Blame is easier than praise: Measuring off-ball defensive performance in football
Authors: Jonas Bischofberger, Runqing Ma, Pascal Bauer, Kilian Arnsmeyer, Arnold Baca
Abstract
The defensive performance of football players is commonly measured through a limited number of actions like tackles and interceptions while their continuous impact through positional behaviour has hardly been studied before. We formulate this problem as an attribution over multi-agent spatiotemporal trajectories without player-level ground truth labels, where event-level changes of expected threat are distributed among individuals. We propose a framework that performs this attribution using player involvement scores calculated from defensive pressure areas (DPAs). By computing role-conditioned baselines within automatically detected team structures, we can determine each defender's expected responsibility for threat created through arbitrary passes. The validity and robustness of this approach are evaluated on a uniquely extensive cross-gender and cross-competition data set, including positional and event data from 64 matches of the men's World Cup, 116 matches of the women's German Bundesliga and 336 matches of the men's German 3. Liga. In the absence of a ground truth, we propose an evaluation protocol that combines multiple relatively weak proxies into robust summary scores. We find a validity score that is improved by around 1 standard deviation compared to the best action-based metric and demonstrate that many popular measures show limited validity. The "blame" for conceding high-value actions shows especially strong correlations with external ratings and market values, making it the first published metric in football to reliably measure positioning errors. All code underlying this work is publicly available to support reproducibility and further research.
Spatial football metrics such as pitch control assume access to the positions of all 22 players, yet the most widely available source of positional data -- the broadcast main camera -- shows only 10-16 of them at any moment. We quantify the resulting distortion with an open, reproducible benchmark: a simulated broadcast viewport applied to open full-pitch tracking data (Metrica Sports; three matches, one held out from method development). Ignoring off-screen players -- the visible-only baseline implied whenever a video-based game-state-reconstruction (GSR) pipeline adds no imputation layer -- inflates hidden-zone pitch-control error to 25.1-26.9 percentage points and a mean absolute control-share error of 11.1-13.4 points across the three matches. We then evaluate a ladder of training-free, online imputation baselines that use only observations from the match being analysed. The best overall on these decision-relevant metrics, role-anchored centroid voting (each visible player votes for the full-team centroid by subtracting its running role offset, attenuating the viewport-induced subset bias), roughly halves hidden-zone error (to 12.2-13.8 points) and cuts control-share error to 28-48% of the ignore policy at every viewport width from 36 m to 60 m in all three matches. For occlusions <=9.6 s -- the regime of the closest learned prior work -- it reaches binwise median position errors of 3.3-8.9 m; but 50-57% of hidden-player observations lie beyond that regime. Integrated end-to-end into a broadcast-video GSR pipeline, imputation moves a downstream possession-quality score (Space-Creation Index) by 15.6 and 17.2 points on two real World Cup broadcast windows, flipping the verdict class in one.
We recast pass evaluation in football (soccer) as a Monte Carlo Tree Search (MCTS)-like evaluation problem whose components mostly exist in the literature under different names: a value model (possession value), a world model (multi-agent trajectories with ball interactions), and a policy over counterfactual actions (sampling pass variants with noise). Building on the first public high-fidelity tracking dataset with 3D ball trajectories from the Bundesliga, we introduce Monte Carlo Pass Search (MCPS), which infers kick parameters for each observed pass, samples execution variants and option variants, rolls each candidate forward with a ball-conditioned world model until the next ball interaction, and scores outcomes with a learned value model to obtain a distribution over gained value. This distribution enables distribution-aware attribution with two complementary execution-surplus scores used for analysis and ranking: mean-based and percentile-based scores. To make the world model sample-efficient under limited public data, we adapt a discrete-token, autoregressive trajectory generator from autonomous driving (SMART) and show it yields strong best-of-20 forecasting accuracy compared to baselines, while supporting fully hypothetical rollouts for downstream evaluation. We have released model checkpoints and code.
Traditional player evaluation in professional handball relies on basic box-score metrics or heuristic indices, which fail to credit the multi-player build-up chain. While football (soccer) analytics has adopted Expected Threat (xT) and Valuing Actions by Estimating Probabilities (VAEP), these event-based action valuation frameworks have not yet been adapted to handball. In this paper, we present the first comprehensive adaptation and evaluation of xT and VAEP for handball, utilizing five seasons of tracking-derived event data from the Handball Bundesliga. We develop Handball-xT (H-xT) using a handball-native court zoning layout, demonstrating via simulations that it is systematically more robust than standard rectangular grids. We optimize Handball-VAEP (H-VAEP) by tailoring its feature space and selecting the context length to limit team-identity leakage. Our evaluation shows that H-VAEP yields exceptionally stable, discriminative, and intuitive player ratings that highlight build-up play. Finally, we release our complete code repository to help professional clubs deploy these models.
Julius Broermann, Oliver Müller, Michael Döring +1