy players - which ultimately is our goal.

Methods

Because this project involves multiple layers of calculation, transformation, and analysis, I chose to build the entire workflow in Python. This is simply the language I am most comfortable with for data manipulation and statistical modelling. Python offers a mature ecosystem that make it ideal for constructing metrics, analysing patterns, and generating visualisations.

Of course, the approach is not language-specific. The same methodology could be replicated in R, Julia, or even specialised analytics tools; many analysts working in academia or recruitment departments use R for its statistical depth or Julia for speed-heavy modelling. The key is not the language, but the structure and reasoning behind the metric.

To create a meaningful performance index, the first step was to ensure that the dataset was filtered in a way that preserves reliability. I only included players with at least 300 minutes played, ensuring the sample size is large enough to avoid extreme noise or misleading results. On top of that, I restricted the analysis to players listed as Center Forwards (CF). This position-specific filtering is essential: combining players across roles would distort the model by mixing responsibilities, tactical profiles, and performance expectations. After isolating the relevant population, I prepared the dataset for the next phase, feature engineering, where the raw data is transformed into more informative metrics that better reflect a striker’s decision-making quality, efficiency, and overall contribution.

Feature engineering

Raw statistics like goals, xG, or shots provide only fragments of a striker’s true profile. To make these numbers more informative, they were transformed into richer, rate-based indicators that capture efficiency and decision-making quality. The first, Shot Conversion %, measures how effectively a forward turns attempts into goals — a pure indicator of finishing precision. xG Accuracy compares actual goals to expected goals (xG), revealing whether a player consistently outperforms or underperforms chance quality. Finally, Shooting Efficiency blends accuracy and power by combining Shots on Target % with Conversion %, effectively reflecting how well a player not only hits the target but makes those shots count. Together, these derived features allow the model to assess how productive each attempt truly is, rather than just counting volume.

Normalisation & Weighting

With these metrics living across different scales and distributions, it required a hybrid normalisation method that merges Min–Max scaling for interpretability and Z-score standardisation for outlier control. That way, truly exceptional players do not skew the scale, yet meaningful performance differences are conserved across the dataset. After normalization, each metric was given a dynamic weight corresponding to its statistical correlation with Goals per 90. Metrics strongly correlated, such as xG per 90 or Shots on Target %, were given more influence, while weaker correlations, like raw shot volume, were less influential. This procedure in turn makes the model self-adjusting, automatically configuring itself to each league’s playing style and scoring trends.

Base Performance Score (BPS)

All normalised and weighted variables are combined into a single composite, the Base Performance Score, or BPS. It is representative of the underlying attacking contribution of a striker, into one comparable number. The BPS is a foundation for all the subsequent variants of CFPI; it captures what the player does on the pitch, abstracting away from external context such as age or stage of development. It is, in essence, the raw number representing how well the forward executes the most salient aspect of his job: converting opportunities into goals with efficiency and consistency.

The Role of Age — CFPI Variants

Player performance is not static, a striker at 19 and a striker at 29 may produce similar raw outputs, yet the interpretation of those outputs should not be the same. To account for this, the model introduces age-adjusted variants of the CF Performance Index (CFPI) that contextualise performance relative to a player’s developmental stage.

The CPFI - Young version rewards young players (particularly those under 23) who are performing at or above senior-level standards. The logic is simple: if a young forward is already producing efficiently, this is a strong signal of future potential. Conversely, the CPFI - Mature variant places value on the stability and refined decision-making of more experienced forwards, especially those between 25 and 30 — typically the age band associated with peak output for strikers. To provide a neutral middle ground, a Balanced CFPI takes the average of both, offering a more rounded perspective. On top of this, a Consistency-Adjusted CFPI multiplies the balanced score by a consistency factor, rewarding players who maintain high levels of accuracy and reliability. This ensures that the model does not simply celebrate spikes in performance but recognises repeatability — the attribute that differentiates a streak from genuine quality.

Introducing the Emergence Index

While the CFPI variants measure how good a striker is right now, the model also aims to illuminate where a striker might be heading. This is where the Emergence Index comes in. This is a metric designed to capture a player’s upward trajectory relative to their expected maturity curve.

The idea is straightforward: compare a player’s youth-weighted score and their maturity-weighted score, then incorporate consistency to temper volatility. In mathematical terms:

Emergence Index=(CFPIYouth−CFPIMaturity)

A high Emergence Index indicates a young striker outperforming what would normally be expected at their age. Which would be a sign of breakout potential. A low or negative value suggests the opposite: an experienced player whose maturity and reliability currently outshine any youth-based upside. Those near zero typically track closely with age expectations, neither emerging nor declining relative to peers.

In the image above you can see the players with their ages on the x-axis, while we have the Youth-weighted CFPI on the y-axis. What we see here is that the players with the highest CPFI adjusted for youth, also are the players that are between the ages of 17 and 22 - which is obvious, since it’s weighted for youth. It shows signs that these young players have potential in the grand scheme of things.

Case study: Young Players

So what does this look like if we focus on the strikers that are young and we want to capture potential? In the image above, we see colored values for the Emergence Index. What’s the Emergence Index?

The Emergence Index measures how much a player is outperforming or underperforming what is normally expected at their age. It compares a player’s youth-weighted performance score with their maturity-weighted score to reveal whether they are trending upward or downward relative to age norms. High values indicate young players exceeding typical development curves, signaling strong breakout potential. Low or negative values reflect experienced players whose reliability outweighs any remaining upside.

In the bar graph above we can see the top 10 players in terms of the Emergence Index. This shows the performance versus the age for players under 23. These players have an indication that they perform very well for their age in relation to the total database.

Key Insights & Findings

Some interesting patterns emerged once the CFPI and Emergence Index were applied to a real dataset. Perhaps the most striking was the discovery that xG per 90 and Shots on Target % consistently held the strongest correlations with goal output, more so than raw shot volume. What this suggests, in other words, is that chance quality and precision matter far more than simply taking many shots. This supports the notion that efficient, thoughtful forwards tend to outperform high-volume shooters.

The top Emergence Index players were often forwards aged 18–22 who outperformed their expected xG and boasted high shooting efficiency. These players are the archetype “breakout candidates”. Athletes whose metrics indicate that they may soon be in line for bigger roles, transfers, or developmental investment. On the other hand, veteran strikers, especially those 27+, often ruled the Maturity-Weighted CFPI. What they lack in pure technical ability, they more than make up for with experience-based consistency, especially in terms of things like xG accuracy and stability of finishing.

This dual view-current performance versus future trajectory-provides a more complete picture of striker quality than any single metric could. It gives analysts the capability to ascertain both the most reliable forwards today and the players most likely to become valuable assets tomorrow.

Basically, I’m really bad at writing intros, but trust me - this is a fascinating article to read. My aim for this article is to delve into American Football, more specifically, the NFL and/or NCAA college football. The reason why? Firstly, I think it can be fascinating to really delve into other team sports all across the globe, because I think we can learn from certain patterns and methodologies and apply them to football. And, perhaps in time, I might actually try to do it vice versa.

The second reason, and perhaps also my biggest motivator, is to look at whether we can gain value from possession based on plays in the NFL. We have been seeing a rise in the reliance on set pieces with accusations that we are looking more and more to NFL plays in football, instead of open play creation. I personally don’t think we are heading that way, but it’s worth exploring nonetheless.

This research aims to convert “plays” to similar possession and add value to these possession sequences with relation to the final third. In essence, I want to add value to possession sequences that end in the final third and start with a certain type of play. In the process of doing so, I’m looking for possession sequences that are neither set pieces nor open play, but a modern hybrid possession style.

This article is part of my bigger project Lessons from which aims to look at analytics and data visualisation from other sports and see whether we can apply it to football. In addition to that, not every form of analytics is good or bad for football, but the real education and improvement for myself is in the actual process. Trust the process and all that.

Contents

1. The data

2. NFL data

3. Converting plays to football

4. Methodology

5. Mathematics

6. Value model

7. Team Analysis

8. Player Analysis

9. Challenges: should we use this?

10. Final thoughts

Data

For this research, I had two different sets of data. The first set of data is NFL data. I can’t just start with the research without having an understanding of what the NFL data is and how it adds value to the game.

For the NFL data, I look at an R Package about NFL data. I’ve used R to understand and get the data, and also being able to clean it. You can read and install this package by going to this link. I accessed the data on Saturday, 18 October 2025. The thing I’m most interested in is the play-by-play data for the players and teams in the NFL. What I want to get from that data is based on plays, rushes and passing - which. I will touch upon it later.

For the football data, I’m looking at raw event data from the Portuguese Primeira Liga from the 2025-2026 season. The data is from Opta and contains all on-ball from the season for the players and teams. I have looked at all matches before 17 October, because at the moment of writing, this round of matches is being played. I’ve accessed the data from the API and collected it with Python.

I’ve mentioned both R and Python; these are the programming languages I use most frequently for all my analyses. I don’t necessarily think one is better than the other, nor do I think you should stick to one or both, but I find that a combination works pretty well.

NFL data

I had a look at the data and I need to stress one thing before we get into this: this can be so overwhelming! Delving into data of a sport you are not as knowledgeable in as football, but have the same level of depth in terms of analytics.

I saw the concept of rushing yards and passing yards, which was very interesting to me. Rushing yards are the total number of yards a player makes while on the ground with the ball. Passing yards are the total number of yards the ball travels when a player makes a pass.

Why is this interesting to me? Because we can use these concepts and use them in football, looking at carries (rushing) and passes (passing). But before we do that, we need to look at another specific thing in American football.

I want to look at the explosive label for both metrics. A play is considered explosive when a rushing exceeds 10 yards and when a passing exceeds 20 yards. They are then named explosive because they have generated a certain progression on the field.

Plays in American football

Okay, what are plays? In the NFL, a play is a single action or strategic sequence of events designed to advance the ball toward the opponent’s goal line. It begins with a snap or a free kick and involves specific roles and movements for each player on the field for a short duration, until the ball is dead or out of bounds. Examples include passes, runs, and kicks like punts, field goals, or kickoffs.

So, when I first started looking at plays, it just didn’t make sense to me. How should I perceive plays? Is this what American Football is? A series of plays? What really helped me is just watching a ton of plays on YouTube. I’m definitely not an expert, but seeing it pan out on the field helped me a lot.

[Click on the image for the link to the YouTube video; the NFL doesn’t allow their content outside YouTube]

The biggest question in this research wasn’t how I would translate passing and rushing to football, because we have passes and carries for that in a certain sense. Explosive plays are easy to calculate as well. The biggest question for me is how I would define plays in football.

My initial thought was that I would go with set pieces. Football is much more fluid and up and down than the American Football we see in the NFL. However, when we look at the plays in the NFL, we see that’s very much a set piece kind of vibe, but it’s almost about advancement, because there is no direct scoring option. What that means is that a set piece in football can be designed to score directly (penalties, free kicks, corners) or with first contact. We should look at something that sits between a traditional football set piece and open play. We should look at strategic areas of the game where we have to progress up the field, but didn’t start as open play.

Methodology

So, as described above, if we are going to use some concepts from the NFL, we need to convert them. As said before, the carries and passes can be straightforward in calculation, but for the plays, we need to find a different way.

Plays in my research, and this can be different for different people, will be going down in football as possessions that happen after a restart. I’m doing this to avoid pure open play possession, but also to look beyond regular set pieces. By doing so, I want to design plays in football as possession that qualify for the following start:

• Goalkicks

• Deep free kicks

• Kick off

• Defensive throw-ins

Goalkicks

Goal kicks are conducted by the goalkeepers during this season. As you can see, the end locations are divided into many passes to the wide areas in the defensive and middle third, and the longer passes into the central areas of the pitch.

Deep free kicks

In the visual above, we see every free kick that was taken in the defensive third of the pitch. I chose deep free kicks because they start a possession like a restart, more than just an attacking free kick, which is often aimed at a direct free kick or second contact shot scoring, rather than advancement on the pitch.

Kick-off

In the visual above, you can see the kick-offs taken during the season. While routines are limited in goalkicks, it’s a restart that determines how you are going to progress.

Defensive throw-ins

In the image above, you can see all defensive third throw-ins from the ongoing season. This shows how defensive third throw-ins are both progressiv,e as going lateral, suggesting retaining possession.

The possessions or plays now start with the above situations. The following step is to look at the end of the possession, which always should end in the final third. The end of the possession, either via carry or pass, always ends in the final third. We are looking at the sequence final third entries after specific start situations. So we define the plays from the above starting locations and what to find possession that ends in the final third.

In the image above, you see the pitch with scatters. These scatters represent every starting location for a play. They are all in the defensive third, bar the kick-offs. We have defined these as such that it will take progression to the attacking third.

In the image above, you see the pitch with scatters in the final third. This represents the end locations of the plays during the 2025-2026 season in Primeira Liga and serves as the blueprint for our value mode. As you can see ,most of the plays end on the edge of the middle third, and the least end in the penalty area, close to the opposition’s goal.

We have now defined what plays are in football, adapted from NFL analytics. So, how do we go on and make a model for explosive models?

Explosive plays model

In the methodology above, we have seen what we define as plays and how they start. But I want to go beyond that and look at an important action. I want to see if the plays have an explosive nature. This means I’m going to look at the plays and flag when if there is a pass or carry that can be considered explosive.

Explosiveness here means:

• Exceeds 10 meters for a carry

• Exceeds 20 meters for pass

While I’ve defined plays as such, I am now going to focus on how explosive teams/players are and what value we can add to it. The following features are important:

1. Forward Progression

2. Total Distance

3. Zone Progression

4. Final Third Arrival

5. Action Type

6. Play Context

The Explosive Play Value Model measures how much impact each attacking action has in moving the ball into threatening areas. Every pass, carry, or restart is given a value between 0 and 1, showing how much it contributes to progressing play and creating danger. To do this, the model looks at several factors, including how far the ball travels, how much it moves forward, whether it shifts between thirds of the pitch, and if it ends in the final third. Each factor is given a specific weight, with the most importance placed on actions that push the ball forward or reach advanced positions. This approach helps separate safe or lateral movements from genuinely progressive plays that help a team advance up the pitch.

Once each action is scored, the results are normalised so that values fall on a clear 0–1 scale. Passes longer than 20 meters and carries over 10 meters are defined as “explosive,” since these are the moments that usually stretch opposition lines or turn defense into attack. By quantifying these events, the model highlights which restart situations, goal kicks, deep free kicks, throw-ins, or kick-offs most often lead to quick, dangerous progressions.

When we look at the different forms of play, which ones carry explosiveness?

In the bar graph above, we see very play type and how their average explosive value is. What we can see is that Goalkicks, Throw-ins and Kick-offs really have explosive value, looking at the percentage of the total. Explosive value is based on the total play, while % Explosive means that there are actual explosive passes in the plays.

So on the pitch, it looks like this:

In we are looking at how plays (so all the restarts) and how passes come from those plays which are more than 20 meters, we see that these are the locations where passes occurred. Most passes have a value between 0.6 and 0.8 on the Explosiveness Value Model.

With Explosive carries - carries with more than 10 meters progression - we see something different. The percentage of actual explosive carries is only found in kick-off and deep FK, but their average value of the plays is much higher.

As you can see, there are fewer carries coming from the defensive third, but they are much more concentrated on the middle third and the attacking third. This also means that there is variance in the value of the different carries. This can be explained by the fact that the threshold of explosiveness is different (10+ meters) and the fact that carries also start higher and go sideways.

Best teams in Primeira Liga

As you can see in the scatterplot above, the average explosive value per pass is higher than the average explosive value per carry. We have seen how that came to be by the pitches. What’s interesting here is that there is great variance in the explosive value of passes, but not so much in the carries.

The biggest Explosive Value is held by Estoril, followed by Gil Vicente, Casa Pia and Nacional. The smallest value is held by Sporting Braga, followed by Sporting CP, Famalicao and Vitoria Guimaraes.

If we look at the carriers, we see that Arouca ranks highest, followed by Alverca and Casa Pia. On the botto,m we see Vitoria Guimaraes, Estrela and Porto.

Best players in Primeira Liga

As you can see, we have plotted the players in this plot. All players who have either o carries or 0 passes have been excluded. The players in yellow oare utliers for either Explosive Values in carries or passes.

Now, if we combine both values, who are the most explosive players in the Primeira Liga?

In this top-15 bar chart, we can see which players are scoring the highest on the Explosive Value. The best players according to this model are MT, Paulo Vitor, Ferro, Bernardo Schappo and Tomas Aurajo.

As the last part of it, we can then look at the pitch map of an individual player and see how they are doing in terms of passes and carries, but also the explosive value they bring to the pitch. In this case, MT, he has 16 actions that warrant an explosive score. He scores higher on carries than passes, so if you are looking for ball progression from plays, you want him carrying that ball.

Challenges

While the explosive value model offers a useful way to quantify how players and teams advance the ball dynamically, it does have several structural and contextual limitations. The biggest challenge lies in how event data simplifies the flow of play. The model also assumes that longer or more direct actions are always more valuable, which isn’t always the case tactically. Likewise, using thirds of the pitch as progress zones is a helpful approximation but misses finer spatial detail that shapes real threat creation.

The model also doesn’t yet account for context. There’s also the issue of sample bias: players with fewer recorded actions can appear overly “explosive” due to a small sample size. While the framework offers strong directional insights, it’s best viewed as a foundation.

Final thoughts

The explosive play model is a creative step toward translating raw event data into a more intuitive measure of impact. It bridges the gap between traditional counting stats and spatial analytics by emphasising progression, direction, and value. Although it still lacks contextual layers, the framework highlights underlying playing styles and player tendencies that are often hard to quantify.

In its current form, it’s less about perfect precision and more about perspective.

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Asserting dominance is what many managers talk about. They talk about controlling midfield, central areas, and “wanting” it more. According to their knowledge and view, this would also lead to winning games thanks to that asserted dominance. It seems a bit of a wild idea, and I’m not sure there is a correlation. However, this is a worthy exercise to conduct in terms of data, so that’s why I’m taking you on this research data.

The aim for this research is to see whether traditional metrics can capture the correlation, if there is a difference with innovative metrics, and whether it’s actually useful research to use going forward. The data is raw event data from Opta and was collected on October 7th 2025. To get a sense of a more global impact, I’ve selected multiple leagues and not just one specific league.

The Traditional Metric: Volume vs. Percentage

First I will start with the traditional point of view. This is the standard quantity vs quality point of view in terms of aerial duels. We want to see the total volume of aerial duels in a game or season (quantity) and compare that too the win % (quality). This gives us an idea of which players, teams or league perform the best in winning aerial duels.

If we look at the above scatterplot, we see the volume of aerial duels on the x-axis and the aerial win rate in % on the y-axis. The top 10% outliers are featured as you can see across the three leagues we are looking at. The correlation between the aerial duels count and the aeriel duels win rate is calculated via the Pearson Correlation Coefficient. The correlation is 0,02 which indicates that there is is a very weak linear correlation → a change in one metric doesn’t predict linear change in the other metric.

In the scatterplot above you can see a different set of metrics. On the x-axis you can see the aerial win rate in % and on the y-axis the Points per Game (PPG). We are looking here at the correlation between winning aerial duels and PPG → does winning more aerial duels lead to more points?

The correlation is 0,26, which is more than 10 times higher than the previous plot, but what does this exactly mean? Teams that win more aerial duels tend to get slightly more points, but many exceptions exist, and aerial strength alone doesn’t explain much of the performance.

Our idea of winning more duels leads to more points, which doesn’t seem like a strong prediction. There’s some correlation, but not so strong that we can say this effectively works.

The New Model: Aerial Spatial Impact Rating

So we have seen that the traditional metrics don’t really hold up in terms of correlation, what could? In other words, can we design meaningful data metrics that can say a bit more about winning aerial duels in relation to winning games. I designed a new rating called: Aerial Spatial Impact Rating.

The Aerial Spatial Impact Rating (ASIR) quantifies a team’s performance in aerial duels by integrating event outcomes with spatial weighting to reflect the tactical relevance of duel locations. The methodology involves four main stages: data collection, spatial zoning, weighting, and aggregation.

1. Data Collection and Preprocessing
Event data were extracted from structured JSON files containing Opta match data for the three different leagues. Each file represents a single match and includes detailed attributes for every on-ball action. Aerial duels were identified using the event type identifier typeId = 44. Each event was linked to a team via its contestantId, with team names mapped using a separate CSV file containing official identifiers. Events without valid positional data (x, y) or team assignment were excluded.

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2. Spatial Zoning Framework
The pitch was divided into a 3×3 grid combining longitudinal thirds (defensive, middle, attacking) with lateral zones (wide, central). Each event’s coordinates were assigned to one of these nine spatial zones. This framework allows for weighting aerial duels based on their strategic context rather than treating all duels uniformly.

3. Spatial Weight Assignment
A weighting function was defined to assign a numerical value to each zone reflecting its tactical significance. Central attacking zones were assigned the highest weight (1.5), followed by half-spaces in the attacking third (1.3), and central defensive zones (1.2). Wide areas received a lower weighting (0.75), as aerial duels in these areas generally exert less influence on match outcomes. This weighting matrix was implemented via a zone weight (x,y) function, which returned the appropriate multiplier based on the event’s location.

4. ASIR Computation
For each team in each match, the ASIR value was calculated by dividing the total weighted number of successful aerial duels by the total weighted number of all aerial duels. In this calculation, every duel is assigned a spatial weight according to its location on the pitch, reflecting its tactical importance. Successful duels contribute their respective weights to the numerator, while all duels—successful or not—contribute their weights to the denominator. The resulting ratio expresses the proportion of aerial duels won, adjusted for spatial significance, and produces a match-level ASIR score ranging from 0 to 1.

In the bargraph above, you can see the top 12 teams according to the ASIR. PSV, Porto and Feyenoord form the top 3. It’s a score that takes aerial duels into account with their specific areas. The Eredivisie is featured the highest, then followed by Belgium and then Portugal.

The Positional and Zonal Breakdown

We know which teams score the highest on our new ASIR-rating, but let’s have a look at how and where they are generated.

In the pitch above, you can see the different third of the pitch with the perecntages of the total ASIR. Aerial duels won in the defensive third are easier to predict than they are in the attacking third, and that’s why the attacking third has a higher percentage of our new score. Attacking third has 50%, middle third has 29,4% and defensive third has 20,6%/

As you can see from the pitch above, for ASIR the highest value comes from the central areas with 36,4% of the ASIR. This is followed by the right half space with 22,7%, the left half space with 18,2%, the right wide area with 13,6% and finally the left wide area with 9,1%.

This gives us a better idea which zones and areas on the pitch are most important for our ASIR-rating and therefore for the qualitative new aerial duels model.So, how does it have a correlation with points per game?

In the scatterplot above we see, ASIR compared to Points per game (PPG). The correlation is 0,31 which 0,05 higher than previous, which indicates that this is a moderate correlation: his means that as one variable increases, the other variable also tends to increase.

This shows the top 15% and the following teams score high in this: Feyenoord, Porto, PSV, Ajax, Club Brugge, Westerlo, Zulte Waregem and Alverca.

Conclusion

This analysis investigates the relationship between Aerial Spatial Impact Rating (ASIR) and Points Per Game (PPG) across multiple European leagues (Netherlands, Belgium, Portugal) during the 2025–26 season.

While ASIR shows a clear positive correlation with team success, the metric alone does not account for all aspects of performance, such as defensive solidity, possession control, or finishing efficiency. Nevertheless, the zonal breakdown provides actionable insight for tactical planning, scouting, and player evaluation.

I don’t think I have to tell you that I love set pieces. The whole reason I started looking at data metrics and models more, was the fact that I felt that there are so few metrics concerning set pieces. I think that’s still the case, but we are getting that there, one day at the time.

In this week’s article I want to look deeper into the teams in women’s football that create the most dangerous from attacking set pieces. That’s why I have structured the piece as follows:

1. Data

2. Expected goals focused on set pieces

3. 3.1 Corners

   3.2 Free kicks
   3.3 Throw-ins

Data

The data, well the raw event data, comes from Opta/StatsPerform and was updated on October, 1st 2025. This data contains all on-ball events during the games for both teams. The leagues we are focusing on here are the WSL, Frauen-Bundesliga, Premiere Ligue, Liga F and Eredivisie.

The expected goals model is my own model and uses different variables from the raw data to convert shot locations and shots into shots with expected goals values.

Expected goals focused on set pieces

Before we go into the actual analyses I think it’s good to know that the model specifies for different type of plays. I want to make a distinction between open play and set pieces, in which these are the variables that consist of set pieces:

• Corners

• Freekicks (indirect-freekicks)

• Throw-ins

These are called FromCorner, DirectFreeKick, SetPiece, Penalty, or Throw-In. That’s where we focus our expected goals on.

We first have a look at our model: how reliable is it? In the visual above you can see how the predictions compare to the actuals. My Brier score is 0,081 and my ROC AUC is 0,748

• Brier score = accuracy of the predicted probabilities → mine is low, so xG is well-calibrated overall.

• ROC AUC = ability to rank shots by likelihood → mine is solid but leaves room for improvement.

• Combined, it suggests my xG model predicts reasonable probabilities but sometimes misses the exact ranking of higher vs lower probability shots.

Now we can focus on the analysis.

Corners

In the scatterplot above you can see the total xG amount of teams in the Eredivisie, Frauen-Bundesliga, Liga F, Premiere Ligue and the WSL. The top performing teams are represented above top 20%, with most teams coming from the Liga F. We look at what percentage of their total xG comes from corners/

When we look at the best performing teams in terms of xG from corners, we see that Chelsea leads, followed by Union Berlind and Bayern München.

Freekicks

In the scatterplot above you can see the total xG amount of teams in the Eredivisie, Frauen-Bundesliga, Liga F, Premiere Ligue and the WSL. The top performing teams are represented above top 10%, with most teams coming from the Liga F. We look at what percentage of their total xG comes from freekicks.

DUX Logrono really relies on freekicks with over 30%, that’s insane!

When we look at the total xG generated from Freekicks, we can see that Hoffenheim leads, followed by Arsenal and Werder Bremen.

Throw-ins

In the scatterplot above you can see the total xG amount of teams in the Eredivisie, Frauen-Bundesliga, Liga F, Premiere Ligue and the WSL. The top performing teams are represented above top 10%, with most teams coming from the Liga F. We look at what percentage of their total xG comes from throw-ins.

What immediately comes to the front is how much of xG PSV collects from throw-ins during the Eredivisie 2025-2026 season so far.

PSV also clearly leads the most xG from throw-ins with 0,74 xG. After that Le Havre, Brighton and Real Sociedad follow. It’s also interesting to see how many clubs from the Frauen-Bundesliga feature in the top 15.

I was waiting for an excuse for me to look deeper into the long throw-ins for a while now, but I couldn’t find the right hook. Now, it’s all over the place, and I know my research is far from innovative, but I do still think there are so many interesting things we could talk about. Long throw-ins seem to be emerging in the Premier League, but is this a league specific trend or can we see some similar development in the other top leagues in Europe? Let me take you on a wonderful trip through long throw-ins.

In this article, I will discuss what a long throw-in is and delve into what this means for football in the specific leagues. Furthermore, I won’t only look at the percentages, but also look at where they occurred, where they landed and which value can be gained from this.

There are two pieces which really got my attention:

1. https://www.nytimes.com/athletic/6613474/2025/09/12/tuchel-england-long-throws/?source=twitteruk

2. https://analyticsfc.co.uk/blog/2024/06/18/long-throw-ins-scouting-to-find-marginal-gains/

I wanted to have a look at what the trends suggest for the 2025-2026 season and whether the Premier League has been doing something different from the rest.

Contents

1. Data collection

2. What is a long throw-in?

3. Which league does long throw-ins the most? (count of long throw in)

4. Where do long throw-ins land?

5. What value do long throw-ins have?

6. Which teams are the best in volume and in quality?

7. Final thoughts

Data collection

Most of the time, this data comes from the Opta API, which I have accessed through Python. I use Python more than R, but both are possible for getting the data and doing the data analysis for. I have collected all raw event data from the 2022-2023, 2023-2024, 2024-2025 and the ongoing 2025-2026 season. All the data was collected on September 25th 2025. This is important for when you read this article in the future.

The data is raw event data, which is all on-ball positional (XY) data for the seasons described above. What I did next was to make sure I only had the specific set pieces from the data: free kicks, throw-ins, penalties and corners. I’ve excluded goalkicks and kick-offs, but perhaps in different research this will pop up.

What is a long throw-in?

Before we get into the data analysis part, we need to engineer and construct the metric we want to use. According to Opta this is what a throw-in is: It refers to the restart of play from a sideline, not a pass. It is a set piece, not an open play event. Now they are a few things I want to change:

• We want a throw-in pass, so we need to calculate end locations (endX, endY)

• Success rate %: successful throw-ins vs total attemped throw-ins.

• A long throw in is characterised by me as a throw-in in the final third that goes into the penalty area.

Long throw-ins: a qualitative comparison

The idea was coined that the long throw in is back following the first few Premier League Matches, especially looking at Manchester City and Arsenal. Let’s have a look at the numbers of the last 10 seasons. We focuson the percentage of total throw-ins that re long throw-ins in the final third going into the box:

In the line graph above you see the results of our calculations. The average percentage of throw-ins that end in the box is 12,4% with a growth starting from 2020-2021 from 8,3% to 14,8% in 2024-2025. What’s interesting to see is that there is an explosive growth happening in this season so far, with more than a quarter of the throw-ins in the final third ending in the box: 25,9%.

One of the bigger questions is: Premier League trend or nah? Let’s have a look at the last 4 seasons and compare them to the other big leagues (Bundesliga, La Liga, Serie A and Ligue 1):

In the graph above you see all top 5 leagues in Europe compared for the long throw-ins. We can see a few interesting things:

• Bundesliga has been leading the trend and always has scored higher, but now Premier League is highest

• Premier League has had an explosive growth, from 4th to 1st place in terms of long throw-ins

• Serie A grows slightly as well, but still under the 20%

• Ligue 1 and La Liga stay steady, but also have no change in terms of long throw-ins.

Where do throw-ins land?

If we look at the more qualitative nature of our comparison, it’s evident that we want to look at the locations of the throw-ins. These locations can say a lot. A long throw-in from the edge of the final third or the middle of the final third, can say a lot about intentions.

Let’s first have a look at the throw-ins:

In the image above, you can see how many long throw-ins every league has so far. The Premier League has the most, followed by the Eredivisie and the Bundesliga. La Liga and Serie A are in the middle, with Ligue 1 definitely not choosing to do many long throw-ins.

It seems that the starting location do seem to be similar, let’s have a closer look to the starting locations, which are the x,y coordinates.

What we can see from the heatmap and the average start of the long throw-in locations is not groundbreaking, to be fair. All leagues bar one start their long throw-ins between 15.3 meters and 15.9 meters. Bar one. La Liga starts its long throw-ins much closer on average, with 14.5 meters from the backline.

But now obviously the thing we came her for - at least in this section of the article - the end locations. Where do these long throw-ins end?

So, here we go. The Premier League has an average end location of 8,5 meter from the goal, which is the closest of them all. Eredivisie follows and then Serie A, Ligue 1, Bundesliga and La Liga.

In terms of development, the Premier League is very interesting. They come closest to the goal, which indicates that they throw the longest on average. But we can measure that too, of course.

As you can see the longest throw-ins happen in the Premier League, followed by Eredivisie and Bundesliga. The average length is quite high during this season, which is a signal that there are developments in that regard.

Which value do long throws have?

Next step is of course, looking at the value of those throws. We have looked at where throws are started and where they ended, but the value on pitch is a different matter. We want to see what we actually can achieve with those long throw-ins. First we need to have a look at the success percentage.

As you can see, some of the success rates do not completely align with the leagues that employ the most long throws, but that also makes sense, because they try more. We can see this in a better light in this scatterplot:

The higher the volume of long throw-ins, the lower the percentage of succes is, which isn’t that weird if we think about. Especially if we see that the top 3 leagues in volume, also tend to have the longest throw-ins with being the closest to goal.

Now the next step is, how do we add value from the successful attempts and evaluate them. In other words, how much threat do these long throw-ins generate? We will have a look at Expected Threat (xT).

The basic idea behind xT is to divide the pitch into a grid, with each cell assigned a probability of an action initiated there to result in a goal in the next N actions. This approach allows us to value not only parts of the pitch from which scoring directly is more likely, but also those from which an assist is most likely to happen. Actions that move the ball, such as passes and dribbles (also referred to as ball carries), can then be valued based solely on their start and end points, by taking the difference in xT between the start and end cell. In the case of Grealish, his ball carry brought a 0.013 xT increase, and the pass added a further 0.26 xT. In short, he moved the ball from a low-xT cell (0.02 xT) to a much more dangerous area of the pitch (0.32 xT). Note that the xT action value can be negative for passes and carries that move the ball away from goal. – Soccerments

In the image above, we can see how each league deals with their successful long throw-ins. What’s interesting is that Serie A and La Liga have the highest average xT per throw-in of 0,031 xT, while Eredivisie, Bundesliga and Premier League have 0,030 xT but they have more successful long throw-ins. This gives us the idea that the quality and intention from the latter three is higher.

Teams: which teams stand out?

If we look at the best 15 teams in the number of long throw, we can see that Freiburg, FC Twente and Brentford are the best 3 teams in terms of volume. Parma, NAC Breda and Bournemouth also score high.

Let’s move now to the teams who create the most value out of the long throw-ins, which means the xT from successful throw-ins.

First of all, it’s good to notice/acknowledge that many teams might have the same xT. As we can see Ligue 1’s Le Havre has the highest value, followed by Lazio, Real Oviedo and Torino.

We can combine this into a scatterplot to see the volume of throw-ins and the xT of the throw-ins.

We see that many teams have had a few successful throw-ins into the final third, mostly between 0 and 10, with the average expected threat being between 0.025 and 0.035.

Outliers here Le Havre with a high average xT per throw-in, however, they have had under 5 throw-ins, so that result should be taken with less representation. On the other end, teams like Freiburg, Brentford, Parma, FC Twente and NAC Breda have had many long throw-ins with success, and around 0.030 xT on average. This is a sign that they keep their quality even with a higher volume.

Players

Just like teams, we can also add value to the players with that throw-in quality. First I want to look at the players who can throw the furthest in terms of length.

If we look at the average length of successful throw-ins, a few players really stand out. Lienhart, Cruz, Richard, Mukiele, Koswal and Kayode, really do make an impact with their length. This means that they can almost reach the penalty spot, and can lead to dangerous situations in front of goal.

In the scatterplot above you can see the average throw-in length compared to the average xT value per throw-in. It’s important to see which players have a high average length and also a high xT per throw-in, which means that they are likely to add the most value to their long throw-ins.

Lienhart from Freiburg is the abolsute leader and most valuable, Mukiele (Sunderland) and Semenyo (Bournemouth) score high too.

Final thoughts

Long throw-ins remain one of football’s most overlooked set-pieces, yet this research shows they can be a meaningful attacking weapon. By filtering only successful throws from the final third into the penalty area, we see clear differences across leagues: some treat them as deliberate tactical tools, while others view them simply as restarts. Measuring not just volume but also xT reveals which teams genuinely create danger through this method.

At the team level, long throw frequency reflects identity — direct sides often lean on them, while possession-focused teams rarely do. At the player level, outliers emerge: some specialise in distance, others in placement, and a small group consistently generates high xT per throw. These individuals act as set-piece playmakers, using their arms rather than their feet.

Ultimately, this analysis highlights a low-cost but high-impact opportunity. For scouting, coaching, and opposition analysis alike, long throw-ins deserve far more attention than they usually receive.

I will be honest with you. This article is a passion project of mine and it combines two things I really like in football: data and dribbles. I get it, this is ridiculously vage and broad, but hear me out. There is something magical about a 1v1, a take-on, a dribble or a carry. A player with the ball on their feet, trusting vision, ability and pace to make something meaningful out of that situation. It's a form of arts and its beauty is perceived differently by anyone looking at it.

So how does this relate with data? Again, I do understand that you might anticipate that I won't only look at regular aggregated data and you are totally right. After spending my time on Jstor reading about sports analytics (100 free articles per month btw, you are welcome) - I became fascinated with several statistical concepts and one of them is the Hidden Markov Model in sports analytics. I didn't trust myself to look at it too much, because of two reasons.

The first reason is simply that I didn't understand it enough to apply it to football. How was I going to be able to convey this methodology to football and make it meaningful? The second reason was the one that followed that thought pattern: football is much harder to grasp than others sports, because there are so many *states*, but more on that later.

This piece will be long and explanatory, maybe a little bit on the heavy side. But I will take you along on the journey of me trying to find out the mathematical and statistical side of it, as well af the pure footballing data side.

To begin at the beginning...

I think it's important to answer a question before I go into the contents of this piece. The general question around every piece that I write: **Why do we need this article and this specific data analysis?**

Is the question of needing the right one? I don't think we really need it, but I do think that's good exercise to know what data can do with dribbles and their next actions, to see what we can learn from high volume data. If we can analyse full seasons, that will lead to more value of data, which we can make actionable in a later stage. So, long story short - it can help us value dribbles and their sequnces to see where and how the most value is added.

Next to that it gives a bridge between tactics and data. Hidden Markov Models deal with states rather than action, and in this context these states can be tactical states. We can learn whether a dribbles lead to progression, chance creation, retention or defensive state. But more on that later.

Contents

1. Data collection
2. Glossary
3. Theoretical framework: Hidden Markov Model
4. Methodology: from data to hidden states
5. Analysis
7. Case Study: Most attacking players in Premier League
8. Challenges and difficulties
9. Final thoughts
10. Sources

Data collection

I always start the articles with this section, but it’s vital to know where and how we collect our data. The providers are different and therefore outcomes can be slightly different as well. For this research I’m using Opta/StatsPerform data from the Premier League 2025-2026 season so far. The data has been collected on September, 17th 2025. I’m working with event data rather than aggeregated data, because the raw positional data (X,Y-coordinates) give me the relative freedom to design metrics and models to my own liking.

As far as changing the data, and with changing I mean manipulating, I’m not doing a lot at the first stage of this research. The only thing I’m doing here is look at end locations. The end locations of passes or dribbles are not automatically in the data, so that’s the first thing I do. I look at qualifiers 140 and 141 for endX and endY for passes. Endlocations of dribbles can’t be drawn in the same way, but I will calculate them by look at the next action and use that specific XY-coordinate to determine this.

Glossary

I am not going to give you the full glossary here, if you are interested in that you can visit this website by StatsPerform that explains most of the uses metrics. I want to focus on what’s central in our research, dribbles:

“This is an attempt by a player to beat an opponent when they have possession of the ball. A successful dribble means the player beats the defender while retaining possession, unsuccessful ones are where the dribbler is tackled. Opta also collects attempted dribbles where the player overruns the ball with a heavy touch when trying to beat an opposition player.”

Using this, we will conduct our further research into dribbles and dribbled modeling using Hidden Markov Models.

Theoretical Framework: Hidden Markov Models

A Hidden Markov Model (HMM) is a statistical model that represents systems where we can observe some data, but the underlying states that generate this data are hidden. Unlike a simple Markov chain, where the states themselves are directly visible (like “hot” or “cold” weather), an HMM assumes that the states are not directly observable. Instead, we only see outputs or emissions that are probabilistically linked to these hidden states. For example, in natural language processing, the hidden states could be parts of speech (noun, verb, adjective), while the observed outputs are the actual words in a sentence.

An HMM is defined by three key components: the state transition probabilities (how likely it is to move from one hidden state to another), the emission probabilities (how likely a hidden state is to produce a particular observable output), and the initial state distribution (the probability of starting in each possible hidden state). These parameters together let us compute the probability of a given sequence of observations, as well as infer the most likely hidden states behind them. This makes HMMs powerful for tasks where the underlying structure is important but not directly visible, such as speech recognition, bioinformatics, and time-series analysis.

The real strength of HMMs lies in their algorithms. The Forward-Backward algorithm allows us to perform inference—calculating probabilities of hidden states given the observed data—while the Viterbi algorithm finds the single most likely sequence of hidden states. In supervised learning, HMMs can be trained with labeled data, but they can also learn from unlabeled data using unsupervised methods like Expectation-Maximization. This flexibility makes HMMs a foundational model for sequential data, bridging the gap between observed behavior and hidden structure.

In football, Hidden Markov Models can be applied to capture the hidden dynamics of a match that aren’t directly observable but influence what we see on the field. For instance, the hidden states could represent a team’s tactical phase—such as defending, transitioning, or attacking—while the observed events are passes, shots, or fouls recorded during the game. By modeling these hidden states, analysts can infer when a team shifts strategy, predict likely outcomes (like the probability of a goal being scored in the next few moves), or even identify player roles that aren’t explicitly labeled in the data. This makes HMMs especially useful in sports analytics, where understanding the why behind observed events is just as important as measuring the events themselves.

Methodology

How do we go about this theoretical framework and apply it to our concrete situation of dribbles and tactics? The idea is to capture dribbles and what their next action will be. Hidden Markov Models is about hidden states and in this case these are tactical states:

1. Attacking state

2. Controling state

3. Evading state

4. Ball retention state

The next action after a dribble determines which state the game is going to be in. And, we can use thise to start our analysis with later - but now we will look at how we use Hidden Markov Models to calculate probabilities that a player’s dribbling will lead to each state.

I’ve started with three tactical states, but I’ve added a ball retention state for a more detailed look at it. Expanding the Hidden Markov Model (HMM) from three to four latent states necessitates a methodological adjustment that emphasises both the statistical underpinnings of the model and its interpretative framework. The four states—Controlling, Attacking, Evading, and Retaining—are conceptualised as unobserved tactical intentions that structure observed footballing actions, such as dribbles, passes, or dispossessions. These states are not directly measurable but are inferred from the observable event sequences through probabilistic modelling. Each state captures a distinct mode of play: Controlling aligns with secure ball maintenance, Attacking reflects forward progression toward goal, Evading corresponds to avoidance of immediate defensive pressure, and Retaining signifies recycling possession or decelerating play. The introduction of the fourth state thus enhances the model’s representational granularity, affording a more nuanced interpretation of player behaviour.

From a computational perspective, the central components of the HMM are the transition probability matrix and the emission probability matrix. The transition matrix, now of dimensionality 4×4, specifies the conditional probabilities of moving from one latent state to another, thereby modeling the temporal dynamics of intent. Each row in this matrix is normalized to sum to unity, reflecting a complete probability distribution over subsequent states. The emission probability matrix, links the latent states to the empirical data. Each row encodes the probability distribution of observed events conditional on the underlying intent. For instance, Attacking might emit with high probability dribbles in the final third, while Retaining might emit lateral passes or safe ball recycling behaviors.

Parameter estimation is conducted using the Expectation-Maximisation (EM) algorithm, specifically the Baum–Welch procedure. In the expectation step, forward–backward calculations yield the posterior probabilities of latent state sequences given the current parameters. In the maximisation step, these posterior probabilities are employed to re-estimate the transition and emission parameters so as to maximise the likelihood of the observed data. Iteration continues until convergence is reached under a defined tolerance threshold. Following training, the Viterbi algorithm is applied to infer the most probable sequence of hidden states underlying each observed sequence. The methodology thereby integrates rigorous statistical estimation with domain-specific interpretation, enabling the identification of latent tactical intentions, Controlling, Attacking, Evading, and Retaining, that govern the observable execution of dribbles and associated actions

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Analysis

So first I want to have a look at a player and see how likely it is that a player moves into a different state when on the ball. In other words, what are the probabilities of a chosen player to move in a different tactical state after taking an action on the ball?

Attacking

This state represents a direct, progressive dribble aimed at creating a scoring threat. It's the most dangerous type of dribble.

• Location: Almost always occurs in the attacking third of the pitch.

• Movement: The dribble moves vertically or diagonally towards the opponent's goal or into the penalty box.

• Distance: Typically covers a medium to long distance as the player breaks through defensive lines.

• Primary Goal: To shoot, assist, or directly create a clear goal-scoring opportunity.

Think of it as a winger running at a defender to get a cross in or a midfielder driving into the box.

Controlling

This state describes a dribble used to manage the tempo of the game and prepare the next phase of an attack. It's about possession with a purpose.

• Location: Most common in the middle third of the pitch.

• Movement: Can be lateral or slightly forward. The player isn't making a bee-line for the goal but is moving into a better position to make a pass.

• Distance: Usually a short to medium distance.

• Primary Goal: To get your head up, assess options, and maintain possession while waiting for attacking movements to develop.

Think of it as a midfielder taking a few touches in space to switch the play or draw a defender before passing.

Evading

This state captures a quick, agile move to beat an opponent who is applying direct pressure. It's a dynamic, one-on-one action.

• Location: Can happen anywhere on the pitch, often in congested areas.

• Movement: Characterized by a sharp change in direction (lateral, diagonal, or even a slight backward touch) to escape a tackle.

• Distance: Almost always a very short distance—a quick burst of movement.

• Primary Goal: To get past an immediate defender and open up space for the next action (a pass, a shot, or another dribble).

Think of it as a player using a feint or a sudden burst of speed to sidestep a lunging defender.

Ball Retention

This state represents a safe, low-risk dribble focused purely on keeping the ball under pressure when there are no forward options. This is the most conservative state.

• Location: Most often occurs in the defensive or middle third, especially near the touchline or when a player has their back to the goal.

• Movement: Very little forward progress. The movement is minimal, often involving shielding the ball with the body. The dribble might go sideways or backwards.

• Distance: The shortest distance of all states, barely more than a single touch.

• Primary Goal: To protect the ball from an opponent and avoid being dispossessed until a safe pass can be made.

Think of it as a player holding off a defender, shielding the ball and waiting for a teammate to get open. It's about security above all else.

In the above matrix you see all hidden states as we calculated them for the Premier League 2025-2026 season. What you can see that there are values with 0,00 and that’s something that can be attributed to the small database in which we operate, but there are still a few interesting things happening here.

For example, if a player is in an attacking state - which we say a dribble is - we can see that the probability of the next tactical state is as follows:

• Keep in the attacking state → 0%

• Move towards a controling state → 48%

• Move towards an evading state → 0,01%

• Move towards a ball retention state → 52%

For me this doesn’t sit right, because it effectively says that after a dribble, the state is always a non-attacking one and always a form of control/ball retention. Let us give some more meaning to the locations of the dribbles begin and end + the areas of the pitch.

After making some alterations to the calculations, we see a very different matrix. In case of a dribble which is in an attacking state, how do the probabilities line up for the next action:

• Keep in the attacking state → 21%

• Move towards a controling state → 46%

• Move towards an evading state → 8%

• Move towards a ball retention state → 25%

That already looks like a more realistic scenario for dribbles. The most likely tactical state for a dribble to end in is a controling state followed by ball retention and attacking state. Dribbles in the Premier League are suggested to be very attacking and then resort to a more controlling state.

Now how does that look on a value grid for a pitch?

In the visual above you can see how the dribbles changed in their xy coordination. Controlliong and Evading change the most, while ball retention and the attacking state change the fewest. This means that the dribbles that stay in the attacking state have the shortest distance, while other more conservative states allow for more distance.

Let’s see how this looks for the players.

In the bar graph above you can see which players have dribbles where the next action also has the tactical state of attacking. In other words, they constantly look for an attacking option and pushing the ball forward.

What I also think is interesting to see, is how players consolidate their dribbles after being in an attacking state: controlling state. Which players score highest in this? These players move towards more controlling areas or do make sure the ball ends up in a less threatening space but consolidates possession.

Challenges

The challenges are definitely present. First of all, I assign the states myself and I like to assign tactical states to data, which is quite sensitive to flaws. Why? Because I make a decision based on what I think is good, but also is very biased in a way. These are the challenges and critical things I need to think of, for next time:

• State definition: Tactical states are subjective and can introduce bias.

• Data limitations: Event data misses micro-actions; positional nuance is lost.

• Markov assumption: Transitions depend only on the previous state, ignoring broader context.

• Sparse events: Rare dribble outcomes can produce unstable probabilities.

• Interpretability: Statistical states may be hard to translate into footballing meaning.

• Player/context variability: Aggregated models may ignore individual style or team tactics.

• Scalability: Large datasets increase computational complexity.

• Validation: No ground truth for hidden tactical states; evaluation is subjective.
  

Final thoughts

Dribbles represent a complex and dynamic component of football, reflecting both individual skill and broader tactical intentions. The application of Hidden Markov Models provides a rigorous statistical framework to infer latent tactical states underlying observed actions, enabling an analytical perspective on progression, possession retention, and offensive transitions.

Despite inherent limitations — including subjective state definitions, data sparsity, and the absence of ground-truth labels for hidden states — this methodology demonstrates the potential of event-level analysis to bridge the gap between qualitative football insight and quantitative modeling. While the results should be interpreted cautiously, the approach underscores the value of combining domain knowledge with probabilistic modeling, contributing to a deeper understanding of player behavior, tactical dynamics, and the evaluative potential of high-resolution match data.

Sources

1. https://web.stanford.edu/~jurafsky/slp3/A.pdf

2. https://www.geeksforgeeks.org/machine-learning/hidden-markov-model-in-machine-learning/

3. Opta/StatsPerform API

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One of the most difficult things in working with data is having the right data. There are different types of data, but sometimes we are not sure what we can do with all the data. Why am I saying this? This is because I have been adament to have tracking data for all the leagues. And, that’s simply not possible.

What I do have for almost all the leagues I’m interested in, is the raw event data. In the absence of tracking data, I could still create meaningful models that infer off-ball actions. Big point to make: this isn’t as correct or representative as tracking data, but we can make a suggestive data model about off ball actions.

In this article, I’m going to exercise that concept and look at off-ball actions of wide players. How can we see whether players stretch play with a value model?

Contents

1. Data: data collection and representation

2. Why this model?

3. The risks of using event data to suggest tracking data

4. Theoretical framework: mathematics and statistics

5. Methodology

6. Results

7. Analysis: NWSL

8. Final thoughts

1. Data collection and representation

First of all, it is important to know what kind of data we use and which things we need to change in order to make sure the model is accurate as can be. The data I’m using is event data from the NWSL 2025 season. This season is ongoing, but I have updated the data until the 12th of September, 2025. The data comes from Opta/Statsperform.

The event data is raw data and it shows the positional data of all on ball data of the players and teams incorporated in the JSON files. I prefer JSON files for processing, but you can convert them to CSV/Excel files as well. My experience is that it will take longer to process if you convert ehm.

I don’t do a lot with the data once I have collected, but since their are no endlocation in the original dataframe, I need to create that explicitly from the qualifiers. Qualifiers 140 and 141 represent the endX and endY, which will be used for the endlocations of the passes, which will play an integral part of this research and calculations.

2. Why this model?

Why the hell would you do this, Marc? Why would you want to create a suggestive off-ball model while you also can do this with tracking data? Now that’s an excellent question, rhetorical Marc. There are two reasons why I do this:

1. Not everyone has access to tracking data, but has some access to event data. There are workarounds which might be less accurate, but still give a pretty decent overall picture.

2. The challenge. I would like to challenge myself to become better in using mathematical concepts and calculations, and this process will definitely play a part.

3. Risks of using event data to infer off-ball actions

Using event data to calculate off-ball stretch of play carries significant risks because it only captures moments when the ball is directly involved, leaving large gaps in the spatial and positional context of players who are not participating in the on-ball action. This can create misleading interpretations of team compactness or width, since stretches of coordinated off-ball movement, such as defenders shifting as a unit or attackers rotating to drag markers, often occur outside the scope of event-based logs.

Another risk lies in the timing and granularity of event data, which is typically sparse compared to tracking systems that capture positions multiple times per second. Because event data is recorded only when specific actions happen (passes, shots, tackles), it overlooks continuous off-ball dynamics, making any reconstruction of player movement heavily assumption-based. This can result in artificial compression or expansion of play stretches depending on how the gaps are interpolated.

4. Theoretical framework: mathematics

The arithmetic mean, often just called the "average," is a single value that represents the central tendency of a set of numbers. It's calculated by summing all the values in the collection and then dividing by the count of those values. Think of it as a way to find a "fair share" value. For instance, if three friends have 2, 4, and 6 cookies respectively, the total is 12 cookies. The arithmetic mean would be 12÷3=4, meaning if the cookies were redistributed equally, each friend would get four. This concept is fundamental in statistics for summarizing data, allowing us to quickly grasp a typical value within a dataset, like the average temperature in a week or the average score on a test.

The Cartesian coordinate system is a graphical framework used to pinpoint the exact location of any point on a flat plane. It's built around two perpendicular number lines: a horizontal x-axis and a vertical y-axis.

Their intersection point is called the origin (0,0). Any point on the plane is uniquely identified by an "ordered pair" of numbers (x,y), which represent its signed distances from the origin along each axis. This system acts like a grid map, allowing us to translate geometric shapes into algebraic equations and vice versa. It's the foundational language of geometry, physics, and computer graphics, enabling precise location and movement tracking.

Euclidean distance is the most intuitive way of measuring the length of the straight line connecting two points. It’s the "as the crow flies" distance, ignoring any obstacles or required paths. In a two-dimensional plane, it's calculated using the Pythagorean theorem by creating a right-angled triangle with the line segment as the hypotenuse. If you have two points, (x1​,y1​) and (x2​,y2​), the distance is found by taking the square root of the sum of the squared differences of their coordinates: (x2​−x1​)2+(y2​−y1​)2​. This measurement is crucial in various fields, from GPS navigation calculating the shortest route to algorithms that group similar data points.

Methodology

The methodology begins by loading and structuring the raw match event data from a JSON file. Each event, such as a pass or a touch, is flattened into a single row in a table. The script then applies a crucial filter, isolating only the passes that are specifically tagged as a "Switch of play." This narrows the focus to long, field-switching passes intended to stretch the opposition's defense. For this analysis, it first identifies all the successful switches of play. This initial step is essential as it creates a refined dataset focused exclusively on the specific type of strategic pass being investigated, clearing away all other irrelevant actions from the match.

Once successful switches of play are identified, the script determines the receiver of each pass. It does this by looking at the event immediately following the pass in the timeline and assigning the reception to the player who performed that next action. After collecting all of a player's receptions, it calculates their personal average receiving position on the pitch by taking the mean of all the (x,y) coordinates where they successfully received these passes. This average point becomes the center of a theoretical circular "receiving zone" for that player. This method effectively creates a data-driven profile for each player, mapping out the specific area on the field where they are most typically targeted for long, stretching passes.

In the final step, the script evaluates every "switch of play" attempt from the match, including both successful and unsuccessful ones. It checks if the end coordinates of each pass fall within any player's predefined receiving zone using Euclidean distance. By counting both the successful receptions and the unsuccessful passes aimed at a player's zone, it calculates the TotalPassAttemptsReceived. This total is then multiplied by the average length of those passes to create a Stretch Value Model score, which quantifies a player's role as a deep target. This score is then normalized to a 0-100 scale, providing a clear, ranked list of players based on their value in stretching the field.

Analysis

Now we have calculated the metrics we want to use:

• PassesReceived

• UnsuccessfulPassesToArea

• TotalPassAttemptsReceived

• TotalTouches

• AverageTargetedPassLength

• Stretch Value Model

• Normalized Stretch Value (0-100)

• AverageReceivedX

• AverageReceivedY

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With all this information we can start having a look at the players who have been target the most with passes from switches. This means from one side of the pitch to the other side of the pitch. These are all passes attempted to that player or the area of the player, including unsuccessful attempts:

In the bargraph above you can see which players have received the most switch passes to the wide areas during the 2025 season. As you can see those are not many passes, but that’s also because we are quite strict with our filtering. Mozingo, Picket and Vignola are most targeted.

Now which players have the highest percentage of actually receiving that specific targeted pass?

As you can see Biegalski, Curry, Bruninha, Lussi and Williams all have 100%. Which is actually great for the passes, but not something we are looking for.

Streched play can be calculated has high attempted passes and not many touches in that area, which we also include lower % of reception. This bar graph above doesn’t tell us a whole lot about this. We don’t get closer to our goal. So let’s have a look at the total of touches in that area in comparison to the attempted passes.

This gives a much better idea of which player are likely to stretch play much more. Low efficiency on receiving passes and lower touches in those area. The players who are interested to follow are Adames, Hanks, Mozingo and also Sentnor.

Now we have to go to the value model, because we will use the Player Stretch Model to do that well.

What we can see in this bargraph above, Mozingo clearly has the highest value of suggested stretched play, but Vignola, Berger and Pickett are very close to each other. These players are players that are often attempted to reach, not often get the ball or have many relative touches in that area. We can therefore imply/suggest that these are players that stretch the play.

Let’s focus on the player who scores highest on the Stretch Value Model. Where does she average her receptions and touches?

As you can see she scores highest because of her reception rate and low touches, but there are also other factors. One of the most important is that she really hugs the side line, that also helps with stretching the play as wide as possible.

Final thoughts

I think this has been a good exercise in using event data to answer a question. Is it as effective and correct as tracking data? Oh no, I don’t think so. It does however, give suggestions to players you could watch on video and see if they stretch the play as suggested. But the main part is about the thought process, how can we be creative and use data to get to innovative insights.

The transferwindow is coming to a close in women’s football and with that I wanted to express the importance of data. This time I don’t want to talk as much about performance data, because I don’t want to measure how well/bad a player performs. I want to gather data that’s important for building a portfolio for recruitment . In short, I like data that give data on biography.

In men’s football we use transfermarkt and we rely heavily on it. Perhaps to heavily? We should be more citical of that. However, since a few years we also have Soccerdonna on the women’s side and it’s only recently that the database has been sufficient so we can use.

I have created a soccerdonna scrape package for Python (R will follow) so you can easily get the right information from that website for your media, scouting or other purposes.

Which information do I need and want?

I want to get an overview of player information concern all teams in the league I choose. This is good for scouting and recruitment, but also will help with writing journalistic articles.

These are the pieces of information I want to pull.

• Name

• Club

• Date of birth

• Nationality

• Position

• Height

• Shirt number

• Profile URL

• Additional attributes from the Soccerdonna player page

I have created a python package that helps with pulling the data from the website.

The soccerdonna_scraper package provides tools for extracting player and club data from Soccerdonna.de, one of the largest databases for women’s football.

It can scrape all clubs in a given league, collect detailed player profiles, and export the data into an Excel file for analysis.

Installation

You can install the package directly from GitHub:

pip install git+https://github.com/marclamberts/soccerdonna_scraper.git

The following dependencies are installed automatically:

• requests (HTTP requests)

• beautifulsoup4 (HTML parsing)

• pandas (data handling)

• openpyxl (Excel export)

Python 3.8 or newer is required.

Usage

You can use the scraper either from Python or via the command line interface (CLI).

from soccerdonna_scraper import run_scraper

# Scrape the Women's Super League (ENG1) and save results
run_scraper("womens-super-league", "ENG1", output_file="WSL_ENG1_players.xlsx")

Parameters:

• league_code: The league slug used in Soccerdonna URLs (e.g., womens-super-league).

• comp_code: The league competition code (e.g., ENG1).

• output_file (optional): Name of the Excel file to save. Defaults to {league_code}_{comp_code}_players.xlsx.

### Using from CLI

After installation, a command-line script wsl-scraper becomes available:

wsl-scraper womens-super-league ENG1 -o WSL_ENG1.xlsx

Arguments:

• league_code: The league slug (e.g., kvindeliga, womens-super-league).

• comp_code: The competition code (e.g., 3FL, ENG1).

• -o, --output: Optional Excel file name.

Examples

Scraping the Kvindeliga 2024-25 season:

from soccerdonna_scraper import run_scraper
run_scraper("kvindeliga", "3FL", "Kvindeliga_2024_2025.xlsx")

Scraping the Women’s Super League:

wsl-scraper womens-super-league ENG1 -o WSL_ENG1.xlsx

It’s been about two years since I first started writing about data away from player or team insight. I started with the Corner Delivery-model and two years later I have designed 20+ metrics, scores, indexes and models. They all took a variety of work, effort and hours - but in the end, they all worked and took some time to develop. Some need time to brew and cook up, effectively shelving them for another time.

There is one model that has come off the shelve and has been put up there repeatedly in my brain. But I think now is the time for me to properly launch into the world. Not only because I think it’s a decent model after time of deliberation and changes, but also because I truly believe in the process. The process is where we learn; it’s where our creativity comes to the surface and converts into meaningful data engineering.

The model I’m talking about is the expected shot danger model.

Introduction

There are always two reasons for me to publish models. First of all, and this is rather selfish, but I’m really proud of myself for finishing a long project. Due to my mental disorder, limitations are often put on what I can produce, but with footbal,l this seems to be different. And, the second one - perhaps more relevant for you who are reading this - is that I think this provides meaningful content for you to read and use the model in your own endeavours.

It’s a question you might have and also one I wanted to answer for myself: why do we need this model when there already exists a quite comprehensive and complex model that values shots in expected goals?

Excellent question, I might add. Expected goals look at the quality of a chance and calculate a probability or likelihood that a certain shot will be converted into a goal. This is based on historical data. This is something I really like, but it feels very focused on goalscoring and the probability of that happening. I want to measure threat and/or danger based on location, and I found that expected goals came short in how I wanted to approach it.

Threat? Is there not another model that deals with threat or expected threat? Yes, there is. Karun Singh developed the expected threat model (xT) a few years back, and it has been instrumental in how we approach bin count values with progression towards the goal. He can explain it much better than I can, so go read his full article here:

https://karun.in/blog/expected-threat.html

These are excellent models that will help going forward, but there are some fundamental elements missing in combining threat with shots, so that’s why I decided to create my own model.

Aim

So why do I do this, and what’s my aim? My aim is to create a shot-based value model that is a hybrid between expected goals and expected threat that seeks to measure outcome danger whilst including blocked shots.

The Expected Danger model is designed to overcome a key limitation of existing football analytics models. It combines the strengths of two popular metrics:

• Expected Goals (xG): This model calculates the probability of a shot resulting in a goal based on factors like shot location, body part used, and play type. Its primary focus is on the final outcome: a goal. However, it assigns a value of zero to shots that are blocked, even if the shot was taken from a high-danger location.

• Expected Threat (xT): This model measures the change in a team's probability of scoring when the ball moves from one location to another. It values passes and carries that move the ball into more dangerous areas, but it doesn't directly value the shot itself.

In conclusion, this new model gives us a better idea of actual shot danger and the inclusion of blocked shots in that model.

Theoretical framework

There are a few theoretical concepts that are included in this particular model that we need to have a look at. Two variables of the models come directly from Ice Hockey analytics and are Corsi and Fenwick. Inside the Rink (article here) describes it as follows:

“What are Corsi and Fenwick? The answer may feel underwhelming. Despite the tendency of the hockey community to refer to them as “advanced stats” Corsi and Fenwick are very simple concepts. Corsi is nothing more than another name for shot attempts. NHL.com defines shot attempts (Corsi) as: any time a player tries to shoot the puck. So, any shot on goal, blocked shot or missed shot is classified as a shot attempt. The name Corsi was given to the stat by a hockey blogger because he liked Jim Corsi’s moustache (Jim was the goalie coach of the Buffalo Sabres at the time).”

“Fenwick is Corsi without the blocked shots. So only missed shots or shots on goal are counted as a Fenwick shot. Compared with Corsi, Fenwick is barely used in practice. We will spend at least one future article on the uses of Fenwick, but for the rest of this piece, we will focus solely on Corsi. However, all the concepts we will discuss with respect to Corsi can also be applied to Fenwick.”

It’s not a wildly innovative set of metrics, not at all, but I like the distinction between blocked shots and unblocked shots in the metrics. Because of how I value blocked shots in this model, I will refer to Corsi and Fenwick danger in the expected models as well.

Mathematical approach

There are three different mathematical approaches towards this model that I employ. These form the basis of how my model is calculated.

1. Rule-based heuristics: Rule-based heuristics are simple decision-making methods that rely on predefined rules to solve problems or guide actions. Instead of complex models or deep calculations, they use “if–then” logic or straightforward guidelines derived from experience or domain knowledge. These heuristics are fast, interpretable, and easy to apply, but they can oversimplify complex situations and may not adapt well when conditions change.

2. Shot-type weights in football are empirical values assigned to different kinds of shots to reflect their likelihood of resulting in a goal. Instead of treating all attempts equally, analysts use historical data to assign probabilities. These weights are built from large samples of past matches, capturing how effective each shot type usually is. They form the backbone of metrics like Expected Goals (xG), though they simplify reality by not fully accounting for defender pressure or game context.

3. In football analytics, supervised learning with logistic regression calibrated to real goal outcomes is a method for estimating the probability that a shot results in a goal. Historical data on shots is collected with features such as distance, angle, body part, shot type, and defensive pressure. A logistic regression model is trained on this data, using actual goal outcomes (goal = 1, miss = 0) as labels. The model learns how each feature influences scoring likelihood and outputs a probability between 0 and 1. Calibrating the model against real match outcomes provides a more accurate estimate than simple shot-type weights.

These form the basis for our data approach as we look to calculate the new model.

Methodolody

How are we going to transform the raw event data into meaningful danger scores? First, we are going to load the data from a series of JSON-files. I want all games played in the Dutch Eredivisie 2024-2025 and I want the JSON-files flattened, so we can create a workable dataframe we can use in Python. I am an avid Python user, but of course, you can also use other programming languages that work with similar calculations. From the dataframe, I will only look at the features/variables I need to work with:

• Player ID, team ID, coordinates (x, y), time

• Event type (goal, on target, blocked, etc.)

• Qualifiers (body part, assist, play type)

The next step is that we are going to process the data. This means that we are going to engineer. We are going to move typeId into shot categories. This means that typeId 13,14,15,16 will move into shot categories: wide shot, shot on post, shot on target and goal. We extract two different features:

1. positional features: Distance to goal (Euclidean), Shot angle relative to goalposts

2. Derived contextual features: Shot body part (foot/head/other), Play type (open play, set piece, counter, penalty), Assist information

We move to the heuristic model. We implemented two possession-based proxies and one geometric danger model, inspired by hockey analytics:

• Corsi: all shot attempts per team, ratio over match total.

• Fenwick: unblocked shot attempts per team, ratio over match total.

• Heuristic danger score (Fenwick-style): combines location geometry into a simple rating: Scorefenwick​=(0.5⋅(1−100d​)+0.5⋅(1−90θ​))×100, where d = shot distance, θ = shot angle.

Additionally, we applied shot-type weighting (goals > shots on target > misses > blocked).

After this follows the statistical model

• Input features: categorical (shot type, body part, play type), numerical (distance, angle, assist flag, etc.).

• Model choice: Logistic regression.

• Calibration: Applied Platt scaling (sigmoid) CalibratedClassifierCV to ensure preot danger per shot.dicted probabilities are well-calibrated with observed frequencies.

This produces a probabilistic estimate of shot danger per shot.

Analysis I: Expected Danger Fenwick + Corsi

In the image above, you can see two pitches with shots plotted. On the left side, you see the shots with the Fenwick Danger Score, which are all shots that are unblocked. The average of the danger is 0,58.

On the second pitch, you see all shots with the Corsi Danger Score. The average per shot is 0,66 - a significant difference of 0,08 per shot. We can conclude from this that unblocked shots do add to the danger of shooting, but are not always considered in traditional shot models.

The main thing we can get from this is that we incorporate blocked shots in our calculations, the danger of a shot is higher because of the potential it stands for. Every shot can have both danger values, but it’s essential for the danger being generated on the pitch that we don’t disregard or ignore blocked shots.

Analysis 2: Expected Danger Blocked Shots

In the shotmap above, we see all shots that have been blocked. We use the corsi-model as it deal with blocked shots as well. The average danger score is 0,6, and what I think is quite interesting is that the shots that are blocked with the highest value are the shots coming from the central areas.

Analysis 3: Expected Danger prevented blocked shots

We have shot locations of blocked shots, but we also have the xy-coordinates of where the shots have been blocked by the opposition. We can use that to calculate the danger prevented by blocking shots using our expected danger model.

As we can see on the pitch, the average danger prevented per blocked shot is 0,35. We can use this kind of information to evaluate opposition defending, but also to evaluate our own players and how much danger they prevent apart from disrupting passes.

Example 1: Expected Danger Build-up + Chains (passmaps + passnetworks)

Now we have seen how the model can work and what the danger can represent, how can we use this in analysis? In other words, how can we make this a bit more actionable?

We are quite familiar with passing networks in football, but we can also create build-up and chains from expected danger, and that’s what we will do.

In the image above, you can see the season passing network of PSV in Eredivisie 2025-2025. The size of the nodes corresponds with the value of the expected danger build-up score. The same goes for the colour. what we can see is that in the expected danger build-up, Dest, Veerman and Saibari score very high.

In the bargraph above, you can see the players in Eredivisie 2025-2026 who have the highest xDanger build-up after three matches (clubs playing European qualifiers have a game less). Karouani, Smits and Sano score really high.

Example 2: Shotmaps with values Expected Danger Shots

What we can do with all this information is create a shotmap just like we do with the expected goals map. You can see all shots by Berghuis (Ajax) and their value. He has shot 14 times and scored 1 goal. Five shots were blocked. His danger with unblocked shots was an average of 0,61 and 0,68 when including blocked shots.

We also look at the average Location Quality Scor,e which is the score of how optimal his location is in relation to his expected danger.

Challenges

There are numerous challenges when creating this model, and what makes this model not entirely flawless:

• Model Limitations: I train a logistic regression to estimate xDangers, but realise it sometimes overestimates danger for simple shots and underestimates complex plays. It ignores the defensive pressure or positioning nuances. Scaling the scores across matches adds another layer of inconsistency.

• Interpretability: Even after calculating the xDanger, I might struggle to explain why a particular action has a certain danger score. Combining distance, angle, and shot type into a single number obscures the reasoning. Plus, a 0.6 xDanger doesn’t directly translate to a probability of scoring unless carefully calibrated.

Final Thoughts

I wanted to create a hybrid between expected goals and expected threat that focuses on shots with a split between Fenwick and Corsi models. This has definitely happened, and I succeeded in it.

Important to know that this is one of the first itterations of the model and that I need to keep evolving this with defensive pressures, off-ball data and tracking data. Will it be an alternative to expected goals? Oh hell no. To me, it’s an extra source of information in which we can measure the danger of shots while also incorporating blocked shots.

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I am a very chaotic person by nature, and I need structure to make sure everything works right. This makes me thrive. But when the structure isn’t good enough, it happens that projects stay on the shelf for a long time. One of these projects was the Goalkeeper Value Model (GVM), but not anymore! I finished it and I’m very happy with it.

I’ve often said that goalkeeper data is not as available in mainstream data sources and providers. That’s one part of the story actually. Goalkeeping is harder to measure in on-ball data because a lot happens that is technical or part of how a defender sets up. Another reason for this phenomena is that media is focused on how goals are scored and not necessarily on how goals are prevented. And, I made it my mission to change that. Okay, that’s very idealistic. I want to play my part in creating understanding for goalkeeping data.

Contents

1. Introduction

2. Data collection, manipulation and explainer

3. Aim

4. Theory

5. Methodology

6. Final product

7. Analysis

8. Final thoughts

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Introduction

Goalkeepers are underrepresented in data studies. Whether this is bias, lack of data or more focused on technical areas, the fact remains that goalkeepers are not evaluated as much via data. When goalkeepers are evaluated on data it is often linked to attackers in the form of shot-stopping: how good is a goalkeeper at preventing goals? What are the difficulties of the shot being faced? All these questions are being raised in relation to scoring metrics.

Goalkeeping is much more than just shot-stopping. We can look at distribution, leaving the line, reflexes, ball handling, and sweeping. Before, we just looked at 1 or 2 categories, but lately we can identify and separate more categories, which makes data analysis of goalkeepers more valuable.

With those distinctions, we can create new metrics, scores, index and models. This could open a whole new spectrum in data analysis, and this article is just a small part of what we can do with goalkeeper data.

Data collection

The data used in this research is event data coming from Opta/StatsPerform. It contains the raw data of the 2024-2025 season of the Italian Serie A of the UEFA confederation. It was collected on August 18th, 2025.

For those who have worked with this kind of data, we need to prepare a few things so that it works before we start the analysis. It is important to look in the qualifiers to find the endX and endY coordinates, so you can create those columns. Believe me, that will make it easier to plot passes. The qualifiers and events are crucial when you are working with Opta data, and you can find some mapping here:

Events: Opta - Events
Qualifiers: Opta - Qualifiers

The last thing, which also is very important, is to use the right filters. We have to deal with goalkeepers, so I only want goalkeepers in my database. Those goalkeepers should also have played a minimum if 900 minutes (equivalent of 10 full games without additional time) for me to properly data analyse them.

When we have done that, we are ready to start the real work.

Aim

So what’s the aim with this article or my research for that matter? My aim is to show what we can do with on-ball event data for goalkeepers. Added to that, I want to show we can use data in goalkeeper to distinguish different categories and evaluate goalkeepers. Ultimately, a model is created that does exactly that and will give different audiences a quick overview of how a goalkeeper has performed in a match or a season.

Theory: What do I want to create?

I want to create something tangible and actionable. But before I can do that, I have to set out my own theoretical framework of how I’m going to achieve that exactly. My aim is to first create 5 scores:

• Shot-stopping

• Leaving line

• Distribution

• Ball handling

• Set piece

All of these scores consist of metrics that exist or that I have to create. My aim is to create the metrics myself as much as possible, because then the model is more in control of what I’m doing and in my decisions in data. Another reminder that data is never unbiased, because a human will create the metrics by making certain choices.

These scores form the essence of my model, because they are features for creating my model. Every action will have a value and be flagged for a specific category. By doing so I can have a total score for each category and one final score for the performance of that match or season.

Methodology

The files I need for this analysis come in either CSV or JSON files. I use Python as my programming language for the calculations and visualisation, but others are good as well: R and Julia are often used for this too.

This model evaluates goalkeeper performance using a Threat-Based Value methodology, which quantifies a goalkeeper's impact on a match by measuring how their actions either reduce or increase the opponent's probability of scoring. The core of the model is a custom expected value grid, which assigns a threat value to every location on the pitch. This value represents the likelihood of a goal being scored from that position. By analysing a goalkeeper's actions, like a pass, a save, or a clearance, the model calculates the change in EPV between the start and end of the event, assigning a positive value for actions that decrease opponent threat and a negative value for those that increase it. The model is built on four key phases of a modern goalkeeper's role:

1. Shot Stopping: This is the most traditional aspect of goalkeeping. The model's value is calculated as the change in threat from the moment a shot is taken to the outcome of the shot. A save that eliminates the threat receives a higher positive value than one that results in a rebound, which still carries a residual threat. A conceded goal, by contrast, yields a significant negative value. This approach accounts for the quality of the save and the subsequent state of play, rewarding goalkeepers who make clean, secure saves over those who push the ball back into a dangerous area.

2. Distribution: A goalkeeper's ability to start an attack is a crucial part of modern football. The value is determined by the xT change from the start point of a pass to its end point. The model rewards a successful, forward-moving pass that progresses the ball into a more threatening area for the goalkeeper's team. Conversely, an incomplete pass is penalised, as it turns over possession and puts the team at risk. The model also distinguishes between short passes for build-up, medium passes, and long passes (launches), providing a breakdown of the goalkeeper's distribution profile.

3. Leaving the Line: This phase measures a goalkeeper's proactive role outside the penalty area, such as sweeping behind the defensive line or claiming crosses. The value here is based on the threat reduction achieved by the goalkeeper's intervention. For example, a proactive clearance that prevents a dangerous through ball from reaching an attacker is highly rewarded, reflecting the threat that was neutralised. Similarly, claiming a cross in a crowded box is seen as a high-value action because it eliminates a scoring opportunity that could have materialised from the cross.

4. Ball Handling: This category covers a goalkeeper's actions when they have the ball in their hands, including securing catches, deflecting shots, and handling spills. It is valued based on whether the goalkeeper securely controls the ball (neutralising threat) or creates a rebound or error, which increases the opponent's threat. A secure catch is a high-value action, whereas a spill that leads to a subsequent shot or goal is heavily penalised. This metric highlights a goalkeeper's reliability and decision-making under pressure.

Final product

The final outputs of the GK Threat-Based Value Model transcend raw data, providing a comprehensive and intuitive overview of a goalkeeper's performance. All individual event values (Vevent​) are aggregated and normalised by the total number of events in each phase. These normalised scores, Vˉphase​, are then combined into a single composite value using a weighted sum:

S=B+ωss​Vˉss​+ωdist​Vˉdist​+ωll​Vˉll​+ωbh​Vˉbh​

Here, B is a baseline score, and the ω parameters are predefined weights for each phase. This linear combination yields a single Match Score on a 0-100 scale, providing a complete picture of the goalkeeper's overall contribution.

The model also generates a series of key visualisations:

1. Half-Pitch Heatmap: This graphic provides a macro view of the goalkeeper’s value creation across their half of the pitch. Areas of high-value actions are represented by warmer colours, offering a high-level spatial analysis.

2. Half-Pitch Points Map: For a more granular view, this map plots every individual event. Each point is color-coded by its value and shaped according to its performance phase, allowing for detailed, event-by-event analysis.

3. Worst 10 Distribution Plot: This visualisation specifically highlights the ten most negative distribution events, providing targeted feedback on areas needing improvement.

Finally, a detailed Scorecard and a quantitative Excel report combine these outputs with traditional statistics (goals prevented, pass completion rate, etc.) to offer a multifaceted and data-rich assessment. The final product is a powerful tool for analysts and coaches to derive actionable insights, moving beyond surface-level observations to a true understanding of goalkeeper performance.

Analysis

So we have done all calculations and there are two visuals which tell me a lot about goalkeepers that I will want to show you here.

The first visual is the worst distribution plot. In terms of value generated, which passes are the lowest?

This pitch shows us the distribution by the goalkeeper Maignan in the game against Roma. These are the 10 worst goalkeeper distributions and every pass has the value next to it. It shows patterns of the goalkeeper in terms of distribution and how much effect in value these have. It this becomes a structural thing, the gk coaches can work on that together the goalkeeper to enhance this part of his play.

Obviously, this is just one part of goalkeeping and we can see a more complete example of goalkeeper performance in the score card I have created based on the aforementioned models.

In this score card you a plethora of information. First, in the tiles we see the total match score (69). This is the weighted total of shot stopping score (72), distribution (66), leaving line (67) and ball handling (63).

The next three tiles show distribution statistics and leaving line. The distribution profile is based on the distribution length. Varied, mixed, launch-heavy and short build-up. Next tile shows how many of the passes were short, medium and long - and a launch % added. The third tile shows how many crosses were claimed in this game.

The text box in the middle shows some regular statistics of the game which arent’t very groundbreaking.

The three visuals on the right are one of the most interesting things about the whole research:

1. Score timeflow: this shows the total score of the goalkeeper throughout the game. Every goalkeeper starts with a score of 65 and the negative/positive values of the actions make the change. This shows what score the goalkeeper is on any given time in the game. He started badly and recovered against the end of the game.

2. Phase Impact: this shows the total impact in score of each specific phase on the game and score. In this case the goalkeeper scores high on shot-stopping, low on ball handling, and slighlty positive on leaving line and distribution.

3. WAR%: Wins above replacement percentage. Based on this game the goalkeeper would contribute 8,3% to a win.

4. League is Serie A and the rank is 33, which is the current Opta Power Ranking.

Final thoughts

It took quite some time to compile this all and it’s a good start to comparing goalkeeper’s performances across games. It gives me critical information about a goalkeeper after the game and can point me in the direction of where I have to improve the goalkeeper’s performance and/or in lesser extent how the defensive units operate in front of the goalkeeper.

I am very well aware this is the beginning of a model. I think the concepts of making performance models or predictive models is easier to create then to improve. So while I think has potential, I really need to have a look again and improve on the things I’m not happy about.

When I’ve done that, I will create a package for Python so it will be easier to use for everyone that has access to event data and can create these kind of visuals for themselves.