Can Clubs Capture Player Evolution in Football?
Modeling Performance Trajectories with Random Effects and Multi-Level Structures
The following summary critically reviews the research paper titled "Estimating Player Impact over Time: Player-Adjusted Hierarchical Models for Scouting & Performance Evaluation in English Football (Soccer)" by Tahmeed Tureen and Irena Chen. All data, figures, and analysis presented here are drawn from their original work; I do not claim any authorship or ownership of the content. This summary has been written to provide a concise and technically informed synthesis of the paper’s findings, methodologies, and implications, while maintaining fidelity to the authors’ intellectual contributions.
1 Introduction
The paper begins by situating football analytics within the rise of probabilistic models such as expected goals (xG), which assign likelihoods to actions like shots based on contextual features. These models typically rely on event data and include predictors such as shot distance, angle, body part, and more recently contextual elements like defender positioning or goalkeeper location.
However, a key limitation is highlighted: most models do not explicitly include the player as a predictor. As the authors note, “two separate shots that have the same measures for the model predictors will be assigned the exact same xG regardless of who is taking the shot”. This omission contradicts the fundamental assumption that players differ in skill and execution ability.
I have discussed similar approaches before:
Attempts to include players in standard machine learning models face practical challenges, including high-cardinality categorical variables and sparse representations. As a result, these models struggle to estimate individual player impact directly.
A second core issue relates to the structure of football data. Event data is inherently hierarchical, with multiple actions nested within players. This leads to correlated observations, violating the common assumption of independence in many statistical models. The paper explicitly states that “two actions taken by the same player are not independent of each other”.
To address these limitations, the authors build on prior work [16] using hierarchical models, specifically Generalized Linear Mixed Models (GLMMs), which allow player-specific effects to be estimated. These models introduce the concept of Estimated Player Impact (EPI), capturing individual contributions beyond observable predictors.
The key extension of this paper is longitudinal. By incorporating five seasons of Premier League data, the authors aim to model how player impact evolves over time, adding a temporal dimension to the hierarchy. They also extend the framework beyond shots to other actions such as carries and passes, and propose practical applications for scouting.
2 Research Aims
2.1 Data
The study uses Hudl StatsBomb event and 360 freeze-frame data covering 1,900 matches across five Premier League seasons (2020/21 to 2024/25). Each event includes detailed contextual information such as player identity, spatial coordinates, and action characteristics.
A crucial aspect is the multi-level structure of the data. Events are nested within matches, matches within seasons, and most importantly, events are repeatedly associated with players. As shown in the hierarchical diagram (Figure 2), this structure can be expanded to include additional levels such as clubs or matchweeks.
This layered structure enables longitudinal analysis but also increases complexity. A single player can accumulate a large number of observations across seasons, reinforcing the need for models that handle repeated measures appropriately.
2.2 Motivation
The motivation builds directly on Tureen & Olthof [16], who demonstrated that hierarchical models can estimate player effects and produce interpretable statistical inferences. Their findings quantified intuitive football concepts, such as defensive pressure reducing scoring odds by around 15%, and wider shot angles increasing scoring probability by 57%.
However, their work was limited to a cross-sectional perspective, focusing on specific seasons without modeling how player impact changes over time. Additionally, it was restricted to xG, leaving other football actions unexplored.
This paper addresses both gaps. It introduces a longitudinal framework to track player evolution across seasons and extends hierarchical modeling to additional actions like progressive carries and passes into the box.
2.3 Aims
The research defines four primary objectives:
To build GLMMs capable of longitudinal analysis of players.
To apply hierarchical modeling to multiple football actions beyond shots.
To estimate player-adjusted impacts for each action.
To derive generalizable relationships between predictors and outcomes in football contexts.
Importantly, the focus is not on predictive performance but on statistical inference and interpretability, particularly for scouting and evaluation use cases.
I recently shared the full video of a talk I gave at one of football’s leading sports analytics conferences, together with the presentation slides for anyone interested in exploring the ideas in more detail:
The Unfinished Revolution: Why Football Analytics Hasn't Gone Far Enough
Around one year ago I had the opportunity to talk in front of hundreds of people at a sports analytics conference. It was my first time on a stage, discussing some of the ideas and gaps in football analytics that had been on my mind for quite a while.
3 Methodology
The methodology adopts a frequentist framework, consistent with prior work, while acknowledging the potential of Bayesian approaches for future extensions. The models are built across three types of actions:
Shots
Carries into the box
Passes into the box.
3.1 Shots for Expected Goals (xG)
The xG model is formulated as a binary outcome (goal vs no goal). Predictors include continuous variables such as shot distance, angle, and player experience (measured as seasons since debut), along with categorical and contextual variables like body part, defensive pressure, and number of defenders in the shot cone.
The inclusion of “season since debut” is particularly important for longitudinal analysis, ensuring temporal effects are properly modeled. The dataset excludes penalties and direct free kicks to maintain consistency in open-play shot evaluation.
Additionally, the models are stratified, with separate specifications for forwards and all players, reflecting positional differences in shooting behavior.
3.2 Progressive Carries into the Box
Carries are defined as ball movements of at least five metres under control. The response variable captures whether a carry leads to a successful outcome, defined broadly as actions like shots on target, completed passes, or fouls won.
Predictors include carry duration, distance, pressure during and after the carry, and the context in which the carry began (e.g., after a pass or dribble). The model estimates the probability that a carry results in a successful attacking outcome.
The definition of success is deliberately broad, capturing the contribution of carries to subsequent phases rather than immediate outcomes.
3.3 Passes into the Box
The pass models focus on attacking passes into the penalty area, split into two categories: passes from wide areas and passes from central midfield zones. This stratification reflects different tactical contexts and expected outcomes.
The response variable is binary (complete vs incomplete pass), and predictors include pass length, angle, pressure, and defensive context. The model aims to estimate the likelihood of successful delivery into dangerous areas.
This separation allows the analysis to capture differences in how passes function depending on pitch location.
3.4 Generalized Linear Mixed Models
All models are specified as logistic GLMMs. The general structure introduces both fixed effects (predictors) and random effects (player-specific terms).
The core formulation includes a random intercept for each player, allowing each individual to have a unique baseline. This is expressed through a player-specific parameter δ, which adjusts the intercept.
The model is then extended to include random slopes for the season variable, enabling player-specific temporal trends. As described, “the random slope enables the estimation of individual level deviations from the average trend”.
This dual structure allows the model to capture both baseline ability and evolution over time.
3.5 Estimated Player Impact
The random intercept is interpreted as Estimated Player Impact (EPI). Statistically, it represents unexplained variation attributable to the player; in football terms, it captures individual skill effects.
A positive EPI indicates that a player increases the probability of success for a given action, while a negative value suggests the opposite. Players near zero are considered average within the sample.
Because the model uses a logit link, these effects operate multiplicatively on the probability scale, rather than additively.
3.6 Random Slope
The random slope captures how a player’s performance changes over time relative to the league average. A positive slope indicates improvement, while a negative slope suggests decline or stagnation.
The interpretation depends on both intercept and slope. A player may start at a high level but decline slightly, or start lower but improve rapidly. Together, these parameters describe both level and trajectory of performance.
3.7 Limitations & Work-Arounds
The authors acknowledge several practical challenges. Random slope models are computationally demanding and may fail to converge, especially with imbalanced football data.
Certain positions, such as defenders, have fewer events, limiting the ability to estimate reliable slopes. Additionally, football is inherently dynamic, with tactical and contextual changes introducing instability in longitudinal estimates.
To address this, the authors propose a two-stage approach. When full models fail, they stratify the data by season and compare player impacts across seasons. This provides a pragmatic alternative, though it sacrifices some statistical efficiency and the ability to model continuous trends.
4 Data Analysis & Engineering
Before modeling, extensive preprocessing is performed. All target variables are binarized, and player attributes such as preferred foot and primary position are derived from event data. Positions are simplified into four groups: forwards, midfielders, centre backs, and fullbacks/wingbacks.
Continuous predictors are standardized, categorical variables are dummy encoded, and binary variables are one-hot encoded.
4.1 Shots
The initial dataset includes over 47,000 shots from 985 players. After filtering for longitudinal consistency and sufficient sample size, the final dataset contains 39,859 shots from 403 players.
A separate forwards-only dataset is constructed to avoid convergence issues due to positional imbalance.
4.2 Progressive Carries into the Box
Carries are filtered based on spatial criteria and contextual information from related events. Additional variables are constructed to capture pressure and preceding actions.
After filtering for sufficient data per player, the final sample includes 17,501 carries from 179 players.
4.3 Passes
Passes are filtered to include only open-play attacking passes into the box. Dead-ball situations are excluded, and only events with complete freeze-frame data are retained.
Players with insufficient data are removed, resulting in two datasets: one for midfield passes and one for wing passes, each containing tens of thousands of observations.
5 Descriptive Statistics
The descriptive analysis demonstrates both league-level trends and player-level variability.
Figure 4 shows fluctuations in goals across matchweeks and highlights the presence of outlier players who consistently outperform the average. This supports the need for models that capture individual differences.
5.1 Shots
Key findings include that around 30% of shots occur under pressure and that shot types (headers vs weaker foot) are similarly distributed.
Forwards tend to shoot from slightly closer distances and face fewer defenders compared to the full sample, reinforcing positional differences.
5.2 Carries
Carries exhibit high variability in distance, and pressure is more common during the carry than after. Most carries originate from ball receptions rather than dribbles, indicating structured build-up play rather than individual actions.
5.3 Passes
Passes from midfield are more likely to occur under pressure than those from the wing. Wing passes show greater variability in angle and are more frequently aerial, reflecting crossing behavior.
An interesting observation is that while high passes dominate from wide areas, a substantial proportion of ground passes still occur, suggesting tactical diversity in attacking approaches.
6 Model Results
For each action type, the models incorporate a player-level random intercept, while random slopes on season are included where feasible. Notably, the carries model does not converge with random slopes, requiring a stratified workaround.
6.1 Shots
The xG model results are expressed as odds ratios, allowing interpretation in multiplicative terms. Values greater than one indicate increased scoring odds, while values below one indicate reduced odds.
Shot angle emerges as the only strongly positive predictor. A one standard deviation increase in angle leads to a substantial increase in scoring probability, quantified as a 65% rise in odds. In contrast, most other predictors reduce scoring likelihood. For example, each additional defender in the shot cone reduces goal odds by approximately 34%, while shots taken with the non-preferred foot reduce odds by around 21% relative to the preferred foot.
Distance to goal, goalkeeper presence, and defensive pressure also show consistent negative associations. Importantly, these effects are explicitly framed as statistical associations rather than causal relationships.
A small but positive season effect is observed, suggesting that, on average, players slightly improve their scoring outcomes as they accumulate experience.
6.2 Carries
The carry model reveals several interesting and less intuitive relationships. Carry duration has a strong positive association with success, indicating that longer carries are more likely to lead to beneficial outcomes.
Surprisingly, defensive pressure during the carry is also positively associated with success. The authors suggest this may reflect decision-making under pressure, where players are forced into actions that still yield positive outcomes.
Conversely, pressure after the carry, longer carry distances, and carries initiated after a dribble all reduce the likelihood of success. This highlights that context and sequencing matter, not just the action itself.
The season effect is not statistically significant, suggesting limited temporal trends in carry success at the population level.
6.3 Passes
The pass models reveal meaningful differences between passes from midfield and from the wings.
Midfield:
Wings:
One of the most notable findings is that pass length has opposite effects depending on context. Longer passes decrease success probability when played from midfield but increase it when played from wide areas. This reflects tactical differences in how space is exploited across the pitch.
Pass height also plays a key role. Both low and high passes reduce success probability relative to ground passes, although high passes dominate from wide areas.
Additionally, passes under pressure reduce completion probability, particularly for wing passes. Some counterintuitive results, such as headed passes increasing success rates from wide areas, are attributed to small sample sizes and wide confidence intervals.
Overall, the results demonstrate that the same variable can have different effects depending on tactical context, reinforcing the importance of model stratification.
7 Estimated Player Impact Rankings
The Estimated Player Impact (EPI) rankings translate the random effects into interpretable player-level metrics. These rankings do not represent absolute player quality but rather relative contributions within the study sample.
7.1 Expected Goals
Among forwards, Heung-Min Son ranks highest in EPI, indicating the strongest positive impact on shot conversion. His slope is near zero, suggesting consistent performance over time.
A particularly insightful comparison is made with Erling Haaland. Although Haaland scores more goals overall, Son significantly outperforms his expected goals by a larger margin. Son scores from lower-quality chances, while Haaland converts higher-quality opportunities. This difference is reflected in their EPI values.
The authors explain that hierarchical models capture residual variance unexplained by predictors. In this context, Son’s ability to score from difficult situations is absorbed into his player-specific effect. As described, “the random intercept attempts to explain some of the remaining variance: the player predictor explains differences in shot conversion”.
Across other positions, similar patterns emerge. Midfielders like James Maddison and Kevin De Bruyne show high EPI values, reflecting their scoring efficiency relative to opportunity quality.
For defenders, results are less stable due to limited sample sizes, which the authors explicitly caution against over-interpreting.
7.2 Carries into Box
Jack Grealish ranks highest in EPI for progressive carries into the box. His consistently positive EPI across seasons indicates robustness and sustained performance.
Other players such as Martin Ødegaard and Jadon Sancho also rank highly, reflecting their ability to generate value through ball progression.
Because the model could not estimate random slopes, longitudinal insights are derived through season-by-season comparisons. Players with consistently positive EPIs across seasons are interpreted as reliable contributors.
7.3 Passes into Box
In the midfield pass model, Jack Grealish again ranks first, highlighting his dual impact across carries and passes. Players like Rodri and Declan Rice also show strong EPIs combined with positive slopes, indicating improvement over time.
For wing passes, Adam Smith ranks highest, an unexpected finding that illustrates how data-driven approaches can uncover less obvious contributors. The authors explicitly encourage readers to challenge such results through further analysis.
These rankings demonstrate how hierarchical models can surface both expected and surprising insights, offering a complementary perspective to traditional metrics.
8 Case Study: Oliver Glasner’s Crystal Palace
The case study applies the models in a practical scouting context before the 2025/2026 season, focusing on Crystal Palace under Oliver Glasner.
8.1 Attacking Data Trends
The analysis begins by examining tactical structure. Palace predominantly used a 3-4-2-1 formation, with frequent in-game adjustments.
Data shows that wingbacks are heavily involved in attacking phases, particularly in wide and half-space zones. The figures below illustrate that most passes into the box originate from wide areas, with zones 1 and 5 being the most active.
The data also highlights the role of specific players. Tyrick Mitchell and Daniel Muñoz rank highly in touches and passes into the box, reinforcing the tactical reliance on wingbacks.
Carries into the box, however, are concentrated in central zones (7, 8, and 9), with players like Eberechi Eze and Ismaila Sarr driving progression. These carries often lead to subsequent actions rather than deep penetrations, suggesting a structured attacking sequence.
Overall, the descriptive analysis reveals a clear attacking pattern: wide progression through wingbacks combined with central ball carrying by attacking midfielders.
8.2 Estimated Player Impacts for Scouting
The case study then demonstrates how EPI metrics can support recruitment decisions.
For example, the club was assumed to be searching for players to complement Mitchell and Muñoz. By filtering players based on shot assists and EPI for wing passes, the analysis identifies potential candidates such as Sergio Reguilón.
Similarly, when replacing Eze, the models suggest that Ismaila Sarr already provides comparable or superior contributions in carries. By relaxing selection thresholds, additional candidates like Emile Smith Rowe are identified.
These examples illustrate how hierarchical models can guide scouting by combining performance metrics with contextual filtering. The approach is flexible, allowing analysts to adjust criteria based on tactical needs.
9 Discussion
9.1 Findings
The study successfully demonstrates that GLMMs can model football actions in a longitudinal framework while accounting for player-level variability.
The models provide interpretable estimates of player impact and reveal meaningful relationships between predictors and outcomes. Importantly, they extend beyond xG to other actions, highlighting the versatility of hierarchical modeling.
The case study further shows that these models can bridge the gap between academic research and practical applications such as scouting and performance analysis.
9.2 Future Work
The authors propose several extensions. One direction is to analyze data at different temporal resolutions, such as match-level or week-level data, which could provide more granular insights but at higher computational cost.
Another extension is the use of Generalized Additive Mixed Models (GAMMs), which allow for non-linear relationships and smoothing of noisy data. This would require careful model selection and validation.
9.3 Bayesian Methods
Finally, the paper highlights the potential of Bayesian approaches. Unlike frequentist models, Bayesian methods provide full distributions over estimates, offering a natural way to quantify uncertainty.
This is particularly relevant in football, where outcomes are inherently variable. Bayesian methods could also help address convergence issues in random slope models by incorporating prior information.
Although not implemented in this study, this direction is presented as a promising avenue for future research.
Presented at the Hudl Conference
This research was also presented at the Hudl Conference, where the authors break down the models, visuals, and tactical implications in more depth.
If you want to see the framework explained directly by the people who built it, the full talk is worth your time: https://www.hudl.com/blog/hpi-25-tahmeed-tureen-irena-chen
Learn More
Here you have a direct link to get the free xG Mini-Guide, suited for those who want to fully understand the model in 5 minutes.
References
Tureen, T., & Chen, I. Estimating Player Impact over Time. https://static.hudl.com/craft/performance-insights-research-stage/2025/EPI-over-Time-in-English-Football-Tureen-Chen.pdf