Blame for data/annotations/annotations.template.csv

paper_id,annotator,annotation_date,in_scope,scope_rationale,model_name,model_family,model_framework,model_valuation_unit,model_inputs,model_target,model_supervision,model_architecture,model_spatial_resolution,model_temporal_horizon,model_atomicity,action_coverage,outputs_value_scale,outputs_aggregation_levels,data_provider,data_type,data_dataset_canonical,data_leagues,data_seasons,data_n_matches,data_is_public,evaluation_metrics,evaluation_tasks,evaluation_baselines,calibration_reported,uncertainty_reported,evaluation_validated_against_expert_judgment,evaluation_bootstrap_or_ci_reported,splits,practical_use_cases,practical_inference_realtime_capable,practical_interpretability_level,practical_compute_intensity,key_claims,limitations,open_questions,code_released,code_url,code_license,code_implementer,code_maintenance_status,relationships,verified_by_pegah,verified_by_pegah_date,verified_by_david,verified_by_david_date,verification_notes
bransen_2018_pass_contributions,pegah,2026-06-29,true,"Proposes a novel approach to value individual passes during football games by computing the expected reward of the possession (sub)sequence before and after each pass, then aggregates per-player pass contributions per 90 minutes. This is squarely within action valuation / pass valuation.",Pass contributions via possession-subsequence expected reward (k-NN + DTW),possession-value,expectation-based,action,"event type;event subtype;timestamp (half and time);team performing the event;player performing the event;start location (start_x, start_y);end location (end_x, end_y);possession sequence trajectories (interpolated x and y coordinates at one-second intervals);shot location, distance to center of goal, angle to goal posts (for the xG sub-model)",Difference between the expected reward (expected goals) of the possession subsequence after a pass and the expected reward of the possession subsequence before that pass,supervised,"k-nearest-neighbors search over possession subsequences with Dynamic Time Warping (DTW) as distance function, accelerated by clustering subsequences by start/end pitch cells (7x4 grid of 15m x 17m cells -> 784 origin-destination clusters); expected reward labels come from an XGBoost expected-goals model (500 estimators, learning rate 0.01, max depth 5)","continuous (x,y) coordinates; clustering uses a 7-by-4 grid of 15m x 17m cells on a 105m x 68m pitch",until end of the possession (sub)sequence,per-event,passes;set_pieces,expected-goals,per-action;per-player-match;per-player-season,Wyscout (via SciSports),event,wyscout-private,English Premier League;Spanish LaLiga;German 1. Bundesliga;Italian Serie A;French Ligue Un;Belgian Pro League;Dutch Eredivisie,2014/2015;2015/2016;2016/2017;2017/2018,9061,false,logarithmic loss (for predicting game outcomes home win / draw / away win via Skellam distribution over Poisson team-goal models seeded by player ratings),player-ranking;win-probability;scouting,"pass accuracy;prior distribution over game outcomes (48.42% home win, 28.16% away win, 23.42% draw)",false,false,false,false,"Chronological match-level split: train = 2014/2015 and 2015/2016 seasons (4,253 games); validation = 2016/2017 season (2,404 games); test = 2017/2018 season (2,404 games). Evaluation predicts outcomes for 1,172 games in the top-five European leagues.",scouting;post-match-analysis;season-evaluation;transfer-target-id,,partially-interpretable,medium,"Section 2 (Dataset) | The dataset comprises game data for 9,061 games in the English Premier League, Spanish LaLiga, German 1. Bundesliga, Italian Serie A, French Ligue Un, Belgian Pro League and Dutch Eredivisie spanning the 2014/2015 through 2017/2018 seasons.;Section 1 (Introduction) | In the dataset, 75% of on-the-ball actions are passes, 13% are dribbles, 10% are set pieces, and only 2% are shots (over twelve million on-the-ball actions).;Table 2 | Train set contains 4,253 games, 1,878,593 possession sequences, 3,425,285 passes, 95,381 shots, and 9,853 goals; validation set contains 2,404 games, 972,526 possession sequences, 1,998,533 passes, 53,617 shots, and 5,868 goals; test set contains 2,404 games, 970,303 possession sequences, 2,023,730 passes, 54,311 shots, and 5,762 goals.;Table 3 | Clustering by 15x17m grid cells reduces total runtime from 270 minutes (no clustering, 1 cluster, avg cluster size 68,907) to 12 minutes (784 clusters, avg cluster size 87.89); the 5x4m setting takes 150 minutes with 127,449 clusters and avg cluster size 0.54.;Table 4 and Section 4.3 | k=10 is the optimal number of neighbors with logarithmic loss 1.0521, tied with k=5 (1.0521); the approach outperforms the pass-accuracy baseline (1.0800) and the prior-distribution baseline (1.0860).;Table 5 | Ragnar Klavan (Liverpool FC) tops the 2017/2018 ranking with an expected contribution per 90 minutes of 0.1133; Mesut Ozil (Arsenal) ranks second with 0.1034; Toni Kroos (Real Madrid) ranks third with 0.0943.;Table 6 | Among players under the age of 21 with at least 900 minutes in the 2017/2018 season in Europe's top-five leagues, the Dutch Eredivisie or the Belgian Pro League, Teun Koopmeiners (AZ Alkmaar) tops the ranking with 0.0806 expected contribution per 90 minutes, followed by Martin Odegaard (SC Heerenveen) at 0.0639 and Nikola Milenkovic (ACF Fiorentina) at 0.0617.;Table 7 | The five most-similar players to Manuel Lanzini (born after July 1st, 1993, >=900 minutes in 2017/2018) under the 'Lanzini similarity function' are Mahmoud Dahoud (0.9955), Joan Jordan (0.9881), Naby Keita (0.9794), Dominik Kohr (0.9717), and Medran (0.9591).;Section 4.2 | The average reward gained from passes (0.07 goals per team per game) reflects approximately 5% of the average reward gained during games (1.42 goals per team per game).;Section 4.2 | The expected-goals model is trained with XGBoost using 500 estimators, learning rate 0.01, and maximum tree depth 5; DTW is computed using the dtaidistance library without restricting warping paths.",The approach does not currently account for the strength of the opponent.;The approach could more accurately value possession sequences by taking more contextual information into account.;Dynamic time warping may not be the best similarity measure; spatio-temporal convolution kernels are suggested as a future alternative.;More sophisticated techniques for clustering possession sequences should be explored.,"Improve the approach by accounting for the strength of the opponent and by more accurately valuing possession sequences with more contextual information.;Investigate spatio-temporal convolution kernels (e.g., Knauf and Brefeld 2014) as an alternative to dynamic time warping for computing possession-sequence similarities.;Explore more sophisticated techniques for clustering possession sequences.",false,,,,,,true,2026-06-29,false,,
bransen_2019_choke_or_shine,pegah,2026-06-29,true,"Unique angle in the corpus: the paper does not propose a new core action-valuation model but instead conditions player action values on quantified mental pressure. It adopts the VAEP-style contribution rating from Decroos et al. as its 'contribution rating' (V(s_j) - V(s_i)) and adds two novel per-action metrics: a 'decision rating' (chosen action's expected contribution rating minus the expected contribution rating across all possible actions, predicted by a GBT) and an 'execution rating' (action outcome indicator minus predicted success probability). All three metrics are then aggregated across pressure strata (top 20% / middle 60% / bottom 20%) defined by a learned pressure model that combines a pre-game pressure score (Gradient Boosted Ranking Trees trained on 330 pairwise expert rankings) with an in-game pressure score derived from a Bayesian (PyMC3 ADVI) future-goals win-probability model. Captures the mental-pressure-adjusted action value design space.","Mental-Pressure-Adjusted Action Value (Contribution / Decision / Execution ratings stratified by Pressure(g, x_t) = Pressure_pre-game(g) + Pressure_in-game(x_t))",hybrid,hybrid,action,"team ambition features (previous-season result clusters, transfer value of top-20 players, spending on loans, Football Manager reputation score);game importance via Elo-based simulation of remaining fixtures + Kendall-Stuart tau-c between each possible game result and each expected final league outcome;recent performance (points obtained and deviation from Elo-expected performance over last five games);game context (home/away, opponent rivalry from Football Manager data, match attendance, time since coach was appointed);in-game state features for scoring intensity: number of goals scored, goal difference, number of yellow and red cards, difference in Elo-ratings of the teams, average number of attacking passes in the previous 10 time frames, average percentage of duels won in the previous 10 time frames;action features for action-success classifier: action start and end locations, body part used, start and end locations of previous actions in the sequence (end location excluded for shots);game-state features for next-action contribution predictor: current location of the ball, start and end locations of the previous two actions, action types of the previous two actions, speed of the sequence (distance traveled and time covered over last two actions)","Three per-action quantities: (1) Contribution Rating CR(s_i, a_i, o_i) = V(s_j) - V(s_i); (2) Decision Rating DR(s_i, a_i) = ECR|s_i,a_i - ECR|s_i where ECR is the expected contribution rating; (3) Execution Rating ER(a_i, o_i) = [o_i+] - P(o_i+). Action values are then conditioned on per-situation mental Pressure(g, x_t), with Pressure_in-game(t) defined as the sum of the increase in win probability and the increase in tie probability if the team would score at time t, derived from independent Binomial future-goals distributions y_>t,home | theta_t,home ~ B(T-t, theta_t,home) and y_>t,away | theta_t,away ~ B(T-t, theta_t,away).",hybrid,"Pre-game pressure: Gradient Boosted Ranking Trees (max_depth: 6, n_estimators: 50) trained on pairwise expert rankings. In-game pressure / win probability: Bayesian temporal stochastic model with logit(theta_t,home) = alpha_t * x_t,home + beta + Ha and logit(theta_t,away) = alpha_t * x_t,away + beta, priors alpha_t ~ N(alpha_{t-1}, sigma^2), beta ~ N(0,10), Ha ~ N(0,10); inference via PyMC3 Auto-Differentiation Variational Inference (ADVI). Contribution rating V(s): inherited from Decroos et al. VAEP framework (22 action types). Action-success classifier (per action type): Gradient Boosted Trees. Next-action contribution predictor (used for ECR|s_i): Gradient Boosted Trees, two heads estimating P(g_{i+1}+ | s_i) and P(g_{i+1}- | s_i) combined as ECR|s_i = [P(g_{i+1}+ | s_i) - P(g_+ | s_{i-1})] - [P(g_{i+1}- | s_i) - P(g_- | s_{i-1})].","continuous (x,y) action start/end locations",match split into T=100 time frames; in-game pressure and win probability evaluated per time frame; contribution rating evaluated per action via V(s_j) - V(s_i) (single-action delta within VAEP framework),per-event,passes;shots;dribbles_carries;defensive_actions;set_pieces;goalkeeper_actions,value-delta,per-action;per-player-match;per-player-season;per-team-match;per-team-season,"proprietary (SciSports; event data covering EPL, LaLiga, Bundesliga, Serie A, Ligue 1, Eredivisie, MLS)",event,other-private,English Premier League;Spanish LaLiga;German Bundesliga;Italian Serie A;French Ligue 1;Dutch Eredivisie;North-American Major League Soccer (MLS),"2014/2015 (EPL only, for long-term evolution);2015/2016 (EPL only, for long-term evolution);2016/2017;2017/2018;2018/2019 (up to November 11th, 2018)",6858,false,"agreement with annotators' pairwise rankings (73.91% vs 79.79% inter-expert agreement) for the pre-game pressure model;probability calibration deviation (within 2.5% typical, max 9.61%) for the in-game win probability model;Area Under the Precision Recall Curve (AUC-PR) per action type for the action-success classifier (Table A.1);probability calibration deviation (within 3%) for the combined action-success model (Figure A.2);Mean Squared Error (MSE) for next-action P(g_{i+1}+ | s_i) and P(g_{i+1}- | s_i) GBT models (Table A.2);Pearson correlation between average contribution per 90 in high-pressure situations and in last-quarter (fatigue) situations: 0.136",player-ranking;scouting;tactical-pattern-discovery;calibration;win-probability;transfer-recommendation,base rate of action success per action type (for AUC-PR comparison in Table A.1);average next game state value of all actions starting in the same location (baseline MSE in Table A.2);inter-expert agreement of 79.79% (reference for the 73.91% ranker agreement),true,false,true,false,"Pre-game pressure ranker: 330 pairwise rankings on 170 games for training; 483 pairwise ratings on 20 diverse games (relegation, rivalries, underperforming teams, end-of-season dead rubbers) for validation. In-game win probability: 4232 EPL/LaLiga/Bundesliga games (2014/15-2017/18), 70-30 train-test split that respects the temporal ordering of games. Action-success classifier: trained on 2014/15 and 2015/16 of EPL, LaLiga, Bundesliga, Serie A, Ligue 1, Eredivisie and Belgian first division (2,430 games, 2.96M actions); validated on 2016/17 of the same leagues (2,404 games, 2.92M actions). Next-action contribution rating GBTs use the same datasets as Appendix A.3.",scouting;transfer-target-id;post-match-analysis;season-evaluation;opponent-analysis;tactical-pattern-discovery;training-feedback,true,partially-interpretable,medium,"Section 1 (Introduction) and Section 5 (Use Cases) | Methodology was applied to event data for 6,858 matches from 7 leagues (English Premier League, Spanish LaLiga, German Bundesliga, Italian Serie A, French Ligue 1, Dutch Eredivisie, North-American Major League Soccer).;Section 2 (Measuring Mental Pressure) | Total pressure for a game g at game state x_t is defined as Pressure(g, x_t) = Pressure_pre-game(g) + Pressure_in-game(x_t).;Appendix A.1 | The pre-game pressure model is a Gradient Boosted Ranking Trees model (max_depth: 6, n_estimators: 50) fit on 330 pairwise rankings of 170 games provided by a panel of 19 soccer experts; on a validation set of 483 pairwise ratings over 20 diverse games it achieved 73.91% agreement with annotators' rankings, compared to inter-expert agreement of 79.79%.;Section 2.2 (In-game mental pressure) and Appendix A.2 | The in-game win-probability model predicts the number of future goals each team will score after time t as independent Binomial distributions y_>t,home | theta_t,home ~ B(T-t, theta_t,home) and y_>t,away | theta_t,away ~ B(T-t, theta_t,away), with T=100 time frames per match.;Section 2.2 and Appendix A.2 (Figure A.1) | The in-game model is trained with PyMC3's Auto-Differentiation Variational Inference (ADVI) on 2014/2015 through 2017/2018 seasons of the English Premier League, Spanish LaLiga, and German Bundesliga (4,232 games total) using a 70-30 train-test split that respects the temporal ordering of games; predicted probabilities are typically within 2.5% of actual probabilities with a maximum deviation of 9.61%.;Section 3.1 (Contribution rating) | The contribution rating reuses Decroos et al.'s formulation CR(s_i, a_i, o_i) = V(s_j) - V(s_i) over 22 action types (each succeeding or failing).;Section 3.2 (Decision rating) | The decision rating is defined as DR(s_i, a_i) = ECR|s_i,a_i - ECR|s_i, where ECR|s_i,a_i = P(o_i+) * CR(s_i, a_i, o_i+) + P(o_i-) * CR(s_i, a_i, o_i-) and the second term is estimated by a Gradient Boosted Trees predictor of the next action's contribution rating.;Section 3.3 (Execution rating) | The execution rating is ER(a_i, o_i) = [o_i+] - P(o_i+), where [o_i+] is 1 if the action succeeded and P(o_i+) is the calibrated success probability.;Section 4 (Measuring Player Performance Under Mental Pressure) | Pressure levels are stratified globally: high-pressure = top 20% of the ranking, normal-pressure = middle 60%, low-pressure = bottom 20%; performance metrics are then aggregated by stratum (per 90 minutes, per action type, and as percentile ranks).;Appendix A.3, Table A.1 | Action-success classifiers (Gradient Boosted Trees, one per action type) trained on 2,430 games and 2.96M actions and validated on 2,404 games and 2.92M actions outperform the base rate of success across all action types; e.g. Pass AUC-PR 0.9561 vs base 0.8265, Cross 0.5397 vs 0.3144, Throw-in 0.9677 vs 0.8821, Shot 0.3689 vs 0.1094, Tackle 0.7267 vs 0.4575, Take-on 0.8357 vs 0.6991, Goal kick 0.8310 vs 0.5665.;Appendix A.3, Figure A.2 | Combined-action-success probability calibration stays within 3% deviation across the predicted-probability range.;Appendix A.4, Table A.2 | The two next-action GBTs achieve lower MSE than the location-only baseline: P(g_{i+1}+ | s_i) MSE 0.0019 vs baseline 0.0023; P(g_{i+1}- | s_i) MSE 4.0413e-06 vs baseline 4.9139e-06.;Section 5.1 (Player acquisition: Replacing Riyad Mahrez at Leicester City), Figure 4 | Riyad Mahrez performs particularly well in his 986 high-pressure minutes, making both better decisions and executing his shots better; among under-28 candidates Houssem Aouar (547 high-pressure minutes) and Xherdan Shaqiri (1,477 high-pressure minutes) improve their contribution under pressure while Rachid Ghezzal (358 high-pressure minutes) chokes.;Section 5.2 (Training: Dom Dwyer's Fouls), Figure 5 | Dom Dwyer commits significantly more fouls inside the opponent's penalty box under high pressure (916 low-pressure vs 2,135 high-pressure minutes) and a majority of these high-pressure fouls have a negative decision rating.;Section 5.3 (Tactical planning - Manchester United: dribble or cross?), Figure 6 | Manchester United's dribbles per 90 minutes more than double in high-pressure situations (from 19.41 to 43.88), but the contribution from dribbles declines under pressure for all offensive players except Rashford, while contribution from crosses increases under pressure.;Section 5.3 (Throw-ins: better decisions under high mental pressure), Figure 7 | Throw-ins show the largest difference between low- and high-pressure situations: contribution and decision ratings increase under pressure for almost all teams while execution ratings remain the same, suggesting teams miss the opportunity to create danger with throw-ins earlier in games.;Section 5.4 (Lineups and substitutions), Figure 8 | Among Juventus central defenders (Benatia 457, Bonucci 201, Chiellini 470, Rugani 278 high-pressure minutes) Benatia and Bonucci outperform Chiellini and Rugani in high-pressure situations; Di Maria outperforms Draxler under pressure; Giroud outperforms Morata under pressure.;Section 6.1 (Neymar's performances decline under mental pressure), Figure 9 | Neymar's average contribution per 90 minutes drops from 'very high' (997 low-pressure minutes) to 'average' (472 high-pressure minutes); the decline is attributed mainly to poor decision making, while executions improve for all action types under pressure.;Section 6.3 (Liverpool recruitment), Figure 11 | Liverpool's signings since 2017/2018 - Alisson, Oxlade-Chamberlain, Robertson, Fabinho, Naby Keita, Virgil van Dijk and Xherdan Shaqiri - obtained higher contribution ratings in high-pressure than low-pressure situations at their previous clubs, with Keita the only exception.;Section 6.4 (Fatigue), Figure 12 | Pearson correlation between a player's average contribution per 90 in high-pressure situations and his contribution per 90 in the last quarter of games (excluding high-pressure situations) is 0.136, indicating the pressure metric is distinct from fatigue.","Pre-game pressure has no ground-truth label, so the model can only be evaluated against pairwise expert rankings; the learned ranker reached 73.91% agreement vs 79.79% inter-expert agreement, indicating residual disagreement that the model cannot resolve.;Because event data is used, the precise locations of off-ball players on the pitch are unknown, so the expected contribution rating across all possible actions in a state must be estimated indirectly by predicting the next action's contribution rating from the current game state.;For action types where the end location might leak information about success (e.g. shots), the end-location feature is excluded from the action-success classifier, limiting the features available for those actions.;Aggregation of execution ratings across different action types is explicitly avoided because the distributions differ (e.g. shots are typically less likely to succeed than passes), restricting how the execution metric can be summarised per player.;Use-case analyses require players to have played at least 900 minutes including at least 180 minutes in both high- and low-pressure situations, which excludes many players from comparison.;For Olivier Giroud the authors include data from his Arsenal period because there were not enough high-pressure moments at Chelsea, a data-availability caveat the authors flag explicitly.",,false,,,,,extends:decroos_2019_vaep,true,2026-06-29,false,,
bransen_2019_pass_value,pegah,2026-06-29,true,"Introduces ECOM (Expected Contribution to the Outcome of the Match), a pass-valuation metric that measures players' involvement in creating goal-scoring chances by valuing the effectiveness of their passes via distance-weighted k-nearest-neighbors search over historical passes.",ECOM (Expected Contribution to the Outcome of the Match),other,expectation-based,action,"pass start (x,y) location;pass end (x,y) location;pass length;ball location 5 s prior to the pass;ball location 10 s prior to the pass;ball location 15 s prior to the pass;possession sequence membership;expected-goals label of possession sequence outcome","Expected added reward of a pass V(p_i) = V_e(p_i) - V_s(p_i), where the reward of a possession sequence is the expected-goals value of any goal attempt it leads to (0 otherwise).",supervised,"Distance-weighted k-nearest-neighbors over historical passes using a learned six-component domain-specific distance function; passes pre-clustered by origin-destination pitch zones; possession-sequence labels produced by an XGBoost expected-goals model trained on shot location, distance to goal center, and angle to goal posts; weights for the distance function learned via Bayesian Optimization (UCB acquisition, 250 iterations, 10 initial weight sets).","Continuous (x,y) on a 105 m x 68 m standardized pitch; pass-clustering grid uses 15 m by 17 m cells; expected start reward V_s computed over a separate 15 m by 17 m grid.","Until end of current possession sequence (label is the expected-goals value of the possession sequence's terminal goal attempt, if any).",per-event,passes,expected-goals,per-action;per-player-match;per-player-season,Wyscout,event,wyscout-private,English Premier League;Spanish Primera Division;German 1. Bundesliga;Italian Serie A;French Ligue 1;Belgian Pro League;Dutch Eredivisie,2014/2015;2015/2016;2016/2017;2017/2018,9061,false,AUC-ROC;logarithmic loss;mean absolute error (MAE) on market value,player-ranking;win-probability;scouting;transfer-recommendation,QPass approximation;QPass approximation xG;Pass accuracy;Historical prior distribution,false,false,true,false,Match-level chronological split: training set = 2014/2015 + 2015/2016 seasons (4253 matches); validation set = 2016/2017 season (2404 matches); test set = 2017/2018 season (2404 matches). 555 matches with missing/incomplete data (mostly Belgian Pro League and Dutch Eredivisie 2014/2015) were omitted. Match-outcome prediction experiments restricted to English Premier League matches.,scouting;transfer-target-id;season-evaluation;post-match-analysis,,partially-interpretable,medium,"Table 7 | Arsenal playmaker Mesut Ozil tops the ECOM ranking for the 2017/2018 season with an ECOM rating of 0.3440 per 90 min; David Silva (Manchester City) ranks second (0.3156) and Lionel Messi (FC Barcelona) third (0.3055).;Table 8 | Among players under the age of 23, FC Bayern Muenchen winger Kingsley Coman tops the ECOM list with 0.2423 per 90 min, followed by Marco Asensio (0.2269) and Frenkie de Jong (0.2122).;Table 6 | On the 2017/2018 English Premier League match-outcome prediction task, the default ECOM configuration achieves a logarithmic loss of 1.0057, outperforming the historical prior distribution (1.0738), QPass approximation xG (1.0758), pass accuracy (1.0765), and QPass approximation (1.1263).;Section 5.2.1 and Figure 2 | Adding the ball location 5 s prior to the pass increases the distance-function AUC-ROC from 0.500 (random) to 0.703, and including the ball location 10 s prior further increases it to 0.712; including ball locations beyond 15 s yields no further improvement.;Table 10 | Including ECOM as a feature in an XGBoost market-value regression reduces the across-all-players MAE from 7.18 million euro to 6.95 million euro on the 2017/2018 test set (2124 players); MAE drops for every position subgroup (goalkeepers 6.50 -> 6.39M, defenders 6.54 -> 6.14M, midfielders 8.68 -> 7.77M, forwards 13.67 -> 12.71M).;Section 6.3.1 and Table 9 | Within the FC Barcelona squad in 2017/2018, Andres Iniesta has an ECOM rating of 0.2511 (second behind Lionel Messi), and Ajax midfielder Frenkie de Jong is the top-ranked player under 25 most similar to Iniesta in passing behavior and impact (similarity 0.9734).;Section 3 and Section 4.2 and Table 2 | The dataset comprises 9061 matches across the 2014/2015-2017/2018 seasons in seven European top-tier leagues, with 7,447,548 passes, 203,309 goal attempts and 21,483 goals; a match yields on average 2.4 goals and 22.4 goal attempts.;Section 5.1.2 | The expected-goals model is an XGBoost classifier trained on 190,762 shots (after mirroring 95,381 training-set shots) using shot location coordinates, distance to goal center, and angle to the goal posts; with 100 estimators, maximum tree depth 4, and learning rate 0.1, the validation-set AUC-ROC is 0.763 on 53,617 shots.;Section 5.2.3 and Table 5 | The optimal distance-function weight set under the default 15 by 17 m clustering uses only the lengths of the passes and the ball location 5 s prior (weights set to one), with the other components set to zero; the origin and destination locations of the passes are already implicitly accounted for by the clustering step.;Abstract / Introduction | Passes constitute around 70% of all on-the-ball actions in soccer matches; in the present dataset 69% of the 10,846,885 on-the-ball player actions are passes.","No ground truth exists for the true value of a pass, so evaluation is performed indirectly by predicting future match outcomes.;Method values only passes; other action types (shots, dribbles, defensive actions, off-ball runs, set pieces, goalkeeper actions) are not assigned ECOM values.;Only event-stream data is used; the distance function does not incorporate spatio-temporal tracking data of all 22 players.;Computational cost of pairwise pass-similarity search at scale required a clustering pre-step (15 by 17 m origin-destination zones) to fit within 32 GB of memory; the 105 x 68 and 52.5 x 34 settings were excluded for memory reasons.;555 matches with missing or incomplete play-by-play data were omitted from the dataset (mostly 2014/2015 Belgian Pro League and Dutch Eredivisie).;Passes occurring during the first 15 s of each half are omitted because historical ball locations are unavailable.",Incorporate spatio-temporal player tracking data into the distance function to better capture the circumstances under which each pass is performed.;Learn the optimal dimensions for the clustering grid cells from data.;Experiment with grid cells that vary in size depending on the distribution of passes over the pitch.,false,,,,,compares-against:gyarmati_2016_qpass;improves-upon:gyarmati_2016_qpass,true,2026-06-29,false,,
brooks_2016_passrank,pegah,2026-06-29,true,"Introduces Pass Shot Value (PSV) and Average Pass Shot Value (APSV), an early data-driven framework for valuing passes based on their association with shot opportunities, using model weights from a supervised shot-prediction classifier. Directly relevant to the action-valuation / pass-value lineage in the SAVANT corpus.",Pass Shot Value (PSV) / Average Pass Shot Value (APSV),other,expectation-based,action,pass origin location (continuous-valued 18-dim zone-closeness vector);pass destination location (continuous-valued 18-dim zone-closeness vector);origin-destination outer-product features (flattened 18x18 matrix);possession-level aggregation (average of per-pass feature vectors),"Binary outcome of a possession: whether the possession (>= 3 completed passes) ends in a shot taken by the offensive team (y in {1, -1}).",supervised,"L2-regularized linear Support Vector Machine (LIBLINEAR) with asymmetric (class-specific) cost parameters; per-pass value PSV(i,j) = w_i^o + w_j^d + w_ij^od derived from learned model weights.",18-zone pitch grid (3 rows x 6 columns) with continuous closeness-weighted representation to the N=2 nearest zones,until end of possession,per-possession,passes,unitless-rating,per-action;per-player-season,unspecified hand-labeled event-data vendor (Opta is referenced contextually but not stated as the source),event,unknown,La Liga,2012-2013,,false,AUROC;F-score,goal-prediction;player-ranking,goals;assists,false,,true,false,"Chronological game-level split: first 80% of games as training, final 20% as holdout; 5-fold cross-validation on the training set with folds constructed at the game level so possessions in a single game are not split across folds.",scouting;season-evaluation;post-match-analysis,,fully-interpretable,low,"Section 5.1 (Classification Results); Figure 3 | The shot-prediction model has an AUROC of 0.79 and an F-score of 0.31 on the holdout set.;Section 5.1; Figure 1 | 6 of the top 10 most influential features for predicting whether a possession ends in a shot involve zone 14 (the 'critical zone' centered in the field in front of the penalty box).;Section 5.1; Figure 1 | Zone 17 (directly in front of the opposing team's goal) does not appear among the top 10 features.;Section 5.1; Figure 1 | Passes to zone 14 from zone 5 or zone 9 (long completed passes into zone 14) have negative model weights, while the top two features overall are passes between corner areas and zone 14.;Section 5.2 (paragraph after Table 3) | Among players in the 'offense' category, APSV correlates significantly with goals scored over the season (rho = 0.27, p < 0.05), even though goals and assists are not used in computing APSV.;Section 5.2 | APSV is computed only over players with more than 200 completed passes in the 2012-13 La Liga season, and only over passes occurring in possessions of 3 or more completed passes.;Section 5.2; Figure 4; Table 2 | APSV is almost always negative because most possessions do not end in a shot; offensive players like Cristian Tello, Cristiano Ronaldo, Lionel Messi and the midfielder Mesut Ozil have a positive APSV.;Section 3.2; Equation 1 | The 18-zone field representation uses a continuous closeness-weighted vector r^l of length 18 with N=2 non-zero entries, normalized so that the L1-norm sums to 1.;Section 4.1 | Each pass is converted into a feature vector of length 360 (18 origin features + 18 destination features + 324 flattened origin-destination outer-product features); a possession's feature vector is the average over its completed passes.;Section 3.1; Table 1 | On average, each La Liga team attempted around 18,000 passes during the entire 2012-13 season; Barcelona made the most (30,283) and Levante the fewest (13,094).",The analysis does not incorporate temporal information such as duration of possession or time elapsed between passes; the authors note that adding such information would provide more situation-specific insights.;The work uses only event data; the authors state that player-tracking data would better allow investigation into strategic aspects of the game not directly involving the ball.;Features do not capture sequential information within a possession; the authors note that expanding to sequential features could give a more detailed understanding of how passing strategy relates to outcomes.;The model is trained on a single team-agnostic dataset; the authors note that team-specific models built from a team's own event data could provide better analysis of strategies most promising in their system.,"Extend the framework to defensive actions: use actions taken by players on defense to predict defensive outcomes and rank players by defensive ability.;Incorporate temporal information (e.g. duration of possession, time elapsed between passes) into the analysis.;Utilize player-tracking data as the source dataset to study off-ball strategic aspects of play.;Expand features to include sequential information within a possession.;Build team-specific models from individual teams' event-data collections.;Extend the methodology to other sports such as basketball, where passing performance is also primarily measured by assists.",false,,,,,,true,2026-06-29,false,,

decroos_2017_starss,pegah,2026-06-29,true,"STARSS is an action valuation method for soccer that splits matches into phases, assigns phase ratings based on similarity (via DTW) to historical phases that end in a goal, and distributes those ratings across individual actions. It directly fits the action-valuation / possession-value literature.",STARSS (Spatio-Temporal Action Rating System for Soccer),possession-value,expectation-based,action,"event stream of actions (type, timestamp, player, team, x-y location);end location for passes;outcome for shots (off target, on target, goal);x and y coordinates of the actions making up a phase",Phase rating = proportion of the k most similar historical phases (by spatial DTW distance) that end in a goal; distributed to individual actions via exponential-decay action weights,supervised,"k-nearest-neighbors over phases using multivariate dynamic time warping (DTW) on (x,y) action sequences; phase rating distributed across actions using an exponential-decay weighting scheme with parameter lambda","continuous (x,y) coordinates of actions",until end of phase (uninterrupted sequence of actions by one team; new phase on possession switch or >10 seconds gap),per-possession,passes;shots;dribbles_carries;defensive_actions;set_pieces,probability,per-action;per-possession;per-player-match;per-player-season;per-team-match;per-team-season,unspecified (play-by-play event data; co-author affiliated with SciSports),event,unknown,English Premier League;German Bundesliga;Spanish La Liga,2012/2013;2013/2014;2014/2015;2015/2016,4253,false,STARSS rating per 90 minutes;player share of team rating (%),player-ranking;team-ranking,"goals and assists per 90 (traditional metrics);hand-crafted weighted-sum approaches (e.g., WhoScored.com, Squawka.com)",false,false,true,false,"Chronological / temporal: for rating a match, only matches from the same league played before the date of that match are used to discover similar phases; no held-out test split with quantitative metrics reported.",post-match-analysis;season-evaluation;scouting,,partially-interpretable,not-reported,"Section 2 (Dataset) | Dataset comprises 4253 matches, 7,569,802 game events, 110,290 shots, and 11,842 goals across the English Premier League, German Bundesliga, and Spanish La Liga for the 2012/2013 through 2015/2016 seasons.;Section 3.1 (Splitting matches into phases) | A new phase is started each time possession switches between teams or more than 10 seconds pass between consecutive actions.;Section 3.2 (Rating phases), Equations 1-2 | Phase rating is computed as the proportion of the k most similar historical phases (by multivariate DTW distance on (x,y) coordinates) that end in a goal; example: 13/100 similar phases ending in a goal yields rating 0.13.;Section 3.3 (Rating actions), Equations 3-5 | Action weights are computed via exponential decay (w_i = (1 - lambda) * w_{i+1}) with the last action weight set to 1, then normalised to sum to one across the phase, so the phase rating is fully distributed across its actions.;Section 4 (Methodology) | For all case studies, parameters are set to k = 100 and lambda = 0.25 based on domain knowledge and empirical analysis.;Table 1 | Alexis Sanchez tops the 2015/2016 Premier League ranking with a STARSS rating per 90 of 0.289 over 2446 minutes (0.478 goals per 90, 0.147 assists per 90).;Table 2 | Zlatko Junuzovic tops the 2015/2016 Bundesliga ranking with a STARSS rating per 90 of 0.271 (0.153 goals per 90, 0.383 assists per 90).;Table 3 | Lionel Messi tops the 2015/2016 La Liga ranking with a STARSS rating per 90 of 0.387 over 2728 minutes (0.759 goals per 90, 0.528 assists per 90).;Section 5.1 (and Table 2) | Five of the top-15 Bundesliga players play for FC Bayern Munich.;Figure 2 (Section 5.2) | In the El Clasico of 2 April 2016, Lionel Messi contributed 19% of FC Barcelona's team STARSS rating and Gareth Bale contributed 21% of Real Madrid's team STARSS rating.;Section 1 (Introduction) and Section 5.1 | Wingers and attacking midfielders tend to contribute more to a team's STARSS rating than strikers.;Section 3.2 (Rating phases) | Unlike most existing approaches to rate phases in soccer (which only take phases that lead to a goal or shot into account), STARSS rewards teams/players for getting the ball into dangerous places even if the phase does not lead to a shot.",,,false,,,,,,true,2026-06-29,false,,

decroos_2019_vaep,pegah,2026-06-29,true,"Introduces VAEP (Valuing Actions by Estimating Probabilities), a framework for valuing any type of on-the-ball player action in soccer using event stream data, along with the SPADL representation language; central to the SAVANT corpus of action valuation methods.",VAEP (Valuing Actions by Estimating Probabilities),VAEP,expectation-based,action,"SPADL features: action type (categorical);SPADL features: action result (categorical);SPADL features: body part (categorical);SPADL features: (x, y) coordinates of action start location;SPADL features: (x, y) coordinates of action end location;SPADL features: time elapsed since start of the game;Complex features: distance and angle to the goal for start and end locations;Complex features: distance covered during the action in x and y directions;Complex features: distance and elapsed time between consecutive actions;Complex features: whether the ball changed possession between consecutive actions;Game context features: number of goals scored by the team possessing the ball after the action;Game context features: number of goals scored by the defending team after the action;Game context features: goal difference after the action;Previous three actions [a_{i-2}, a_{i-1}, a_i] used to represent each game state","Two binary probabilistic classification problems: P_scores(S_i, x_i) = P(goal scored by team possessing ball in next k=10 actions | S_i) and P_concedes(S_i, x_i) = P(goal conceded by team possessing ball in next k=10 actions | S_i). VAEP value: V(a_i, x) = Delta P_scores(a_i, x) + (-Delta P_concedes(a_i, x)).",supervised,"Gradient-boosted decision trees (CatBoost), chosen over Logistic Regression, Random Forest, and XGBoost based on Brier score and ROC AUC comparison","continuous (x, y)",next k=10 actions,per-action-pair,passes;shots;dribbles_carries;defensive_actions;set_pieces;goalkeeper_actions,value-delta,per-action;per-player-match;per-player-season,Wyscout,event,wyscout-private,English top division;Spanish top division;German top division;Italian top division;French top division;Dutch top division;Belgian top division,2012/2013;2013/2014;2014/2015;2015/2016;2016/2017;2017/2018,11565,false,Brier score;ROC AUC,goal-prediction;player-ranking;scouting,Logistic Regression;Random Forest;XGBoost;No features (predicts mean class probability);Location-only feature set;Action type-only feature set;Location + action type feature set;Goals per 90 minutes;Assists per 90 minutes;Goals + assists per 90 minutes,true,,true,,"Temporal/seasonal split (match-level): first model trained on 2012/2013-2015/2016 to produce outcomes for 2016/2017; second model trained on 2012/2013-2016/2017 to produce outcomes for 2017/2018. Only league games considered; friendlies, cup, and European games excluded.",scouting;post-match-analysis;season-evaluation;transfer-target-id;tactical-pattern-discovery,,partially-interpretable,low,"Section 2.2 and Appendix A.1 | The paper introduces SPADL, a language with 21 possible action types (including passes, crossed corners, dribbles, throw-ins, tackles, shots, penalty shots, clearances, keeper saves), up to four body parts, and up to six possible results.;Section 3.1, Equation 3 (Definition 1) | VAEP value of an action is defined as V(a_i, x) = Delta P_scores(a_i, x) + (-Delta P_concedes(a_i, x)).;Section 4.1 | The framework uses k=10 future actions as the temporal horizon for the scoring/conceding labels, chosen based on domain knowledge and preliminary experiments.;Section 4.2 | Each game state S_i is represented using only the previous three actions [a_{i-2}, a_{i-1}, a_i].;Section 5 and Appendix A.2 | The dataset contains 11,565 games played in the 2012/2013 through 2017/2018 seasons in the English, Spanish, German, Italian, French, Dutch, and Belgian top divisions, with each game containing approximately 1250 actions on average.;Appendix A.2, Figure 4 | The most frequent action types in the converted Wyscout data are passes (64.63%), dribbles (8.69%), and interceptions (5.01%).;Table 3 | CatBoost with all features achieves Brier score 0.01376 and ROC AUC 0.7693 on P_scores, and Brier 0.00547 / AUC 0.7313 on P_concedes; CatBoost performs best across all design choices.;Section 5.6.1, footnote 5 | Only 1.5% (0.5%) of all game states lead to a scored (conceded) goal in the data.;Section 5.6.2 and Table 3 | The full feature set outperforms baseline feature sets (no features; location only; action type only; location + action type) on both Brier score and ROC AUC for both P_scores and P_concedes.;Section 5.2 and Table 1 | The VAEP top-10 player ranking for the 2017/2018 English Premier League season features players (e.g., Kevin De Bruyne, Eden Hazard, Riyad Mahrez) who do not appear in traditional goals/90, assists/90, or goals+assists/90 top-10 lists; the combined market value of the VAEP top-10 (1,110 million euro) exceeds those of goals (862 million), assists (760 million), and goals+assists (947 million) top-10s.;Section 3.2, Equation 4 | Player ratings are computed per 90 minutes as rating(p) = (90/m) * sum_{a in A_p^T} V(a_i), where m is the number of minutes played by player p during time frame T.;Appendix A.3 | Experiments were run on a server with Ubuntu 16.04, 128GB RAM, and two Intel Xeon E5-2630 v4 @ 2.20GHz CPUs (max 20 cores / 40 threads).","The VAEP framework only values on-the-ball actions; defending is often more about preventing the opponent from gaining ball control by clever positioning and anticipation, which is not captured.;It is hard to accurately compare players across leagues because it is easier to perform highly valuable actions in minor leagues (e.g., French, Dutch, Belgian) than in tougher leagues (e.g., English and Spanish); young talents in minor leagues receive higher ratings than those in English and Spanish leagues.;It can be hard to accurately compare players across clubs in the same league, as it is generally easier to perform valuable actions in a top club with strong teammates than in a mid-table club with weaker teammates.;Building trust in the ratings is challenging because traditional scouts are unfamiliar with the way of rating soccer players.;The ratings are slightly less intuitive than traditional metrics such as goals per 90 minutes, which complicates the task for analytically less inclined scouts to understand precisely what the ratings measure.",,true,https://github.com/ML-KULeuven/socceraction,,authors,,extends:decroos_2017_starss;compares-against:singh_2018_xt,true,2026-06-29,false,,

dick_2019_positioning,pegah,2026-06-29,true,Paper learns a value function over multiplayer positionings (game states) from tracking data using deep reinforcement learning; this is an off-ball/state-valuation method directly relevant to the action/state valuation literature.,Deep RL player positioning value function (Dick & Brefeld),neural,reinforcement-learning,state,"x/y positions of all 22 players at 25 fps;x/y position of the ball;partial speeds (sx, sy) movement vectors of all players;ball movement vector;ball possession indicator (+1/-1) for which team has the ball;image-like 9-channel tensor representation (positions of left-to-right team, right-to-left team, ball; x,y speeds for each team; ball x,y speeds)","Value function V(s) = expected discounted return G(s_t) over an episode, where reward is 1 if the ball possession episode ends in a 'success action' (team carries ball into final 25 m of opponent half, or into 18 m area around opponent goal in alternative scenario) and 0 otherwise",reinforcement,"Deep convolutional neural network: three convolutional layers with 32 kernels of size 6x6 and ReLU activations, followed by a fully connected layer of 256 nodes with ReLU, and a single output node V; trained with TD(lambda) (lambda-return) batch reinforcement learning","continuous (x,y) rasterised into a 9-channel image-like tensor of width x height pixels","until end of ball-possession episode (episode terminates when team loses ball, play stops, or a 'success action' is performed)",per-frame,off_ball_actions,probability,per-frame;per-possession,Deutsche Fussball Liga (DFL) / Sportcast GmbH,tracking-2d,other-private,European topflight (unspecified; provided by DFL/Sportcast),,5,false,AUC (area under the ROC curve);standard errors of AUC,goal-prediction;tactical-pattern-discovery,trivial baseline using ball's distance from the goal as a measure of dangerousness (AUC = 0.5 diagonal line),false,true,false,false,"Leave-one-game-out (LOGO) cross-validation: train on four games, test on the remaining game; episodes are flipped in x and/or y during training for data augmentation",post-match-analysis;tactical-pattern-discovery;opponent-analysis,,partially-interpretable,medium,"Section 'Time-dependent AUC' and Figure 3 | Even 13 seconds before the end of a possession phase, the AUC is still strictly above 0.5, indicating the learned value function captures positioning information well beyond uninformed guessing.;Section 'Experimental setup' | The first success scenario (final 25 m) yields 380 successful episodes and 715 unsuccessful episodes with an overall of 11,045 states; the second scenario (18 m around opponent goal) yields 224 successful episodes and 866 unsuccessful episodes with 11,340 states.;Section 'Area-dependent AUC' and Figure 4 | Using only positional information performs worse than using all available information (positions + movement vectors), though the differences are not significant in Figure 3.;Section 'Training procedure' | Discount factor gamma = 0.95 and lambda = 0.7 (chosen via grid-search) were used; batch size of 30 episodes and the Adam optimizer; early stopping via LOGO cross-validation on the training set.;Figure 3 | Average AUC ranges from approximately 0.85 (3 seconds before end of episode) down to approximately 0.65 (15 seconds before end) for the Movements + 25 m success scenario.;Section 'Area-dependent AUC' and Figure 4 | The approach easily beats a trivial baseline using ball's distance from the goal as a measure of dangerousness, which would yield AUC = 0.5.;Conclusion | Authors claim this work constitutes the first purely data-driven approach to machines that read and understand games and thus bridges the gap toward computational tactics.","Experiments are based on only five games of topflight European soccer.;The second success measure (18 m around the goal) has a reduced number of positive training episodes and increased influence of chance on the outcomes, leading to comparable but noisier AUC results.;Authors are not focusing on learning optimal controllers (i.e., not modelling how players should behave optimally) but only how good real players' behaviour is.","Correlations between the dangerousness metric and traditional performance indicators like playing speed, passing, or expansion of teams could be used to group historic episodes against an opponent.;Such groups could be used to automatically devise strategic insights for an opponent (e.g., indicating that counterattacks were more promising than slow play-making or that cross passes led to more dangerous situations) and implemented in the respective game plan.",false,,,,,,true,2026-06-29,false,,
dick_2021_actions,pegah,2026-06-29,true,"Presents a data-driven model that rates actions of players in soccer with respect to their contribution to ball possession phases, using a graph recurrent neural network (GRNN) over players and the ball to jointly predict trajectories and ball-possession success. Extends Dick and Brefeld (2019) from positioning to actions, and derives aggregate performance indicators for player comparison.","GRNN action/positioning rating model (Dick, Tavakol, Brefeld 2021)",graph-neural,reinforcement-learning,state,"Tracking data: xy positions of all 22 players and the ball at 25 frames per second;Velocity of each player and the ball (estimated from differences over the last 0.12 s);Team indicator: whether the player's team is currently in ball possession;Per-player indicator: whether the player currently has ball possession;Indicator whether the team plays in positive x-direction (or vice versa);Indicator whether the player is a goalkeeper;Event data (passes, shots, tackles, etc.) augmenting tracking data for episode/success annotation;Sequence of player and ball states S_T^{0:N} fed into the GRNN","Two jointly learned predictions: (i) movement prediction p^i(Delta x | t, S_T^i) modelled by an MDN over relative xy movements of each player, learned by minimising the negative log-likelihood of observed movements; and (ii) value function V(S_T^{0:N}) = phi_V(u_T), the expected discounted future reward of a ball possession phase, where reward R(S_T^{0:N}) in {-1, 0, +1} is +1 if the team in positive x-direction completes their ball possession by entering the dangerous area while in ball possession, -1 if the opposing team does so, and 0 otherwise; trained with the lambda-return algorithm.",hybrid,"Graph recurrent neural network (GRNN) over a fully connected graph of all 22 players and the ball; two graph layers (GL) with GRU width 1024; attention functions alpha^type, alpha^v and function f_v have a single hidden layer of 512 units; input feature function phi_I has layers of sizes 128 and 256; Mixture Density Network (MDN) head with K=6 Gaussian components (means mu_k and variances sigma_k via two-layer MLPs of 512 units, ReLU and linear/exponential outputs respectively); value head phi_V is a two-layer MLP with 512 units and linear output. Implemented in TensorFlow.","continuous (x, y) from tracking data; evaluation/visualisation also bins the pitch into areas (e.g., 6 m x 6 m cells in Figure 2)","until the end of the current ball possession phase (discounted future reward with gamma in (0,1)); episodes have average length 10.6 s",per-frame,passes;dribbles_carries;defensive_actions;off_ball_actions,value-delta,per-frame;per-action;per-zone;per-player-season,Deutsche Fussball Liga (DFL) / Sportec Solutions,tracking-2d;event,other-private,Bundesliga,2017/2018,54,false,"ROC AUC (overall and per pitch area);L2 distance between observed and simulated player trajectories (with SE and Cohen's d, 95% CI);Mean difference in V between observed and simulated possessions (x 10^-4);Good dribbles per minute;Good passes per minute",goal-prediction;player-ranking;tactical-pattern-discovery;scouting,ConvNet value model of Dick and Brefeld (2019);Trajectory prediction model of Yeh et al. (2019),,true,true,true,5-fold cross-validation over the 54 matches; results reported as averages with SE error bars.,scouting;post-match-analysis;opponent-analysis;tactical-pattern-discovery;season-evaluation,,black-box,high,"Section 3 and Section 4 | A ball possession phase is considered successful if the team carries the ball into an area that extends 2 m outside the penalty box of the opponent (the 'dangerous zone'); this signal appears 1,879 times in the data and serves as a proxy for success.;Section 2 and Section 4 | The model is learned and evaluated on 54 Bundesliga matches from the 2017/18 season, with ball and player positions captured at 25 frames per second, augmented with event data on passes, shots, tackles, etc.;Section 3 | During the 2017/18 Bundesliga season, teams took on average 27 shots per game but only 2.79 were converted into goals; the data sample used here contains 148 goals and 1,450 shots (i.e., 1 goal out of 9.8 shots).;Section 4 | The data consists of 10,626 ball possession phases with an average length of 10.6 s; of those, 1,879 phases possess a non-zero success signal.;Section 3 (Success paragraph) | Reward R(S_T^{0:N}) is +1 if the team playing in positive x-direction completes their ball possession (ball S_T^0 inside the dangerous area and team in possession), -1 if the team in the other direction completes successfully, and 0 otherwise; V(S_T^{0:N}) = E[sum_{t=0}^{T_E - T} gamma^t R(S_{T+t}^{0:N})] with gamma in (0,1), learned by lambda-return.;Section 4 | The architecture used consists of two graph layers with GRU width 1024 and attention functions with a single hidden layer of 512 units; the MDN uses K=6 Gaussian components with two-layer 512-unit MLPs for pi, mu_k, sigma_k; phi_V is a two-layer MLP with 512 units.;Section 4, footnote 4 | The model was implemented in TensorFlow and learning took about 5 h on an Nvidia V100 GPU.;Section 4.1 and Figure 2 (right) | AUC values comparing V as a predictor for true success per small pitch area never fall below 0.64, even well inside the attacking team's own half (center-line at 52.5 m).;Section 4.1 and Figure 4 (right) | On AUC of true outcomes vs learned value functions per ball-to-goal-line distance, the proposed GRNN model significantly outperforms the ConvNet baseline of Dick and Brefeld (2019).;Section 4.2 and Table 1 | For trajectory prediction, the proposed model significantly outperforms the approach of Yeh et al. (2019) in all six role/whole-team settings under a paired t-test with p < 0.01; e.g., over the first 4 s, Whole Team distance is 1.91 +/- 0.07 m (this model) vs 2.16 +/- 0.07 m (Yeh et al., 2019), Cohen's d = -2.44 (95% CI -3.35 to -1.52).;Section 4.3 (Quantifying Player Performance) and Section 4.3.1 | A 'good dribble' is defined as one that increases V by at least 0.06 between the start and end of the dribble; analogously, a 'good pass' increases V by at least 0.06 between the time of the pass and the reception; dribble and pass effectiveness scores are aggregated per player among those who played in at least two full games.;Tables 2 and 3 | Top players by Good Dribbles per Minute (Table 2) include Kingsley Coman (0.078), T. Ito (0.063), A. Rebic (0.059), Jadon Sancho (0.053), A. Robben (0.053); top players by Good Passes per Minute (Table 3) include Jadon Sancho (0.058), Thiago (0.054), L. Rupp (0.054), K. Demirbay (0.050).;Table 4 | Top pass receivers by Good Passes per Minute (Table 4) include Breel Embolo (0.058), R. Lewandowski (0.057), A. Kramaric (0.056), James Rodriguez (0.054).;Section 4.3 and Table 5 | Mean differences in V (x 10^-4) between simulated and observed defending-team trajectories are small (~10^-4); during successful possessions, midfielders, wingers and attackers have a stronger negative influence on the outcome than defenders (e.g., Midfield: 1.0; Striker: 0.8; Winger: 1.0; Defense: 0.4).","The data only contains coordinates of players; their pose is ignored, so it is not always clear whether players are standing or lying, walking forward or backward.;A player who loses the ball due to a tackle may be physically pushed to the ground (without being fouled) and thus not able to track back immediately; this fact is unknown to the model.;Due to the conceptual approach, the model provides the same solution for all players in the same situation; it is not personalized and does not remember players across games or take a player's in-game history into account.;The model is oblivious to the state of the player regarding mental and physical fatigue.;Personalization would require access to additional data sources (load monitoring, self-perception of fatigue, stress, hours of sleep, muscle pain).;The dataset consists of only 54 games, and several players simply do not have enough games in the dataset to qualify for the player rankings.;The model is trained to estimate whether a ball possession phase reaches the dangerous zone just outside the penalty box, so many strikers may not appear on the player lists just because they typically operate closer to the goal.;Many shots and goals originate from set pieces and are not suitable for use as an outcome of a ball possession phase; the authors instead use a 'dangerous zone' proxy.","Incorporating additional 'orthogonal' physiological or psychological data via a player embedding layer or by extending the input function phi_I (Equation 6) to personalise the model.;Whether the value function and derived performance indicators can serve as the basis for retrieval systems that automatically find complex tactical situations (pressing, counter-attacks) in match databases.",false,,,,,extends:dick_2019_positioning;compares-against:dick_2019_positioning,true,2026-06-29,false,,
fernandez_2019_epv,pegah,2026-06-29,true,"Introduces a soccer-specific Expected Possession Value (EPV) framework that estimates the instantaneous expected outcome of a possession frame by frame from full-resolution spatiotemporal tracking data, decomposing EPV into independently estimated pass, ball-drive, and shot sub-models; a foundational EPV-style method for the SAVANT corpus.",EPV (Expected Possession Value) framework for soccer,EPV,expectation-based,state,"Full-resolution spatiotemporal optical tracking data (22 players + ball);Pitch control surfaces (from a recent statistical pitch-control model, ref [9]);Pitch influence surfaces;Spatiotemporal features for passes and ball-drives (positional, motion, contextual);Relative location features defined by the opponent's dynamic formation lines (first, second, third pressure lines obtained via spectral clustering of mean X coordinates of defending players in a fixed 2-second window with 3 clusters);Movement, distances, and angles between players and locations;Expert-guided handcrafted contextual features","Instantaneous expected possession value EPV(t) = E[X | T_t], a real number in [-1, 1] expressing the likelihood of the possession ending in a goal for the attacking team (+1) or a goal by the defending team (-1) after an immediate possession regain; decomposed as EPV(t) = E[X|A=rho]·P(A=rho) + E[X|A=zeta]·P(A=zeta) + E[X|A=delta]·P(A=delta) over pass (rho), shot (zeta), and ball-drive (delta) actions, with the pass component further decomposed into expected value of successful pass, expected value of turnover, and pass probability.",supervised,Decoupled / decomposed model with independently estimated component sub-models: pass and turnover probabilities estimated with logistic regression; action likelihood modeled by a convolutional neural network on top of pitch control and pitch influence surfaces; pass and ball-drive value expectations learned by carefully designed deep neural networks; shot/expected-goals component described as a variant of expected-goals models. All components calibrated for accuracy at the component level as well as at the joint EPV level.,"continuous (x, y) over full-resolution tracking; value surfaces evaluated for every possible destination location on the pitch; defensive pressure lines obtained by spectral clustering into 3 vertical groups (relative zones Z1–Z4)","until possession ends (expected outcome of the current possession, evaluated frame by frame; ball-drives discretised every quarter of a second for the decision-making analysis)",per-frame,passes;shots;dribbles_carries;off_ball_actions,probability,per-frame;per-action;per-possession;per-player-match,"STATS LLC (optical tracking, 2012-2013 Premier League season); Footvision (optical tracking, FC Barcelona matches in 2017-2018 and 2018-2019 La Liga seasons)",tracking-2d,other-private,Premier League;La Liga,2012-2013;2017-2018;2018-2019,,false,,tactical-pattern-discovery;player-ranking;decision-recommendation,,true,,,,,post-match-analysis;opponent-analysis;tactical-pattern-discovery;in-game-decision-support;scouting,,partially-interpretable,,"Section 2 (An expected possession value (EPV) framework) | EPV is defined as a real number in the [-1, 1] range, expressing the likelihood of a possession ending in a goal for the attacking team (1) or a goal by the defending team (-1) after an immediate possession regain.;Section 2, Equation (1) | EPV is decomposed as EPV(t) = E[X|A=rho]·P(A=rho) + E[X|A=zeta]·P(A=zeta) + E[X|A=delta]·P(A=delta), where the three components are passes (rho), shots (zeta), and ball-drives (delta).;Section 2, Equation (2) and Figure 2 | The passing component is further decomposed as E[X|A=rho] = E[X|A=rho, O_rho=1]·P(A=rho, O_rho=1) + E[X|A=rho, O_rho=0]·P(A=rho, O_rho=0), separating expected value of successful pass, expected value of turnover, and the pass probability model.;Section 2 (paragraph after Figure 2) | Pass and turnover probabilities are estimated using logistic regression; action likelihood is modeled through a convolutional neural network on top of pitch control and pitch influence surfaces; pass and ball-drive value expectations are learned from a set of carefully designed deep neural networks.;Section 2 (last paragraph) | Models were fitted using optical tracking data provided by STATS LLC for the 2012-2013 Premier League season, as well as optical tracking data provided by Footvision for FC Barcelona matches in the 2017-2018 and 2018-2019 La Liga seasons.;Section 2 (paragraph after Figure 2) | All component models are carefully tuned and calibrated for accuracy at the component level as well as at the joint EPV level.;Section 3 (The role of context within the unpredictable sport) | Defensive formation lines are extracted by applying spectral clustering to mean X-coordinate positions of each defending team player in a fixed 2-second time window, with the number of clusters fixed to three, yielding first, second, and third pressure lines.;Section 4 (Value: The missing key to pass analysis) | Passing is the most frequent action in soccer, reaching over 800 passes per match on average.;Section 2 and Figure 1 | In a Real Madrid vs FC Barcelona possession example, at the start of the possession EPV reaches -0.09 due to high spatial pressure from the opponent; a subsequent back pass increases EPV considerably (up to 0.04) by providing better conditions to further the possession up the pitch.;Section 5.1 (Off-ball demands according to positions) | Off-ball value is computed every time a pass is taken and every 1 second of ball-drives, taking into consideration all 10 teammates in each case (not just the player receiving the pass).;Section 5.1 and Figure 8 | Defenders are positioned in locations with low expected loss of value and low expected gain of value; the distribution widens for midfielders to a [-0.1, 0.1] range of expected EPV added; forwards show a higher tendency to move towards locations of higher value.;Section 6 (Decision making analysis) | For the decision-making analysis, ball-drives are split into discrete actions every quarter of a second; the set of possible actions is discretised by selecting the best pass location for every teammate, the location of the player in the next second according to his velocity for the ball-drive component, and the event of shooting from the current location.;Section 6 (Decision making analysis) | In a possession example, Sergi Roberto's ball-drive starts from a current EPV of 0.04 with two passing options that would have increased EPV up to 0.082; intense pressure during the drive decreases EPV down to -0.11.;Section 6 (Decision making analysis) | The model is trained to obtain the expected result for every action on an average player of the Premier League and Spanish League (the data used for training), but does not have individual player information.","The tracking data lacks body orientation information, so the model cannot understand that certain passes are more difficult than they appear (e.g., a forward pass requiring significant body rotation).;The model is trained on an average player of the Premier League and Spanish League and does not incorporate individual player information; in particular, individualised effects for players such as Messi keeping the ball would likely change the expectation of ball-drive in those situations.","Identification of possession plateaus — windows of time where the possession is stabilised without variation — and extraction of actions that produce the jump between one plateau and another.;Extension to derive a wide set of metrics from frame-by-frame EPV curves (e.g., actions that increase/decrease possession EPV above/below a threshold) filtered by action type, field location, opponent relative location, and other contextual variables.;Application to opponent scouting by identifying locations and situations where a player is more likely to be located to increase the likelihood of the possession ending in a goal.",false,,,,,,true,2026-06-29,false,,
liu_2020_deep_soccer,pegah,2026-06-29,true,"Paper develops a Deep Reinforcement Learning model to learn an action-value Q-function for evaluating all types of on-the-ball soccer actions from event data, and derives the Goal Impact Metric (GIM) player ranking. Directly within SAVANT's action-valuation scope.",Two-Tower Dynamic Play LSTM (TTDP-LSTM) with Goal Impact Metric (GIM),neural,reinforcement-learning,action,"Game Time Remaining;X Coordinate of ball;Y Coordinate of ball;Manpower Situation;Goal Differential;Action (one-hot);Action Outcome (success/failure);Velocity of ball;Event Duration;Angle between ball and goal;Home or Away Team;play history sequence (s_t, a_{t-1}, x_{t-1}, ..., x_0)","Q_team(s,a) = P(goal_team = 1 | s_t = s, a_t = a): probability that team (Home/Away/Neither) scores the next goal given current state and action",reinforcement,"Two-tower stacked LSTM (one tower per home/away team); each tower is a two-layer LSTM with 256 hidden nodes plus an embedding layer and two hidden layers with 256 nodes; outputs normalized via softmax to produce Q_Home, Q_Away, Q_Neither; trained with on-policy Temporal Difference (Sarsa) and a dynamic-possession LSTM trace length (max 10 steps); Adam optimizer with initial learning rate 10E-04 (general) and 10E-05 (fine-tuning). Interpretability via CART mimic regression tree.","continuous (x,y) on adjusted [0,100] x [0,100] pitch",until end of current goal-scoring episode (next goal or end of game),per-event,passes;shots;dribbles_carries;defensive_actions;set_pieces,probability,per-action;per-player-season,Opta,event,opta-private,English Premier League;Dutch Eredivisie;EFL Championship;Italian Serie A;German Bundesliga;Spanish La Liga;French Ligue 1;German Bundesliga Zwei,2017-2018,2976,false,"Mean Absolute Error (MAE) between estimated and empirical scoring probabilities;Correlation with standard success measures (Goals, Assists, Shots per Game, Pass Success percentage, Key Passes per game, Yellow cards, Red cards);Round-by-round correlation with season totals (assists, goals);Paired t-test (significance test between player evaluation metrics)",player-ranking;calibration;action-ranking;goal-prediction,"Plus-Minus (PM);Expected Goals (XG);Scoring Impact (SI) (Schulte et al. 2017a Markov model);VAEP (Decroos et al. 2019);M-GIM (merged single-tower variant of TTDP-LSTM);DP-LSTM (Liu and Schulte 2018, ice hockey)",true,false,true,false,Not explicitly described as train/val/test splits; model is fit on the full 2017-2018 multi-league dataset (over 4.5M events) with fine-tuning on EFL Championship league-specific data. No explicit match-level holdout described.,season-evaluation;scouting;transfer-target-id;post-match-analysis,,partially-interpretable,high,"Section 6.2 and Table 4 | The trained TTDP-LSTM achieves average MAE below 0.1 for all bins of context features (Manpower, Goal Differential, Period), significantly outperforming the discrete-state Markov Model baseline.;Table 10 | GIM achieves the highest correlation with 4 out of 5 positive success measures (Goals 0.844, Assists 0.498, SpG 0.596, KeyP 0.562) over players in all 10 leagues; only GIM and M-GIM show negative correlations with yellow/red cards.;Table 11 | Fine-tuned FT-GIM achieves the highest correlations with Goals (0.736), Assists (0.585), SpG (0.569) and KeyP (0.592) for EFL Championship players, and the largest negative correlations with Yellow (-0.110) and Red (-0.171) cards.;Section 9.1 (Significance Test) | Significance test (paired t-tests) rejects the null that GIM equals other player evaluation metrics with p-values 9.33E-2, 5.27E-281, 8.03*E-218, 4.82E-14 and 1.02E-118 for PlusMinus, XG, SI, VAEP and M-GIM respectively.;Section 7.3 (Proposition 1) and Appendix A | Proposition 1: For each player i, his Q-value-above-replacement equals his goal impact metric (QAAR^i(D) = GIM^i(D)), unifying the two fundamental approaches to player evaluation in an RL framework.;Table 3 | The dataset contains 4,679,354 events, 5,510 players, 2,976 games, 164 teams across 10 European leagues in the 2017-18 season.;Section 8.1 and Table 7 | Top-ranked player by GIM over the EFL Championship 2017-2018 season is Matej Vydra (GIM=18.017, 21 goals, 4 assists), who won the 2017-18 Golden Boot and was signed by Burnley the next season.;Section 6.1 (Spatial Projection) and Figure 5 | Spatial Q-value generalization shows that shot, pass, and cross Q-values increase with proximity to the opponent's goal, while defensive tackling Q-value increases with proximity to the team's own goal.;Section 5.2 (Training Settings) and Section 9.1 | TTDP-LSTM training uses Adam optimizer with initial general learning rate 10E-04 over 4.5M events (4,386,894 gradient steps) and fine-tuning learning rate 10E-05 on EFL Championship data (818,120 gradient steps).","Partial observability: the dataset records only positions and actions of the on-the-ball player; positions of off-ball players are unknown. The recurrent model partially compensates by inferring missing information from history, but performance is still limited by partial observability.;Big input data problem: the dataset has over 4M events including spatial/temporal features, making it difficult to use standard machine learning packages that fit entire data in memory; future work will explore online learning methods.;Convergence of on-policy TD with non-linear (neural) function approximators is not theoretically guaranteed; the authors mitigate by constraining look-ahead to the next goal and removing the discount factor.;Sparsity of goals in soccer makes reinforcement-learning style training challenging; the TD solution propagates scoring signals to previous events to address goal sparsity.","Building a multi-agent reinforcement learning framework that combines fully observable tracking data with event categories, possibly by combining the deep RL tracking model of Dick and Brefeld (2019) with this event-based deep RL model.;Exploring on-line learning methods to improve scalability on large sports datasets and to update player assessments after every round.;Incorporating tracking data into the framework.",false,,,,,compares-against:decroos_2019_vaep;improves-upon:decroos_2019_vaep,true,2026-06-29,false,,
llana_2020_off_ball_advantage,pegah,2026-06-29,true,"Introduces off-ball advantage (a probabilistic detector of when a player controls a valuable space such that passing to that player would substantially increase EPV) and effective value added (a long-term attribution of EPV to on-ball and off-ball actions), built on top of EPV pass-component values computed from tracking data. Also introduces a defensive area assignment via dynamic Voronoi over the opponent's expected formation to detect 'passes behind the back'. Directly relevant to action valuation, off-ball value, opponent scouting, and tactical pattern discovery in the SAVANT corpus.",Off-ball advantage detector + effective value added (with defensive-area passes-behind-the-back metric),hybrid,hybrid,both,"EPV before the execution of the pass;Distance and angle to the opponent's goal of the origin of the pass;Distance and angle to the opponent's goal of the destination of the pass;The potential value added by the pass, as the difference between the EPV expected at the destination of the pass and the current EPV just before the execution of the pass;Spatiotemporal tracking data (25 fps) and event data from FootoVision and Metrica Sports;Dynamic formation lines of the defending team computed via k-means clustering with k=3;Dynamic defensive formations built from mean vectors between players in 2-minute defending windows, resized and centroid-aligned to the current defensive block at each pass;Voronoi diagram over the expected (formation-derived) positions of defenders to assign defensive areas",Probability that a potential pass would become a short-term off-ball advantage (i.e. that the receiver's subsequent action ends with a higher possession value than at the start of the previous pass); effective value added per action as a fraction of the final possession EPV.,supervised,"XGBoost binary probabilistic classifier (best hyperparameters: 2000 estimators, learning rate 0.01, max depth 4; random state 10; stratified shuffle split 70/30; 10-fold cross-validation). Auxiliary rule-based / geometric components: k-means (k=3) for dynamic formation lines; dynamic Voronoi diagram over defenders' expected positions for defensive area assignment; deterministic attribution rule that distributes the final possession EPV across on-ball actions proportionally to their (positive) value added (effective value added).","continuous (x, y) from tracking; defensive zones derived from a Voronoi tessellation over the defenders' expected positions; defensive formations clustered into 3 lines via k-means","short-term for off-ball advantage (the receiver's immediately following action, with EPV evaluated when the pass arrives and at the end of the following action); until possession ends for effective value added; dynamic defensive formations built over 2-minute windows of defending",per-action-pair,passes;dribbles_carries;defensive_actions;off_ball_actions,probability,per-action;per-possession;per-player-match;per-team-match,"FootoVision (event data) and Metrica Sports (spatiotemporal tracking data, 25 fps)",event;tracking-2d,club-proprietary,La Liga;UEFA Champions League,2018-2019;2019-2020,65,false,"ROC curve / ROC-AUC (curve shown in Figure 3; train log-loss 0.554, test log-loss 0.578 as labelled in the calibration legend);calibration plot (reliability curve, Figure 3)",tactical-pattern-discovery;player-ranking;scouting,,true,,,false,"Stratified shuffle split into train/test with a 70/30 ratio, preserving the percentage of positive and negative samples; 10-fold cross-validation for hyperparameter tuning; random state 10. Splits are at the example (pass) level rather than at the match level.",opponent-analysis;scouting;post-match-analysis;tactical-pattern-discovery,true,partially-interpretable,low,"Section 3 (Exploiting spaces of value) | Off-ball advantage is defined as a situation where a player is in a favorable disposition to receive a potential pass and, in case of receiving it, the player would likely improve the possession's value.;Section 3.1 (Methods) | The off-ball advantage detector is a probabilistic binary classifier whose features are: EPV before the execution of the pass; distance and angle to the opponent's goal of the origin and destination of the pass; and the potential value added by the pass (EPV expected at the destination minus current EPV just before the pass).;Section 3.1 (Methods) | The dataset consists of 65 matches played by FC Barcelona during the 2018-2019 and 2019-2020 seasons (both La Liga and UEFA Champions League), with event data and spatiotemporal tracking data provided by FootoVision and Metrica Sports at a frame rate of 25 fps; selecting all passes and the receiver's following action yields 46,780 examples; passes with negative potential value added are excluded.;Section 3.1 (Methods) | An XGBoost classifier was trained and tuned via 10-fold cross-validation; the best hyperparameters were 2000 estimators, learning rate 0.01 and depth 4; random state 10; stratified shuffle split into train and test sets at a 70/30 ratio, preserving the percentage of positive and negative samples.;Section 3.1 and Figure 3 | The model is correctly calibrated and the ROC curve achieved is shown in Figure 3; the figure legend labels XGBoost train log-loss 0.554 and XGBoost test log-loss 0.578.;Section 3.2 (Where do players create positional advantages?) | Three attack phases are defined for regular play (buildup, progression, finishing), and the three formation lines of each team are computed dynamically using the k-means clustering algorithm with a fixed value of k=3.;Section 3.2 and Figure 4 | Messi creates positional advantages between the middle and rear defensive lines mostly in the center of the block (even though his nominal position is right winger), while Coutinho produces somewhat fewer off-ball advantages mostly inside the defensive block but less centric — a typical trait of FC Barcelona wingers leaving the wings free for the full backs.;Section 4.1 (Methods) | Dynamic defending formations are built using the mean vectors between players in 2-minute windows when the team was defending; the formation is then resized to match the spread of defenders at the moment of the pass and its centroid aligned with the current centroid of the defensive block.;Section 4.1 (Methods) | A Voronoi diagram over the expected (formation-derived) defender positions assigns the area of the field to each player; the defender responsible for a pass is the one whose expected defensive location is closest to the position of the receiver. A 'pass behind the back' is detected when the receiver of the pass is closer to the goal than that defender.;Table 1 (Section 4.2) | Table 1 reports the number of passes received behind the back of midfielders when a center back was the closest player in front of the ball, for Team A (3 games, seasons 2018-2019 and 2019-2020) and Team B (4 games, season 2018-2019); Team A: LCB-LCM 14, LCB-RCM 7, RCB-LCM 9, RCB-RCM 13; Team B: LCB-DM 3, RCB-DM 10.;Section 5 (Attributing the long-term contribution) | Effective value added is defined as a percentage of the final EPV of the possession assigned to each on-ball action, calculated by dividing the value added to the EPV by that action by the sum of the equivalent values for all on-ball actions of the possession; actions with negative value added are discarded from the sum.;Section 5.1 and Figure 9 | Figure 9 reports two defensive stats normalized per 90 minutes for two UEFA Champions League group stage games (TOT-FCB 2018-2019 and INT-FCB 2019-2020): number of passes received behind the back per defender and mean effective value added of those passes; Barcelona generated their most dangerous attacks against Tottenham via key passes behind Trippier and Davies, whereas Inter generally maintained a more compact block, with Barella as the main exception (bypassed twice with high effective value added).","Deciding the threshold to discern true off-ball advantages from noise is not straightforward because EPV is non-linear and is affected by several dynamic factors (opponent pressure, player movements, pitch control).;Deciding who is responsible for a defensive error is a complex task; it is normally not a single action but an accumulation of events, so the passes-behind-the-back metric is intended to highlight trends across game sequences rather than to attribute a single error definitively.;A static defensive area approach would be expected to produce noisy and imprecise estimates due to the constant movement of the defensive block and role changes, motivating the dynamic formation-based assignment used here.",,false,,,,,extends:fernandez_2019_epv,true,2026-06-29,false,,

merhej_2021_daxt,pegah,2026-06-29,true,"The paper introduces DAxT (Defensive Action Expected Threat), a deep-learning model that values defensive actions (interceptions and tackles) in football event-data by predicting the xT of the passage of play that the defensive action stopped from happening. This is a canonical defensive-action valuation method.",Defensive Action Expected Threat (DAxT),neural,expectation-based,action,"xT of preceding events in the sequence;x,y pitch coordinates of preceding events;fixed number of actions a=2 preceding the defensive action (per Experiment 1);SPADL-converted event-stream data (event type, location, time, player/team ID, result)","xT of the event that would have happened after the defensive action (i.e. f(e_n) = Theta(S_a)), where the predicted xT is then used as the value (I_V or T_V) of the interception or tackle",supervised,"Multi Layer Perceptron (MLP) built with Keras; 3 dense hidden layers with 10 neurons each, ELU activation, MAE loss, Adadelta optimizer, trained for 50 epochs; inputs MinMax-scaled with Scikit-Learn's MinMaxScaler","16x12 pitch grid (inherited from the xT model in Equation 2); raw (x,y) coordinates used as MLP inputs",next event after a sequence of a=2 preceding actions (i.e. predict xT of the event that would have followed the defensive action),per-event,defensive_actions,value-delta,per-action;per-player-season,StatsBomb,event,statsbomb-private,English Premier League,2017/2018;2018/2019,760,false,Mean Absolute Error (MAE);Levene test (variance of residuals);Kolmogorov-Smirnov (KS) test;Q-Q plot of normalized residuals;Pearson correlation coefficient (r) vs. actual values;Pearson correlation coefficient (r) vs. market value (Transfermarkt),player-ranking;action-ranking,baseline model predicting 0's (MAE = 0.0267);CIES Football Observatory and InStat Performance Index (2019 season) for ranking comparison,false,false,true,false,Random 80-20 train/validation split on event-level instances (not by match); test set used in Experiment 3 for MAE evaluation.,scouting;transfer-target-id;post-match-analysis;season-evaluation,,partially-interpretable,low,"Section 1 (Introduction, contribution 2) | Using real-world data from 760 real-world football games from the past two seasons of the English Premier League (EPL), we train and test our model and find that we can accurately predict the impact of future events to an MAE of 0.015.;Section 5.3 (Experiment 3: Model Prediction) and footnote 8 | On the test set, the model returned an MAE loss of 0.016 (compared to a baseline model predicting 0's which would have a MAE of 0.0267).;Table 2 (Section 5.1) | a=2 was selected as the optimal number of actions in a passage of play; Training Loss = 0.0154, Validation Loss = 0.0153, Training Data = 802,046, Interceptions = 75,691, Tackles = 17,423.;Section 5.3 | Levene test returned a statistic value v = 1.209 and p-value p = 0.272 (>0.05), indicating training and testing residuals have the same variance.;Section 5.3 | Kolmogorov-Smirnov test returned v = 0.0174 and p = 0.8333 (>0.05), suggesting the two probability distributions are the same.;Section 5.3 (Q-Q plot discussion, Figure 3) | 96.1% of the data was between 0.05 and -0.05 in the residual visualization.;Section 5.3 | Pearson correlation test between model predictions and actual values resulted in r = 0.0985 with p-value less than 0.05.;Section 5.4 (Experiment 4: Valuing Defenders) and Figure 4 | Pearson correlation between defender score and market value (top 25 center backs, full backs and defensive midfielders) resulted in r = 0.533 and p = 3.37 x 10^-6.;Table 3 | Top 10 players with most cumulative I_V (interception value): James Tarkowski (1.605), Ben Mee (1.576), Nathan Ake (1.537), Lewis Dunk (1.508), Shane Duffy (1.473), Harry Maguire (1.457), Virgil van Dijk (1.447), Christopher Schindler (1.411), Jamal Lascelles (1.386), Steve Cook (1.357).;Table 4 | Top 10 players with most cumulative T_V (tackle value): Wilfred Ndidi (0.435), Christopher Schindler (0.4), Idrissa Gana Gueye (0.384), James Tarkowski (0.38), Cesar Azpilicueta (0.353), Nathan Ake (0.335), Luka Milivojevic (0.318), Aaron Wan-Bissaka (0.315), Ben Mee (0.292), Harry Maguire (0.286).;Tables 9 and 10 (Section 7.1) | Center Back ranking by defender score is topped by Virgil Van Dijk (37.901), Harry Maguire (36.3), Ben Mee (35.942), James Tarkowski (34.733), Shkodran Mustafi (34.636); 5 of the top 6 full backs (Table 10) have a low average of goals conceded/appearance with a high number of assists relative to the rest.;Equation 4 (Section 4.3 / start of Section 5) | The overall defender score is computed as Sc = ((I_V + T_V + CxT) / 3 + PxT) / 4, where I_V is interception value, T_V is tackle value, CxT is Clearance xT, and PxT is Pass xT; cumulative values per player are normalized to a 0-100 score.;Appendix A.1 (Data Conversion) | The dataset (StatsBomb event data for EPL 2017/18 and 2018/19, 760 games) was converted with SPADL; 75,691 interceptions and 17,423 tackles were available to value.","Some defensive actions will be valued less than they should be due to unique passages of plays; e.g., in a 3v1 counterattack situation in the middle of the pitch, even if the defender intercepts the ball, the model would not highly reward this action because similar passages of play are not usually of high threat (without taking into consideration the number of defenders behind the ball).;Future work for valuing defenders' contributions should be centered around the growing collection of tracking data to assess off-ball contributions and movement of defenders with models such as pitch control, evaluations of opposition marking, and stopping events before they have happened; however, due to the low availability of tracking data at this time, especially across different leagues, event-data approaches remain key.;DAxT depends on another player metric (xT), which becomes a problem in terms of interpretation: people need to understand Expected Threat first in order to comprehend the DAxT model.;Metrics such as Possession Adjusted Interceptions and True Tackle Win % are slightly more intuitive than DAxT ratings, complicating the task for analytically less inclined scouts to fully grasp the ratings.;Comparing DAxT to other baseline models remains difficult due to the lack of similar work; only one analogous paper [29] (Stockl et al.) uses tracking data to understand the defensive impact of players.","Extend defensive valuation to leverage tracking data (pitch control, opposition marking, anticipating/intercepting events before they happen).;Develop methods that allow defensive actions to be valued from event-data in smarter ways, given the low availability of tracking data across leagues.;Normalize defensive action counts based on possession of the team to assess how much defending a player does relative to opportunity.",false,,,,,extends:singh_2018_xt,true,2026-06-29,false,,

nakahara_2023_multiagent_rl,pegah,2026-06-29,true,"Proposes a valuation method for on- and off-ball soccer players in a single holistic framework based on multi-agent deep reinforcement learning, estimating Q-values per player per action including off-ball movement directions.",Multi-agent deep RL with action supervision (on- and off-ball valuation),other,reinforcement-learning,action,"2D position coordinates of all 22 players;velocity data of all 22 players;2D position and velocity of the ball (23 x 2 x 2 dimensions, 92-dim state);one-hot action vector for each agent (14 actions);event labels (passing, shooting) from event data","Q-value (state-action value) of each of 14 actions for each of 10 attacking players at each frame, trained via SARSA TD-loss with terminal rewards (Goal: +1, EPV at terminal no-goal, Conceding: -1)",reinforcement,"Recurrent neural network with single 64-dim GRU middle layer (ReLU), input 106 x 64 (state 92-dim + action 14-dim), output 64 x 14 Q-values; trained with SARSA TD loss + cross-entropy action-supervision loss (L_AS) + L1 regularization; Adam optimizer; lambda_1 = 0.01, lambda_2 = 0.1","continuous (x,y) 2D coordinates","until end of possession (attack sequence; min 50 frames, max T=300 frames equivalent to 30 seconds at 10 Hz)",per-frame,passes;shots;dribbles_carries;off_ball_actions,other,per-frame;per-player-match;per-player-season,Data Stadium Inc. (event + tracking); J.League (season goals); Soccer-digest (expert ratings),event;tracking-2d,other-private,Meiji J1 League,2019,54,false,TD loss (L_TD);action supervision loss (L_AS);Spearman's rank correlation coefficient (rho);average Q-value (on-ball and off-ball),player-ranking;action-ranking,RL without action supervision (ablation);OBSO (Off-Ball Scoring Opportunities) [Spearman 2018];C-OBSO (Creating off-ball scoring opportunity) [Teranishi et al. 2022];season goals;expert ratings (Soccer-digest),false,true,true,false,Match/team-level: training and validation data = attack sequences from teams other than Yokohama F. Marinos (1669 train + 186 val); test data = Yokohama F. Marinos attack sequences (1236 series). Player valuation restricted to attacks within the attacking third.,scouting;post-match-analysis;season-evaluation;tactical-pattern-discovery,,partially-interpretable,medium,"Section 3.1 | TD loss with action supervision (0.0034 +/- 0.0001) was smaller than that without supervision (0.0063 +/- 0.0004), while L_AS with supervision (3.9550 +/- 0.0005) was slightly larger than without supervision (3.9407 +/- 0.0005).;Section 3.1 | Average on-ball Q-values with supervision (0.0137 +/- 2.597 x 10^-4) were larger than those without supervision (0.0008 +/- 4.431 x 10^-5); average off-ball Q-values with supervision (0.0008 +/- 0.0035) were also larger than those without supervision (-7.123 +/- 0.0018).;Section 3.2, Fig. 3a | There was a high negative correlation (rho = -0.761) between season goals and average Q-values obtained by the proposed method, indicating the indicator tends to value defensive players who provided many passes.;Section 3.2, Fig. 3b | There was a moderate positive correlation between average on-ball and off-ball Q-values (rho = 0.618), suggesting the indicator tends to value similar play style between on- and off-ball situations.;Section 3.2, Fig. 4a | Low negative correlation between average rating by experts and average Q-value (rho = -0.218).;Section 3.2, Fig. 4b | Low negative correlation with average OBSO (rho = -0.305).;Section 3.2, Fig. 4c | No significant correlation with average C-OBSO (rho = 0.182, p > 0.05).;Section 1, Section 2.1 | The proposed method values on- and off-ball actions of multiple players (including those far from the ball) in a single holistic framework using multi-agent deep RL with discrete action space (14 actions) over continuous state space inspired by Google Research Football.;Section 1 | Off-ball players spend approximately 87 min of 90 min without the ball, motivating evaluation of off-ball contribution.","Since there is no true value for the Q-value, the performance of the model cannot be directly validated; only relationships with existing indicators were investigated.;Action supervision requires careful interpretation: too little supervision (lambda_1 << 0.01) yields insufficient learning of counterfactual action values, while too much (lambda_1 >> 0.01) may overfit to actual actions and not consider counterfactual actions.;Sample size for correlation analysis was small (N = 14 players who played at least 10 games), so rho was used as an effect size rather than p-values.;Tracking data for all players and timesteps in the J1 League are not publicly shared in such amounts, limiting reproducibility.;Goalkeeper was excluded; only 10 attacking-player RL agent models were constructed.;Player valuation was restricted to attacks within the attacking third for simplicity.;The model can only qualitatively investigate effectiveness in terms of modeling soccer agents, not quantitatively validate which model is best in a practical sense.",Improve RL models for a more valid valuation of players.;Use more sophisticated rewards per action.;Combine with forward RL simulation.,false,,,,unknown,compares-against:spearman_2018_beyondxg,true,2026-06-29,false,,

pappalardo_2019_playerank,pegah,2026-06-29,true,"PlayeRank is a data-driven framework for multi-dimensional, role-aware evaluation and ranking of soccer players. It learns per-feature weights via a team-level classification task (LSVC predicting match outcome), then aggregates per-action contributions into a per-match player performance rating and role-based player rankings. Although it operates at the player/match level rather than the per-action probability level of VAEP/xT, it is an action-valuation framework: each event type/subtype/tag combination receives a weight that determines its contribution to player performance.",PlayeRank,other,hybrid,action,"soccer-logs (event data) from Wyscout;event type, subtype, and tags (e.g. pass cross/simple, accurate/not accurate, key pass, assist, opportunity);spatio-temporal coordinates (x,y) of each event used for role detection (player average position / centers of performance);match outcome (win vs non-win) used as supervisory signal for feature weighting;76 features per player-match obtained by counting events of a given (type, subtype, tag) combination","Per-match player performance rating r(u,m) = (1/R) * sum_i w_i * x_i, where w_i are feature weights learned by a Linear SVM classifier trained to predict team match outcome (win = 1, non-win = 0) from the team's aggregated feature vector.",supervised,"Three-phase pipeline: (1) Learning phase - Linear Support Vector Classifier (LSVC, L2-SVM via scikit-learn svm.LinearSVC) trained on team-aggregated feature vectors to predict match outcome, yielding feature weights w; k-means clustering (k=8) over players' centers of performance (average event positions) with soft-clustering (k-silhouette, delta_s=0.1) for hybrid roles. (2) Rating phase - per-player-match rating computed as scalar product r(u,m) = (1/R) * sum_i w_i * x_i; goal-adjusted rating r*(u,m) = alpha * norm_goals + (1-alpha) * r(u,m); series aggregation via Exponential Weighted Moving Average (EWMA). (3) Ranking phase - role-based rankings R_1,...,R_z assigning a player to role R_i if assigned to it in at least x=40% of matches.","Continuous (x,y) positions on a normalised 0-100 pitch; centers of performance computed as per-match average event coordinates and clustered into 8 roles; spatial query module uses a tessellation into 100 equal-sized zones (one per ~m^2 region, with note that solutions scale to ~10^6 zones if desired).",Per-match rating aggregates all events of player u in match m; player rating over series of matches uses EWMA across matches.,per-event,passes;shots;dribbles_carries;defensive_actions;set_pieces,unitless-rating,per-action;per-player-match;per-player-season,Wyscout,event,wyscout-private,Spanish first division;English first division;Italian first division;German first division;French first division;Portuguese first division;Turkish first division;Greek first division;Austrian first division;Swiss first division;Russian first division;Dutch first division;Argentinian first division;Brazilian first division;European Champions League;Europa League;World Cup 2018;European Cup 2016,last four seasons (as of 2018) for club competitions; 3 seasons for Champions League and Europa League; 1 season for European Cup 2016 and World Cup 2018,19619,false,"AUC (Area Under the ROC Curve) of the LSVC classifier (AUC = 0.89);F1 (F1 = 0.81);accuracy (= 0.82) on 5-fold cross-validation;Normalized Root-Mean-Square Error (NRMSE) between competition-specific and overall feature weights (avg ~6%);silhouette score (ss = 0.43) for k-means clustering of roles at k=8;majority concordance c_maj with three professional scouts (overall 68%);unanimous concordance c_una with scouts (overall 74%);Pearson correlation between player average rating and standard deviation across roles;Shannon-entropy-based versatility V(u,M)",player-ranking;scouting;other,"Flow Centrality (FC) by Duch et al. [12];Pass Shot Value (PSV) by Brooks et al. [6];majority-class baseline classifier (AUC=0.50, F1=0.48, accuracy=0.62);random baseline classifier weighted by class frequencies (AUC=0.50, F1=0.53, accuracy=0.53)",false,false,true,false,"5-fold cross-validation for the LSVC feature-weighting classifier on 19,619 team-match examples (80% train / 20% test per fold). Splits are at the team-match level, not match level; the same match contributes two team-match rows (one per team) to the dataset, which could enable mild cross-team leakage within a match. Player rankings are evaluated against a survey of 211 player pairs judged by three Wyscout professional scouts.",scouting;transfer-target-id;post-match-analysis;season-evaluation;tactical-pattern-discovery,false,fully-interpretable,low,"Abstract; Section 5; Figure 11 | PlayeRank achieves an improvement of up to 30% (relative) and 21% (absolute) with respect to the state-of-the-art Flow Centrality algorithm, and up to 16% (relative) and 13% (absolute) over PSV, on agreement with three professional Wyscout scouts.;Section 4.1, Table 1 | The dataset comprises 31,496,332 events across 19,619 matches and 21,361 distinct players (21K reported in text) over four seasons of 18 prominent soccer competitions.;Section 4.2; Appendix A, Table 7 | 76 features (Table 7) were extracted per player-match, defined by combinations of event type, subtype, and tag (e.g. pass-simple pass-accurate, foul-hand foul-red card).;Section 4.4 | The Linear SVC trained to predict match outcome from team performance vectors achieves AUC = 0.89, F1 = 0.81, accuracy = 0.82 on 5-fold cross-validation (vs AUC=0.50 for the majority-class and random baselines).;Section 4.3, Figure 4, Table 4 | The role detector (k-means with k=8 on centers of performance) yields the best silhouette score ss = 0.43; eight roles are identified: right fielder, central forward, central fielder, left fielder, left central back, right forward, right/central back, left forward.;Section 4.4, Figure 5 | Top-10 (most positive) feature weights are dominated by assist-related features (simple pass assist, cross assist, head pass assist, smart pass assist, high pass assist, touch assist, launch assist, key launch pass, accurate free kick, accurate shot); bottom-10 (most negative) are red-card and second-yellow fouls (hand, violent, protest, late, normal).;Section 4.4, Figure 6 | The average NRMSE between the overall feature weights w and competition-specific weights w^(j) is around 6%, and 16 out of 18 competitions have NRMSE < 7%; the two outliers are the European Cup 2016 (17%) and World Cup 2018 (20%) which are national-team competitions with fewer matches (51 and 64).;Section 4.5, Figure 7(a) | The distribution of player performance ratings is strongly peaked around mu = 0.39 with sigma = 0.05; ~94% of ratings lie within [mu-2sigma, mu+2sigma]; 'excellent' performances (r(u,m) > mu+2sigma) account for ~5% of the total and are unevenly distributed across players.;Section 4.5 | Only 11% of players achieve an excellent performance at least once; on average 9% of players reach excellence at least once; the maximum excellence rate is 21% for Neymar.;Section 5; Figure 11 | Validated on 211 player pairs (involving 202 distinct players) judged by three Wyscout professional scouts, PlayeRank achieves majority concordance c_maj = 68% and unanimous concordance c_una = 74% overall (vs 50% random baseline); concordance grows with ranking-distance gap, reaching c_maj=86% and c_una=91% when the gap is >=20.;Appendix C, Figure 14 | Inter-Rater Agreement Rate (IRAR) between two Wyscout operators tagging the same match is approximately 0.70 overall, indicating good agreement at both event and player level.","The framework excludes goalkeepers from the analysis because they have different game rules and would require a dedicated analysis.;Soccer-logs do not include off-ball actions, so important aspects of performance such as pressing and the ability to create spaces cannot be assessed in the current version of PlayeRank.;PlayeRank's role detection is based on a player's average position via k-means clustering, which is one of several possible approaches; more sophisticated role models (e.g. heatmap- or event-direction-based) are possible but were not adopted here.;There is no objective ground-truth definition of performance quality; the team-outcome supervision is used as a proxy.;There is no consolidated and widely accepted metric for measuring performance quality in all of its facets; the authors propose PlayeRank as a candidate.;Disagreement between PlayeRank and scouts is non-trivial when compared players are close in the ranking (ranking distance < 10), where unanimous scout agreement itself is only around 58%.","Designing more sophisticated role-detection algorithms (e.g., AI-based methods proposed in the Soccer Data Challenge) and embedding them in PlayeRank.;Designing more sophisticated feature-weighting techniques to plug into the framework.;Extending PlayeRank to work with other data sources such as video tracking data and GPS data to describe spatio-temporal trajectories and out-of-possession actions.;Plugging new performance metrics into PlayeRank's architecture and evaluating its applicability to other team sports (basketball, hockey, rugby).;Investigating alternative ways to combine the spatial-query score s(u,Q) and player rating r-bar(u,M) for the player-retrieval application.;Designing role detectors that operate at the level of fractions of a match rather than the whole match.",true,https://github.com/mesosbrodleto/playerank,,authors,unknown,compares-against:brooks_2016_passrank;improves-upon:brooks_2016_passrank,true,2026-06-29,false,,

power_2017_passes,pegah,2026-06-29,true,"Paper introduces a supervised pass risk/reward valuation model on tracking + event data, valuing individual pass actions and applying the values to player and team ranking. Squarely in scope for action valuation (pass-value subset).",Pass Risk and Reward Model,other,expectation-based,action,"ball X and Y location (origin and destination of pass);speed of the player in possession and the intended receiver;speed of the nearest defender toward the passer and the receiver;distance of nearest defender to the passer and receiver;nearest defender angle to the passing line;first time pass indicator;time from regaining possession;expected receiver membership (distance/min-distance x angle/min-angle);tactical game-state features (build-up, counter-attack, unstructured-play);formation features (high-block, medium-block, low-block; left/centre/right) via k-means clustering on aligned player and ball data;polar coordinates of all players relative to the goal being attacked;polar coordinates of defenders to the passer and receiver",Pass risk: probability (0-1) that the player will successfully execute the pass given the situation. Pass reward: probability that the pass made will result in a shot within the next 10 seconds.,supervised,Logistic regression classifier (chosen over non-linear black-box models for interpretability); features hand-crafted from tracking data; tactical and formation context added via tree-structured feature augmentation including k-means clustering on player XY positions,"continuous (x,y) tracking at 10Hz",pass execution (risk) and next 10 seconds (reward),per-event,passes,probability,per-action;per-player-match;per-player-season;per-team-match;per-team-season,STATS LLC,event;tracking-2d,other-private,English Premier League,2013-14;2014-15;2015-16,726,false,Log-Loss;RMSE,action-ranking;player-ranking;team-ranking;tactical-pattern-discovery,Naive (average pass completion rate);Ball-Only (start and end position of pass);Tracking (micro features from tracking);Tracking + Tactics;Tracking + Formation,false,false,true,false,"Training set of 352,466 examples; parameters tuned on evaluation set of 114,257 examples; test set of 114,257 examples. For reward classifier: 7,427 positive and 136,180 negative training examples; 3,062 positive and 58,484 negative test examples. Split methodology (match-level vs event-level) not explicitly stated.",post-match-analysis;season-evaluation;opponent-analysis;transfer-target-id;tactical-pattern-discovery;scouting,,partially-interpretable,low,"Section 3.1 Data Inventory | Of 571,287 passes attempted across two full seasons, 468,265 were successful, with an average of 380.46 attempted and 320.91 completed (84.35%) per game.;Table 1 | Table 1 reports All Passes total 580,980 with 492,337 successful (84.74%); backwards 95.61%, sideways 92.85%, forwards 71.51%; short 82.07%, medium 85.02%, long 64.94%; first time 81.58%, final third 57.65%, penalty area entry 36.19%.;Table 2 | On pass risk prediction the Tracking + Formation model achieves the best Log-Loss 0.2125 and RMSE 0.2438, improving over Naive (0.4317 / 0.3621), Ball-Only (0.3623 / 0.3306), Tracking (0.3268 / 0.3194), and Tracking + Tactics (0.2918 / 0.2960).;Table 2 | On pass reward prediction the Tracking + Formation model achieves Log-Loss 0.1391 and RMSE 0.1939, improving over Naive (0.1977 / 0.2174), Ball-Only (0.1771 / 0.2185), and Tracking (0.1566 / 0.2045).;Section 6.1, Equation 2 | The authors introduce Passing Plus-Minus (PPM), the per-90-minute difference between credits for completed risky passes and penalties for failed passes, used to rank players by passing ability.;Section 6.1, Equation 3 | Difficult Pass Completion (DP%) measures the fraction of high-risk passes (in the 75th percentile of pass risk) that a player completes.;Section 6.2, Equation 4 | Passes Received Added (PRA) credits receivers of difficult passes (1 - XD_pr) and is normalized to per 90 minutes.;Section 6.3 | A 'Dangerous Pass' is defined as a pass with greater than 6% chance of leading to a shot in the next 10 seconds (75th percentile of reward).;Section 6.1, Figure 9 (left) | Creative players such as Cesc Fabregas (+1.19/90%), Mesut Oezil (+0.96/95%) and Eden Hazard (+0.79/65%) rank highest on combined PPM and DP%, while Craig Gardner is the worst passer that season at -1.09 passes per game and 47% DP%.;Section 5.1, Figure 6 | In Manchester City vs Manchester United (March 20 2016), City had 55% possession, 402 total passes, 354 completed (88%) vs United's 45%, 322 passes, 266 completed (82%); City made 131 dangerous passes vs United's 72, with pass risk 14% vs 17% and pass danger 16% vs 13.5%; United won 1-0.;Section 7, Figure 11 | Sixteen clusters of dangerous passes were identified by k-means on origin/destination XY coordinates, with the most dangerous passes located around the edge of the penalty area (clusters 1, 2, 3).;Figure 11 cluster table | Average risk and reward by cluster: cluster 1 (24% risk, 25% reward), cluster 2 (22% / 23%), cluster 3 (22% / 23%), cluster 10 (3% / 12%), cluster 16 (8% / 10%).","Expected receiver model is simple and has limitations when two players are close to each other or the ball is intercepted early in its flight path.;The expected receiver model does not predict where the ball may have been passed to and just uses the absolute position of the 'expected receiver' (e.g., a pass intended in front of an attacker to run onto is not captured).;Human-labeled approach is inherently subjective; using event-outcome labels is preferred but consensus on what a good pass is remains ambiguous.;Shots occur sparsely, leading to imbalance between positive and negative examples for the reward classifier.",,false,,,,,,true,2026-06-29,false,,

rahimian_2022_beyond_av,pegah,2026-06-29,true,"Proposes a deep RL framework that goes beyond action valuation by deriving optimal team policies for ball-destination decisions, using tracking + event data modelled as a Markov Decision Process with policy-gradient optimisation.",Expected Possession Outcome (EPO) optimisation framework,neural,reinforcement-learning,both,"(x,y) locations of all 22 players and the ball at 25 Hz;x and y velocity components of attacking and defending players;Euclidean distance of the ball to each pitch location;Euclidean distance of the defending team goal to each pitch location;angle between the ball and the goal for each pitch location;cosine of the angle between the ball and the goal for each pitch location;sine of the angle between the ball and the goal for each pitch location;ball destination location label;binary outcome of actions (success / turnover);11 input channels of size 105x68 representing the pitch","Selection probability surface (softmax over 105x68=7140 pitch zones for ball destination) and success probability surface (sigmoid per zone for possession retention); optimised via policy gradient to maximise Expected Possession Outcome (EPO) in (-1, +1)",reinforcement,"Encoder-decoder convolutional policy network over 11 x 105 x 68 pitch channels with two output heads (softmax selection surface, sigmoid success surface) and a reconstruction decoder; off-policy policy-gradient fine-tuning",105x68 pitch grid (7140 disjoint 1x1 m zones); continuous action space also used,until end of possession (discounted with gamma=0.99),per-frame,passes;shots,probability,per-action;per-zone;per-possession;per-team-match;per-team-season,Stats Perform,event;tracking-2d,other-private,Belgian Pro League,2020-21;2021-22,430,false,log-loss;inference time (seconds);number of parameters;Expected Possession Outcome (EPO);EPO difference;improvement in expected goal difference per game,decision-recommendation;tactical-pattern-discovery;action-ranking;team-ranking,Naive (85% average pass completion);Logistic regression;XGBoost,false,false,false,false,Chronological 80%-10%-10% train/validation/test split respecting game order,in-game-decision-support;post-match-analysis;opponent-analysis;tactical-pattern-discovery;training-feedback,,partially-interpretable,high,"Table 1 | The proposed policy network achieves a log-loss of 0.18 with inference time 7.78 seconds (431,354 parameters) for the selection surface, beating logistic regression (0.68 log-loss, 151s) and XGBoost (0.65 log-loss, 127s) on all passes in the test set.;Table 1 | For the success surface, the proposed network achieves log-loss 0.22 with inference time 2.27 seconds (331,276 parameters), beating Naive (0.45), logistic regression (0.57, 372s) and XGBoost (0.58, 351s).;Section 5.3 and Figure 7 | In a league-wide model, behavioural policy EPO is focused around -0.01 (likely to lose a possession by 1% chance), while following the optimal policy yields EPO focused around 0.015 according to importance sampling (1.5% chance of scoring), an improvement of +2.5 expected goals per game over 100 possessions.;Table 2 | Club Brugge's behavioural mean EPO is 0.0046 versus optimal mean EPO 0.0215, an EPO difference of 0.016 corresponding to +1.6 improvement in expected goal difference per game.;Table 2 | Beerschot has the largest team-level EPO difference of 0.032 (+3.2 expected goal difference per game improvement) when switching from behavioural to optimal policy.;Table 3 | Optimal policy proposes a larger propensity of backward passes on the wings (+63% left wing, +87% right wing), a smaller propensity of backward passes in the half-spaces (-53% left half-space, -41% right half-space), and a larger propensity of forward passes (+33%) and sideway passes (+50%) in the centre.;Section 6.2 and Table 2 | Teams at the top of the table (e.g., Union SG) show small EPO improvements (0.005, +0.5 goals) because their behavioural policy is nearly the same as the optimal policy, while teams at the bottom of the table show larger improvements.;Section 4.2 | The discount factor gamma is set to 0.99 after tuning with the discount trap method.;Section 2 (Dataset description) | The dataset consists of all 330 games of the 2020-21 season and 100 games of 2021-22 of the Belgian Pro League collected by Stats Perform up to October 2021; tracking is sampled at 25 observations per second.;Section 5.3 and Figure 7 | The authors evaluate the optimal policy with three off-policy evaluation methods: importance sampling, doubly robust, and reconstructed possessions (Sim), all of which show similar improvements over the behavioural policy.","The assumed +2.5 expected goal-difference improvement per game in the league-wide model is not realistic in the real world, as it assumes all players can perfectly follow the optimal policy.;Online experiments to validate the optimal policy in a real match are infeasible; evaluation must rely on off-policy methods.;Hand-crafted features such as team tactics and formations can decrease log-loss further but have long inference time that makes them impractical for the analysis.;Authors could not construct a Naive baseline for the selection surface, only for the success surface.;The choice of negative reward for unsuccessful actions (negative xG for the opponent) is described as an arbitrary choice.",Expand the current framework to capture the contributions of individual players so they could adapt themselves to their team-specific optimal strategy.,false,,,,,,true,2026-06-29,false,,

rahimian_2022_data_driven,pegah,2026-06-29,true,"Proposes a deep reinforcement learning framework on event and tracking data of soccer matches to discover the most impactful actions at the interrupting point of a possession, providing optimal offensive and defensive action recommendations.",Deep RL policy-gradient framework for optimal offensive and defensive actions,neural,reinforcement-learning,action,"44-dimensional (x,y) normalized positions of the 22 players on the pitch from tracking data;angle to goal;distance to goal;time remaining;home/away indicator;action result (successful or unsuccessful);body id (head/body/foot);one-hot vector of actions A excluding the ending action","Categorical probability distribution over interrupting offensive actions (shot, foul, ball out) and defensive actions (foul, clearance, out, tackle, interception) at the end of a possession; trained via policy gradient to maximize expected goals for the offensive team and minimize the attacking team's scoring probability for the defensive team within the next 10 actions.",reinforcement,CNN-LSTM network (convolutional layers + max pooling + LSTM with 100 memory units + fully connected + softmax) trained with Policy Gradient (PG). A separate CNN-LSTM binary classifier estimates P(score within next 10 actions) used as the reward signal.,"continuous (x,y) from tracking data; reported per pitch zone (left wing, left half-space, centre, right half-space, right wing) for aggregation",next 10 actions within a possession (possession length truncated/padded to 10),per-possession,shots;defensive_actions,expected-goals,per-action;per-possession;per-zone;per-team-season,InStat,event;tracking-2d,instat-private,"11 different national leagues of Portugal, Russia, Hungary, and Germany",2017-2018,104,false,accuracy;categorical cross entropy loss;inference time;number of parameters;off-policy policy evaluation (OPE) with importance sampling;Chi-square distance (team effectiveness);mean reward (expected goal difference);Kernel Density Estimation (KDE) of mean rewards,decision-recommendation;action-ranking;team-ranking;tactical-pattern-discovery,3D-CNN;LSTM;Autoencoder-LSTM;CNN-LSTM (selected),false,false,false,false,"Chronological split of attacking possessions: 80% train, 10% validation for hyperparameter tuning and model selection, 10% hold-out test.",in-game-decision-support;post-match-analysis;tactical-pattern-discovery;training-feedback,,partially-interpretable,medium,"Section 'Dataset' (p. 3) | The dataset includes 98922 actions (including on-ball and defensive actions), 9462 possessions terminated by either one of the defensive actions of the opponent players or a shot, out, foul performed by the offensive players, and 329 goals.;Table 2 | CNN-LSTM achieves 80% accuracy and 0.55 loss with 1.39s inference time and 201,019 parameters, outperforming 3D-CNN (70%/0.65), LSTM (66%/0.71), and Autoencoder-LSTM (76%/0.65) on the test set.;Section 'Expected Goal Results' (p. 6) | The expected goal prediction binary classification model (CNN-LSTM) achieved 78% accuracy on the test set.;Section 'Optimization Results' (p. 7-8) | For the offensive team, the amount of expected goal difference before and after the interrupting action would be -0.1 following the actual policy, and 0.22 following the optimal policy on average of all episodes (0.32 improvement).;Section 'Optimization Results' — Offensive approach (p. 7) | In Centre, the optimal offensive policy proposes more shots and less fouls; modification in action frequencies results in 0.4 increase in mean rewards from -0.1 to 0.3 on average of all teams.;Section 'Optimization Results' — Offensive approach (p. 7) | In Half-Spaces, the optimal offensive policy suggests more fouls and more shots (long-distance shots); mean rewards increase 0.3 from -0.1 to 0.2.;Section 'Optimization Results' — Offensive approach (p. 7) | In Wings, the optimal offensive policy suggests increasing ball out actions and committing less fouls; mean rewards change from -0.1 to 0.15.;Section 'Optimization Results' — Defensive approach (p. 9) | For the defending team, the optimal policy can decrease the attacking team's expected goal difference by 0.2 following the actual interrupting defensive action, and 0.22 following optimal policy (0.02 improvement on average of all episodes).;Section 'Game State Representation' (p. 3) | Only 2.3% of the attacking possessions were truncated due to their length exceeding 10 actions.;Table 3 | Team A has the largest effectiveness in offensive actions (0.71), team E in defensive actions (0.78); team K and team I show the worst effectiveness in offensive (0.41) and defensive (0.39) actions, respectively.;Sections 'Game State Representation' and 'Training protocol and return' | Discount factor gamma is set to 0.99; possession length is truncated/padded to 10 actions; LSTM uses 100 memory units.","In this work the policies are optimized independently and assume that the behavior of the opponent team is not adapted to the optimal policy; multi-agent RL is left for future work.;Focus is on on-ball defensive actions; positioning decisions of teams are not considered.;Further information of the game context (e.g. pass height, length, angle, etc.), teams' and players' abilities and their specific strategies would significantly improve the results but are not included.","Use multi-agent reinforcement learning to adapt the opponent teams with the optimal policy as well, which might decrease the amount of improvement in mean rewards reported in this paper.;Incorporate off-ball positioning decisions of teams in the optimization.;Include additional game-context attributes (pass height, length, angle) and team/player abilities and strategies.",false,,,,,extends:rahimian_2022_beyond_av,true,2026-06-29,false,,

rudd_2011_markov,pegah,2026-06-29,true,Foundational possession-value / action-valuation work that models soccer possessions as a Markov chain over discrete game states and weights each action by its incremental change in P(Goal). Direct conceptual predecessor of xT and VAEP.,Markov chain possession-value framework,markov,markov-decision-process,state,"(x,y) coordinates;event type;defensive pressure;defensive ""state""","P(Goal) — probability that the current possession ends in a goal, computed by iterating the transition matrix until the probability of ending in an absorbing state converges (n=20)",supervised,Closed-form discrete-time Markov chain over 39 states (2 absorbing states + 7 set pieces + 30 states defined by zonal location and defensive state); transition matrix repeatedly multiplied until absorption probabilities converge,7 zones (zone 0 = own half + center circle area; zones 1-6 partition the attacking half into a 3x2 grid around the penalty area),until possession ends (absorbing states: Goal or End of Possession),per-event,passes;shots;dribbles_carries;set_pieces,value-delta,per-action;per-zone;per-team-season;per-player-season,StatDNA,event,other-private,English Premier League,2010/11,123,false,R^2 (expected vs. actual goals);linear regression slope/intercept of expected vs. actual goals,goal-prediction;player-ranking;team-ranking;tactical-pattern-discovery,,true,true,,true,"Monte Carlo bootstrapping with 1000 samples with replacement; 5-fold cross-validation (4 training folds, 1 evaluation fold). Split granularity (match vs. event) not specified in the slide deck.",post-match-analysis;season-evaluation;tactical-pattern-discovery;scouting,,fully-interpretable,low,"Slide 16 ('Validation – expected vs. actual') | Monte Carlo bootstrapping validation of expected vs. actual goals yields y = 0.9417x + 0.0134, R^2 = 0.99034.;Slide 16 ('Validation – expected vs. actual') | 5-fold cross-validation of expected vs. actual goals yields y = 0.9126x - 0.0832, R^2 = 0.97564.;Slide 18 ('Results – Set Pieces') | P(Goal) for set-piece states: Penalty 71.55%, Long Corner 2.39%, Short Corner 1.67%, Long Free Kick 1.67%, Shallow Throw-in 1.46%, Deep Throw-in 1.09%, Short Free Kick 1.08%.;Slide 6 ('States') | The state space comprises 39 total states: 2 absorbing states (Goal or End of Possession), 7 set pieces, and 30 states defined by zonal location and defensive state.;Slide 5 ('Dataset') | The dataset covers the English Premier League 2010/11 season with 123 matches, a minimum of 11 matches per team, and approximately 100,000 'deliberate' actions (about 800 actions per match).;Slide 14 ('Transition Matrices') | Iterating the transition matrix until the absorbing-state probabilities converge requires n=20 multiplications.;Slide 25 ('Top Performers') | Top individual offensive performers identified by the framework include Tim Cahill (0.286), Yaya Toure (0.283), and Cesc Fabregas (0.256).;Slide 26 ('Worst Performers') | Worst offensive performers include Darren Bent (-0.282), Peter Odemwingie (-0.195), and Gael Clichy (-0.176); many of the lowest contributors are goalkeepers, strikers, and defenders.;Slides 22-24 ('Not all passes are created equal', 'How does it work?', 'Another example') | Player offensive contribution is computed as the sum of incremental improvements in P(Goal) attributable to each of the player's actions in the possession chain (illustrated by worked examples giving e.g. Player 1: -0.08, Player 2: +0.11, Player 3: +0.72; and a penalty example with Player 1 (earner) +0.56 and Player 2 (missed taker) -0.71).;Slide 17 ('Comparing P(Goal)') | Comparing P(Goal) across teams reveals tactical patterns: as teams move lower down the table, scoring becomes harder; notable exceptions are Manchester City (3rd, underperforms offensively) and Wolves (17th, overperforms offensively).;Slide 26 ('Worst Performers') | Darren Bent's low ranking is explained by sample artefacts: only 1 of his 17 season goals was in the sample, and he had 19 opportunities with the ball at >10% chance of scoring (22% average) but converted only one.","Markov assumption: the current state is treated as independent of the previous state (it doesn't matter how the possession reached the current state — transition probabilities are the same regardless of history).;Hard to capture all information about game state; off-the-ball movement is just as important as on-the-ball movement but is not directly modelled.;Sparse data: not all possible combinations of game situations have been observed, and those that have been observed often have only a few data points.;Difficulty of dividing credit among players involved in a possession.",Digging deeper into per-player data to identify specific situations (e.g. whether Clichy/Young/Kolarov are poor crossers) in which low-rated players underperform.,false,,,,,,true,2026-06-29,false,,

singh_2018_xt,pegah,2026-06-29,true,"Canonical introduction of Expected Threat (xT), a possession-value/action-valuation method that assigns a threat value to every pitch zone using a Markov-style model and then values on-ball actions (passes, dribbles) by the difference in xT between start and end locations.",Expected Threat (xT),expected-threat,markov-decision-process,state,"start location (x, y) of action discretised to a 16x12 pitch grid;end location (z, w) of action discretised to a 16x12 pitch grid;per-zone move probability m_{x,y};per-zone shoot probability s_{x,y};per-zone move transition matrix T_{x,y} over the 192 zones;per-zone goal probability g_{x,y} (simple xG)","xT_{x,y}: probability of scoring within the next n actions when in possession in zone (x, y); after iteration n the value represents the chance of scoring in the next n actions (post writes 'next 5 actions' when using 5 iterations).",rule-based,"Closed-form Markov-style recurrence xT_{x,y} = (s_{x,y} * g_{x,y}) + (m_{x,y} * sum_{z,w} T_{(x,y)->(z,w)} * xT_{z,w}), solved by fixed-point iteration starting from xT = 0 for all zones; 4-5 iterations sufficient for convergence.",16x12 pitch grid (192 zones),next n actions (n = number of iterations; ~5 in the post),per-zone,passes;shots;dribbles_carries,probability,per-zone;per-action;per-player-season;per-team-season,unspecified (event-level Premier League data),event,unknown,Premier League,2017/18,,false,,player-ranking;tactical-pattern-discovery,assists;xGChain;xGBuildup;difference in xG,,,false,false,,post-match-analysis;opponent-analysis;tactical-pattern-discovery;scouting;season-evaluation,,fully-interpretable,low,"Section 'Deriving xT' | xT can be formulated as the recurrence xT_{x,y} = (s_{x,y} * g_{x,y}) + (m_{x,y} * sum_{z=1..16} sum_{w=1..12} T_{(x,y)->(z,w)} * xT_{z,w}).;Section 'But wait, there's more...' | Starting from xT = 0 for all zones, iterating the formula converges in approximately 4-5 iterations.;Section 'But wait, there's more...' | At iteration 1 the formula collapses to xT_{x,y} = s_{x,y} * g_{x,y}, which is essentially an xG model.;Section 'But wait, there's more...' | xT after n iterations represents the probability of scoring within the next n actions.;Section 'Applying xT' | For the Arsenal vs Burnley example, Ozil's pass moves the ball from xT = 0.077 to xT = 0.158 (delta xT = 0.081); Kolasinac's pass moves it from xT = 0.158 to xT = 0.171 (delta xT = 0.013); xT therefore attributes 0.081 / (0.081 + 0.013) = 86% of the credit to Ozil and 14% to Kolasinac.;Section 'Top xT creators' (table) | Top xT creators in the 2017/18 Premier League season include Kevin De Bruyne (28.033), Cesc Fabregas (20.538), Jose Holebas (18.487), Alexis Sanchez (17.432), Riyad Mahrez (16.756), Granit Xhaka (15.834), Christian Eriksen (15.700), Cesar Azpilicueta (15.187), Xherdan Shaqiri (15.079), Ashley Young (14.988), David Silva (14.970), Jonjo Shelvey (14.728), Fernandinho (14.005), Paul Pogba (13.954), Mesut Ozil (13.914).;Section 'Visualizing per-team xT' | Per-team xT maps reveal that teams with similar shape (e.g. Manchester City and Spurs) can have very different magnitudes, indicating that City are more threatening given the ball in the same position due to a higher conversion rate of possessions into goals.;Section 'Deriving xT' (note) | The model is constructed over a 16x12 grid on the pitch, giving 192 zones.","Treating the action value as the xT difference between start and end zones makes the framework behave like a conservative force: dribbling path is irrelevant (path independence) and moving the ball in a loop yields zero reward, which is an inaccuracy tolerated for simplicity and due to the lack of tracking data.;The simplified model only considers successful moves (passes/dribbles completed without losing possession); unsuccessful attempts are excluded for tractability.;Only on-ball events (shoot or move) are modelled; defensive actions, off-ball runs, and goalkeeper actions are not valued.;Discretising start and end locations to grid cells loses precision; the author notes bilinear interpolation as a more precise alternative.","Identifying and analyzing patterns of play such as counter-attacks by looking at how xT changes during the course of a possession sequence.;Assessing an individual player's decision-making relative to their team's xT profile (e.g. is the player making high-reward passing choices, or would shooting/dribbling be better in certain areas?).;Player scouting: predicting whether a player who has never played for the team will fit the system by checking whether his historical actions would lead to high xT gains for the new team.",false,,,,,,true,2026-06-29,false,,

spearman_2018_beyondxg,pegah,2026-06-29,true,"Constructs a probabilistic physics-based pitch-control model that values game states (off-ball scoring opportunities, OBSO) from spatiotemporal tracking data, directly addressing action/state valuation in soccer.",Off-Ball Scoring Opportunity (OBSO),possession-value,physics-based,state,"spatiotemporal player tracking data (positions and velocities of all players at 25 Hz);on-ball event data (match time, on-ball player, event type: pass, shot, goal, etc.);distance to goal",Probability that the attacking team will score with the next on-ball event given the instantaneous game state (P(G|D)),physics-based,Probabilistic physics-based model decomposed into three conditional components: (1) Potential Pitch Control Field (PPCF) modeling per-player control probability via a differential equation using time-to-intercept (logistic CDF) and ball time-of-flight with aerodynamic drag; (2) Transition model as a 2D normal distribution over next on-ball location scaled by PPCF^alpha; (3) Score model as a monotonic function of distance to goal raised to a power beta. Parameters fit via Bayesian MAP with normally distributed priors.,"continuous (x,y) on the pitch, integrated as probability densities; PPCF computed per-player per-location",next on-ball event,per-frame,off_ball_actions,probability,per-frame;per-player-match;per-team-match,Hudl,event;tracking-2d,other-private,anonymized 14-team professional soccer league,2017-2018,58,false,Pearson correlation coefficient (PCC),player-ranking;team-ranking;tactical-pattern-discovery,shots;goals,,,,,5 games reserved as training set for parameter fitting; remaining 53 games used as test set. Split is at match level.,post-match-analysis;opponent-analysis;scouting;tactical-pattern-discovery,,fully-interpretable,,"Table 2 | OBSO is more correlated with future goals than either shots or goals themselves are; per-player game-to-game PCC values are OBSO->OBSO 0.60, OBSO->shots 0.37, OBSO->goals 0.26, shots->shots 0.35, shots->goals 0.17, goals->goals 0.12.;Figure 8 | The average goals/match versus average opportunity/match across the 14 teams in the 53-game test set has a Pearson correlation coefficient of 0.76.;Table 1 | MAP fits of the model parameters: s=0.54 sec (temporal uncertainty), lambda=3.99 Hz (control rate), kappa=1.72 (defensive advantage), sigma=23.9 m (transition spread), alpha=1.04 (PPCF exponent), beta=0.48 (score exponent).;Figure 3 | The standard deviation of the average displacement between subsequent on-ball touches is 14 m.;Figure 5 / Section 3.4 | For the example in Figure 5, the integrated magnitude of the OBSO is 1.1%.;Figure 7 / Section 5.2 | In the example match between Team I and Team D with a final score of 1-1, integrated scoring opportunities are 1.32 versus 1.47 despite Team I dramatically outshooting Team D.;Section 3.1.1 | Player acceleration and maximum speed are modeled with fixed values of 7 m/s^2 and 5 m/s respectively for the time-to-intercept calculation.;Section 3.1.3 / Equation 5 | The model assigns lambda_i = 0 to attacking players in an offside position, removing them from the control field.;Table 3 / Section 5.4 | The top 20 players ranked by mean OBSO/match are predominantly center forwards, but include a right winger, attacking midfielders, a center midfielder, a left winger, and notably a right back from Team A.","Score model ignores game state D apart from distance to goal; defensive positioning is only proxied through the PPCF rather than explicitly modeled in the score term.;Time-of-flight modeling choice (selecting the flight time that most closely matches the arrival time of the nearest attacking player) advantages successful passing to counteract limitations of the decision model.;The next on-ball event probability density lacks a preference for events that move the ball closer to the target goal, so opportunities that appear as clear scoring chances to a domain expert may be under-estimated.;The model does not directly account for the difficulty of crossing while running at speed, over-estimating chances in such scenarios and under-estimating chances for stationary, unpressured passers (footnote 7).;The opportunity for the player currently in possession is not considered in OBSO (footnote 8).;Small training set (5 games) and event-data synchronization issues motivate the Bayesian MAP approach with strong priors.;Event data timestamps carry stochastic noise on the order of three seconds, leading to moderate errors in player positions.;Future work is needed to refine the scoring model (Section 3.3) and the effect that defensive pressure and player speed have on the ability of a player to successfully deliver the ball to a teammate.",Refine the scoring model to account for defensive pressure and player speed on pass completion.;Replace beta-based score adjustment with an improved scoring probability model in future iterations (footnote 6).;Incorporate a preference term for events that move the ball closer to the target goal in the transition density (footnote 5).;Allow per-player acceleration and maximum speed values to better model break-away situations (footnote 3).;Use the constituent control (PPCF) and transition models for additional soccer analyses beyond scoring.,false,,,,,,true,2026-06-29,false,,

vanroy_2020_xt_vs_vaep,pegah,2026-06-29,true,"Critical conceptual and empirical comparison of two canonical action-valuation frameworks (xT and VAEP). The paper proposes no new method, but analyses design-choice differences, computes both rankings on StatsBomb Premier League 2018/2019 data, and contrasts the two methods on illustrative action types, top-25 player rankings, correlation with goals/assists, and split-half robustness.",xT vs VAEP (critical comparison),hybrid,hybrid,both,"ball location (zone on M x N pitch grid) for xT;previous three actions including action type, start/end location, distance and angle to goal for VAEP;action-context features such as distance covered and time elapsed between consecutive actions for VAEP;game-context features such as time remaining in the match and current score differential for VAEP","For xT: probability of scoring within the next i actions (zone value). For VAEP: P_score and P_concede within the next k actions, action value = delta P_score - delta P_concede.",hybrid,"xT: closed-form Markov chain solved iteratively over an M x N grid (16 x 12 in this paper, converged after 6 iterations). VAEP: two separate XGBoost gradient boosted tree classifiers (one for P_score, one for P_concede) trained on a feature representation of the last three actions plus game context.",16 x 12 pitch grid (xT); continuous location features (VAEP),xT: probability of scoring within the next i actions (iteratively expanded until convergence). VAEP: next k actions (fixed-length action window).,per-event,passes;shots;dribbles_carries;defensive_actions;set_pieces,probability,per-action;per-player-season,StatsBomb,event,statsbomb-private,English Premier League,2017/2018;2018/2019,,false,Jaccard similarity coefficient between top-k rankings;Pearson correlation with goals per 90 minutes (g/90);Pearson correlation with assists per 90 minutes (a/90);Pearson correlation between split-half player ratings (robustness),player-ranking;action-ranking,"xT (Singh, 2019);VAEP (Decroos et al., 2019);goals per 90 minutes;assists per 90 minutes",false,false,true,false,Models trained on StatsBomb English Premier League 2017/2018 season and used to rate actions in the 2018/2019 season. Robustness analysis splits the data into two random disjoint subsets and computes Pearson correlation of per-player ratings across them.,scouting;season-evaluation;post-match-analysis;transfer-target-id,,partially-interpretable,low,"Section 'Comparison of top-25 player rankings'; Figure 3; Table 1 | xT and VAEP produce different top-25 player rankings; their top-25 rankings have a Jaccard similarity coefficient of 0.48.;Section 'Comparison of top-25 player rankings'; Figure 3 | After the top 25 players, the Jaccard similarity coefficient between xT and VAEP rankings drops to 0.35 before steadily increasing.;Section 'Comparison with traditional performance metrics' | VAEP correlates more strongly with goals per 90 minutes than xT (rho_g/90 = 0.41 for VAEP vs 0.26 for xT).;Section 'Comparison with traditional performance metrics' | xT correlates more strongly with assists per 90 minutes than VAEP (rho_a/90 = 0.53 for xT vs 0.33 for VAEP).;Section 'Robustness'; Figures 4a and 4b | xT ratings are more robust across two random disjoint subsets of the season than VAEP ratings (Pearson rho = 0.89 for xT vs rho = 0.25 for VAEP).;Section 'Robustness'; Figure 4c | When restricted to offensive values of passes, dribbles and crosses (the actions xT can value), VAEP's split-half robustness improves to rho = 0.59.;Table 1 (a) and (b) | Top-25 xT player ranking for 2018/2019 Premier League is led by Eden Hazard (rating 0.547, g/90 = 0.49, a/90 = 0.46); top-25 VAEP ranking is also led by Eden Hazard (rating 0.558).;Section 'Comparison of top-25 player rankings' | Virgil van Dijk, a top-class defender, is ranked 81st by VAEP and 142nd by xT, illustrating that both rankings favour attacking players.;Section 'Comparison of top-25 player rankings' | Sergio Aguero is ranked 19th by VAEP but absent from xT's top 25, attributed to VAEP rewarding his overperformance on shots (finishing skill).;Section 'Comparison of top-25 player rankings' | Alexis Sanchez is ranked 7th by xT but absent from VAEP's top 25, attributed to xT crediting his key passes into high-value zones even though his shot volume halved.;Section 'xT can only value ball-progressing actions' and footnote 4; Figure 2c | xT cannot value actions that do not move the ball between zones (e.g., short dribbles inside the penalty box, take-ons within the same zone) and assigns them a value of zero by definition.;Section 'Backward passes into a team's own penalty box'; Figure 2a | Backward passes into the own penalty box occur roughly 19 times per game; xT does not capture their risk/reward whereas VAEP assigns more diverse positive and negative values.;Section 'First ball progression of counter attacks'; Figure 2b | First ball progressions of counter attacks occur roughly 2 to 3 times per game; VAEP's value distribution has higher mean and variance, while xT values are extremely skewed towards zero.;Section 'Forward dribbles inside the penalty box'; Figure 2c | Successful forward dribbles inside the penalty box occur roughly four times per game; xT assigns zero to a major part of them because they do not change zone.;Section 'Completed forward passes to the border of the penalty box'; Figure 2d | Completed forward passes to within 3 metres of the penalty-box border occur roughly 5 times per game; xT, on average, values such through balls higher than VAEP does.;Section 'Data' | The xT model in this paper uses a 16 x 12 grid and reaches convergence after 6 iterations; the VAEP model uses XGBoost.;Abstract; Conclusion; Section 'Comparison with traditional performance metrics' | Both xT and VAEP rankings deviate from traditional metrics such as goals or assists per 90 minutes, suggesting they provide additional insight into player performance.","Determining the ground truth of action values is very difficult, if not impossible; deciding which of xT and VAEP gives the better estimate for specific action types is not straightforward.;Both rankings are biased towards attacking players because offensive actions have access to higher rewards in both frameworks, so defensive players are ranked much lower.;VAEP's detailed feature-based representation comes at a cost in interpretability: explaining why a particular value is assigned to a specific game state is no longer straightforward.;Because VAEP assigns goals high action values, aggregated player ratings can vary significantly based on whether a small number of goals are included; for defensive players a difference of only three goals can double or halve their ratings.",,true,https://github.com/ML-KULeuven/socceraction,,authors,actively-maintained,compares-against:singh_2018_xt;compares-against:decroos_2019_vaep;critiques:singh_2018_xt;critiques:decroos_2019_vaep,true,2026-06-29,false,,

vanroy_2021_leaving_goals,pegah,2026-06-29,true,"Paper proposes a Markov Decision Process framework learned from event-stream data to evaluate team shooting policies via counterfactual reasoning (probabilistic model checking), assigning location-based shot values and analyzing decision making (shoot vs. move). Directly relevant to action valuation and decision recommendation for shots.",MDP-based counterfactual shooting-decision framework (Van Roy et al. 2021),markov,markov-decision-process,both,"ball location (state defined by current location of the ball);field partitioned into a 22-by-17 grid over the offensive half plus a single state for the defensive half (375 field states);three absorbing states: s_goal, s_no_goal, s_loss_possession;event-stream data of passes, dribbles and shots (StatsBomb);characteristics of actions and what happened prior to the actions (used by GBDT to predict intended end location of actions);StatsBomb xG values for individual shots (used to approximate the frequency-vs-efficiency trade-off)","Per-team MDP comprising: P(s, move_to(s'), s') (probability of successfully moving the ball from s to s'), P(s, shoot, s_goal) (location-based xG, i.e., probability of scoring from s), and policy pi(a|s); used to compute E[goals | pi] = sum_s E[shots in s | pi] * P(s, shoot, s_goal).",supervised,"Closed-form Markov Decision Process learned per team from event data; Gradient Boosted Trees Ensembles used to predict intended end locations of move actions (to estimate transition probabilities); PRISM probabilistic model checker used to compute properties (e.g., probability of generating a better shot later) and STORM mentioned as an alternative; counterfactual policy alteration via proportional re-weighting of action probabilities; expected number of state visits computed from the MDP fundamental matrix N = (I - Q)^-1.",22-by-17 grid over the offensive half (3.1m x 3.1m cells) plus a single state for the defensive half; 375 field states in total,"until possession ends (absorbing states s_goal, s_no_goal, s_loss_possession); also aggregated to a full season via expected number of state visits",per-possession,passes;shots;dribbles_carries,probability,per-zone;per-team-season,StatsBomb,event,statsbomb-private,English Premier League,2017/18;2018/19,,false,average relative error between estimated and actual number of goals per team (11.38%);expected number of goals per season under a policy (E[goals | pi]);difference in xG between move-then-shoot scenarios and shooting immediately;probability of ever generating a better shot than the current one within the same possession,decision-recommendation;tactical-pattern-discovery;team-ranking,,,,,,Per-team MDPs learned from 17 teams that appeared in both the 2017/18 and 2018/19 EPL seasons (76 matches per team); no explicit train/test split reported. Accuracy assessed by comparing estimated number of goals scored (under the observed policy) to actual goals recorded in the data for each team.,in-game-decision-support;post-match-analysis;opponent-analysis;tactical-pattern-discovery;training-feedback;season-evaluation,,partially-interpretable,not-reported,"Section 1 (Introduction), page 2 | The seven high-volume long-distance shooters (Eriksen, Pogba, Kane, De Bruyne, Son, Hazard, Sigurdsson) converted 6.5% of their 416 long-distance shots across the 2017/18 and 2018/19 EPL; in the 4455 times these seven players touched the ball in the long-distance zone and did not shoot, their teams only ended up scoring a goal in 2.1% of these possessions.;Section 2.1 and Figure 2, page 4 | The MDP partitions the offensive half of the pitch into a 22-by-17 grid and uses a single state for the defensive half, yielding 375 field states (cells are 3.1m x 3.1m).;Section 2.2, page 5 | The MDPs are learned per team using StatsBomb event stream data from the 2017/18 and 2018/19 English Premier League, considering only the 17 teams that appeared in both seasons (76 matches per team).;Section 3.2.2 (Accuracy of estimating the number of goals), page 10 | The average relative error between the estimated number of goals scored according to the observed-policy analysis and the actual number of goals recorded for each team is 11.38%; for an average team scoring around 50 goals per season this corresponds to roughly six goals.;Section 4.2 and Figure 7, page 14 | The probability of ever generating a better shot in the same possession can be as low as 5% in some locations; on the edge of the box directly in front of goal it is only between 5% and 10%; in other locations (e.g., Manchester United's left side of attack) it can be around 20%.;Section 4.3 and Figure 8, page 15 | Uniformly increasing the frequency of long-distance shooting by 5%, 10%, or 20% increases the expected number of goals per season for most teams (e.g., Chelsea +0.3 / +0.5 / +1.0; Everton +0.2 / +0.4 / +0.8); some teams (Burnley, Liverpool, Newcastle United) see no gains or a slight decrease.;Section 4.4 and Figure 9, page 16 | A targeted increase in long-distance shooting (only from locations where shooting was deemed better than moving) yields expected-goal gains for all teams: shooting 10% more often yields about an additional half a goal per season, and 20% more often yields roughly an extra goal for most teams (e.g., Chelsea +1.6 at +20%).;Section 1 (Introduction, summary of findings), page 3 | Per-team analysis identifies specific long-distance zones where increasing shot frequency by 10-20% would likely lead to an increase of 0.5-1.5 goals in a season.;Section 4.4 and Figure 10, page 17 | Using data from the last ten EPL seasons (2010/11 to 2019/20), the figure shows that every goal scored during a season equates to roughly one point in the final table (fit Points = 0.956 x Goals scored + 2.451).","The 6.5% conversion figure for the seven long-distance shooters is likely an underestimate as rebounds (i.e., other chances created due to a shot from distance) are not taken into account (footnote 1, page 2).;Event stream data records the location where the ball went out of bounds but not the location it was intended to reach; hence the number of unsuccessful move actions from state s intended to reach state s' cannot be directly estimated from data and must be approximated using a Gradient Boosted Trees Ensemble (Section 2.2, page 6).;The MDP uses a coarse partitioning (22-by-17 in the offensive half, single state for the defensive half) chosen as a trade-off between expressiveness and data sparsity (Section 2.1, page 4).;Accurately modeling the frequency-versus-efficiency trade-off when altering the policy would be a complicated undertaking in its own right; the paper approximates it with a simpler adjustment based on the StatsBomb xG distribution within each state (Section 3.2.2, 'Estimating P'(s, shoot, s_goal) in pi'', pages 9-10).","Extend the framework to other aspects of the game, e.g., analyzing whether a forward or a backward throw-in is more suitable in a specific situation, and how to effectively play out from the back (Section 6, Conclusions).;Further investigate the full potential of the framework (Section 6, Conclusions).",false,,,,,compares-against:vanroy_2020_xt_vs_vaep,true,2026-06-29,false,,

vanroy_2021_markov_reward,pegah,2026-06-29,true,"Paper learns a Markov Decision Process model of soccer from event stream data to evaluate in-game decision making, including rating players' decision-making riskiness and analyzing shooting policies.",Markov model for soccer decision making (Van Roy et al. 2021),markov,markov-decision-process,state,"event stream data;on-the-ball action type (pass, cross, dribble, shoot);start location of action;end location of action (observed);body part used to execute the pass;direction of the pass;start and end locations of the previous three actions in the sequence;success/failure flag;xG values of shots (used in counterfactual policy use case)",Per-state value V_pi(s) = probability of eventually scoring from state s under the team's policy; intermediate models predict P(action success) per state-action and pi(a|s) per state.,supervised,"Hierarchical Bayesian model (Bernoulli/Categorical with Normal log-odds and Half-Normal variances, weakly-informative priors via Gaussian-smoothed counts) fit with PyMC3 ADVI; XGBoost gradient boosted trees ensembles for predicting intended end locations of failed passes and crosses; domain-knowledge post-processing; Bellman value iteration / fundamental matrix for derived quantities; PRISM probabilistic model checking for policy queries.",Two grids: (a) offensive grid with defensive half as one state and offensive half split into 3m x 3m zones; (b) regular grid of 12 x 16 cells,"until end of possession (absorbing states: lost_possession, no_goal, goal)",per-event,passes;shots;dribbles_carries,probability,per-action;per-zone;per-player-season;per-team-season,whoscored.com (scraped),event,other-public,English Premier League,2017/18;2018/19,,false,AUROC;Brier score;expected log pointwise predictive density (PSIS-LOO-CV);mean absolute error vs. empirically derived state values,player-ranking;tactical-pattern-discovery;decision-recommendation;calibration,Baseline predicting prior distribution over observed end locations (for end-location prediction);Non-hierarchical (unpooled) Bayesian model with zero-mean Normal prior (sd=5.0) per team (for transition/policy models),true,true,false,true,70-30 train-test split with 5-fold cross-validation for XGBoost hyperparameter tuning on successful passes/crosses; Bayesian models evaluated using PSIS-LOO-CV; complete Markov model validated by comparing model-derived state values to empirically computed state values from raw data. Splits are event-level for end-location prediction (not match-level).,post-match-analysis;season-evaluation;tactical-pattern-discovery;scouting;in-game-decision-support,false,partially-interpretable,medium,"Table 1 | With domain-knowledge post-processing, the pass intended-end-location model achieves AUROC 0.99 (+/- 0.00) and Brier 0.54 (+/- 0.02) on the offensive grid, and AUROC 0.99 (+/- 0.00) and Brier 0.69 (+/- 0.03) on the full regular grid, outperforming the XGBoost-only and prior-distribution baselines.;Table 1 | With domain-knowledge post-processing, the cross intended-end-location model achieves AUROC 0.95 (+/- 0.01) / Brier 0.77 (+/- 0.06) on the offensive grid and AUROC 0.95 (+/- 0.02) / Brier 0.58 (+/- 0.08) on the full regular grid.;Table 2 | Hierarchical Bayesian models outperform non-hierarchical (unpooled) versions on PSIS-LOO-CV expected log pointwise predictive density for both policy and transition probability models and for both state spaces (e.g., policy on offensive grid: -167.6 +/- 0.79 hierarchical vs -182.7 +/- 0.80 unpooled).;Section 5.3 | Mean absolute error between model-derived state values and empirically computed state values, averaged over the six teams, is 0.029 (+/- 0.01) using the offensive grid and 0.018 (+/- 0.01) using the full regular grid.;Figure 5; Section 6.2 | Counterfactual policy analysis indicates that shooting 20% more often from the identified good long-distance locations would add an estimated 2.5 additional goals per season for Chelsea, 1.6 for Huddersfield/Man City/Man Utd, 1.2 for Newcastle, and 0.7 for Burnley.;Tables 3 and 4; Section 6.3 | All players evaluated received a negative net risk rating, meaning all players perform more conservative actions than risky ones; least-risky top-10 is dominated by Manchester City players (e.g., Zinchenko -50.107), while most-risky top-10 is dominated by Burnley and Newcastle players (e.g., Jacob Murphy -7.697).;Figure 4; Section 6.1 | Team-specific good shooting locations exist outside the penalty box where shooting immediately yields higher chances of scoring than moving once prior to shooting; locations lie on both sides of the penalty arc for Chelsea, more on the left for Huddersfield, and more centrally for Manchester City.","Event stream data does not record the intended end location of failed actions, requiring predictive modeling and domain-knowledge post-processing to estimate them.;Data is sparse, particularly near the opponent's goal, motivating the hierarchical Bayesian shrinkage toward a global prior.;No ground truth model is available, making validation of the learned Markov model difficult; the authors must resort to indirect evaluation strategies.;Counterfactual policy changes cannot be implemented in real matches solely for evaluation purposes.;Event stream data contains no information about the location of off-the-ball players, limiting the amount of context that can be included in the model.",,false,,,,,compares-against:vanroy_2020_xt_vs_vaep,true,2026-06-29,false,,

wu_2023_offball,pegah,2026-06-29,true,"The paper develops an automatic, quantitative metric (defensive anticipation) for evaluating off-the-ball defensive actions in soccer, using machine learning over player tracking data. This is squarely within the action-valuation / off-ball-action literature.",Defensive Anticipation Metric (P-score),tree-ensemble,hybrid,action,"location of the player (2-dim);player velocity at time t-Delta (2-dim);location of the ball (2-dim);distance of the player to the ball (1-dim);distance of the player to offensive goal (1-dim);angle of the player to offensive goal (1-dim);location of the goalkeeper (2-dim);distance of the player to goalkeeper (1-dim);indicator for the player on offensive or defensive side of the field (1-dim);indicator for player belonging to the home or road team (1-dim);seconds remaining in the half of the game (1-dim);seconds remaining in the full game (1-dim);for each of the player's three nearest teammates: location (2-dim), velocity (2-dim), distance of the player to teammate (1-dim), distance of the ball to teammate (1-dim), relative angle of the teammate to the player of interest (1-dim);for each of the player's three nearest opponents: location (2-dim), velocity (2-dim), distance of the player to opponent (1-dim), distance of the ball to opponent (1-dim), expected possession value EPV of opponent (1-dim), relative angle of the opponent to the player of interest (1-dim)","Two-dimensional velocity vector (y1, y2) — directional components — of a defensive player in a given spatio-temporal situation; derived metric p compares observed vs predicted velocity to score defensive anticipation.",supervised,"Two LightGBM gradient-boosted tree models (one per velocity component, x and y), trained over a 61-dimensional covariate vector built from tracking data. Per-instance score p is a closed-form projection (Eq. 1) of the observed velocity onto the predicted velocity direction; season-long P-score is the mean of p across instances scaled by 100% (Eq. 2).","continuous (x,y)","next instant (predict velocity at time t given state, with Delta = 0.5 seconds prior velocity covariate; analysis stepped every epsilon = 1 second)",per-frame,defensive_actions;off_ball_actions,unitless-rating,per-frame;per-player-season,Shandong Luneng Taishan FC (CSL data provided by Daniel Stenz),event;tracking-2d,club-proprietary,Chinese Super League (CSL),2019,237,false,mean absolute error of 0.319 m/sec in the x-coordinate velocity;mean absolute error of 0.398 m/sec in the y-coordinate velocity;correlation r ≈ 0.9 between predicted speed at time t and actual speed at time t-Delta (with Delta = 0.5 seconds);rank consistency of P-score across even vs odd weeks (Table 1: identical ranks for top-10 Shandong Luneng players);Pearson correlation between P-score and fouls = 0.60;Pearson correlation between P-score and successful tackles = 0.65;Pearson correlation between P-score and interceptions = 0.49;Leaguewise scatterplot correlation R = 0.32 (interceptions per game) and R = 0.29 (tackles won per game),player-ranking;tactical-pattern-discovery,,false,false,true,false,"20-week season partitioned into training (even weeks 2,4,...,20) and test (odd weeks 1,3,...,19); leave-one-week-out cross validation used to select LightGBM tuning parameters. Split is by week rather than strictly by match; potential within-week leakage not discussed.",scouting;season-evaluation;transfer-target-id;post-match-analysis,,partially-interpretable,medium,"Section 3.3 (Computational Overview) | Using roughly four million spatio-temporal instances, the LightGBM models predict the two-dimensional velocity vector of a defensive player; the fitted model provides a mean absolute error of 0.319 m/sec in the x-coordinate velocity and 0.398 m/sec in the y-coordinate velocity.;Section 3.3, Figure 1 | The tuning parameter Delta = 0.5 seconds was selected such that the correlation between predicted speed at time t and actual speed at time t-Delta is approximately r = 0.9 (Figure 1).;Section 2 (DATA) | The 2019 CSL dataset consists of 237 regular season matches (from a potential 240; 3 missing) across 16 teams, with tracking data recorded every 1/10th of a second (roughly one million rows per match across 7 variables).;Section 3.3 (Computational Overview) | The design matrix used for model training contained 3,770,289 rows and required just under 100 hours of computation on a laptop computer; LightGBM training itself required approximately 1.5 hours.;Section 4 (Results and Assessment) | Observations with predicted speed less than the threshold of 0.20 m/sec (0.72 km/hour) were removed from the metric; in the test dataset, 1.8% of observations were removed due to the threshold constraint.;Section 4.1 (Reliability), Table 1 | Reliability: for the 10 Shandong Luneng players with N > 10,000 instances in both even and odd weeks of 2019, the rankings produced by the defensive anticipation metric are identical across the two sets of weeks.;Section 4.2 (Validity), Table 2 | Validity: correlations between the P-score and season-long aggression statistics for the 10 Shandong Luneng players are 0.60 (fouls), 0.65 (successful tackles) and 0.49 (interceptions).;Section 4.2 (Validity), Figure 5 | League-wide, for all CSL players with at least 500 minutes played in 2019, scatterplots relate P to interceptions per game (R = 0.32) and tackles won per game (R = 0.29).;Section 4.2 (Validity), Figure 6 | Averaged across all CSL players in 10-minute intervals, P decreases as the match progresses, with a sharp drop after the 70th minute; this conforms to the common-sense expectation that defensive anticipation declines as players tire.;Section 4.2 (Validity) | Among CSL players with regular minutes, the two highest P-scores are Chang Feiya of Wuhan Zall (P = 5.71) and Yang Shiyuan of Shanghai SIPG (P = 5.33).;Section 4.2 (Validity), Figure 4 | Validity by playing position: among all 438 outfield CSL players (n = 79 wide midfielders, n = 77 wide defenders, n = 86 forwards, n = 110 central midfielders, n = 86 central defenders), there is little difference in P across playing positions; central midfielders have slightly larger values on average and forwards exhibit greater variability (Figure 4).","There is no gold standard for 'defensive anticipation' to validate against; the authors note that they 'do not know with certainty which players play with more and less defensive anticipation'.;The approach considers off-the-ball actions only for defensive players (i.e. when the player's team does not have possession); offensive off-ball movement is acknowledged as a more challenging future-research direction because there are multiple potential paths offensive players may choose.;Inferences are specific to the 2019 CSL season, although the methods are claimed to be applicable to any league with tracking data.;Three of the 240 potential regular-season matches are missing from the dataset.","Investigating alternative predictive models beyond LightGBM for predicting average player movement.;Extending the framework to evaluate off-the-ball actions for players on the team in possession (offensive off-ball movement), which is harder because there are more viable options for offensive players.",false,,,,,,true,2026-06-29,false,,