A Statistical and Machine Learning Framework for Quantifying Offensive Impact in Professional Box Lacrosse

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.

How would the probability of scoring change if a different player took the same shot? Although expected goals models describe the difficulty of scoring opportunities, comparing players on identical chances requires accounting for uncertainty in their estimated conversion probabilities. We address this question through a hierarchical Bayesian framework that evaluates alternative shooters under the same observed circumstances. Using 35,700 eligible shots from four leagues during the 2015/16 season, we compare a contextual benchmark with a primary player-intercept model and a provisional extension that allows player differences to vary with shooting conditions. Paired posterior draws preserve shared uncertainty when individual probability differences are aggregated across opportunities. Chronological validation demonstrates improved predictive performance relative to a constant-rate baseline, but introducing player effects provides negligible additional gains. Controlled single-seed experiments show that greater information per player improves estimation accuracy and narrows uncertainty intervals, although distinguishing small differences remains difficult and confident conclusions about near-null effects can become more frequent. Applications involving Giroud--Vardy and Berardi--Sansone similarly yield estimated differences that are small relative to their posterior uncertainty. These findings highlight an important distinction between predicting the outcome of a shot and establishing whether one player would be more likely to convert it. The proposed framework makes this distinction explicit by evaluating alternative shooters on fixed recorded opportunities while accounting for their contextual exposure. The resulting comparisons concern conditional conversion rather than the causal consequences of replacing a player in a match.

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.