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.
Pass receiver selection is a fundamental task in football analytics, aiming to predict the intended receiver under a given game state. This task is challenging with event-centered freeze-frame observations, a broadcast-like setting that provides only partial and variable player visibility without complete trajectories or stable player identities. The model must therefore reason over anonymous visible candidates, opponent pressure, and recent context under partial observation. To address this setting, we propose a Hierarchical Possession-aware Graph Pointer Network (HPGPN), which formulates pass receiver selection as variable-size candidate prediction over visible teammates. HPGPN jointly models current player interactions, local event context, and possession-level temporal dynamics. It represents the current pass situation with a graph, incorporates fixed event context, and uses dynamic possession history to capture how the attacking sequence evolves. Candidate representations are refined hierarchically by integrating spatial, contextual, and historical evidence, and a glimpse pointer head scores the receiver candidates. Experiments on public football event and freeze-frame data show that HPGPN improves pass receiver selection performance. Ablation studies demonstrate the effectiveness of graph-based interaction modeling, fixed event context, and dual-branch dynamic possession-history modeling.
Dense pass surfaces give, for every pitch cell, whether a pass played there would arrive, whether the carrier would choose it, and what the possession would then be worth. The networks that draw them read the state as a raster of per-cell counts, losing where inside a cell each player stands. LiDAR detectors, bird's-eye-view perception and graph weather models move entity features onto a grid, binning each entity to a cell or learning the transfer. We evaluate the interpolated form: each player's features are scattered bilinearly onto the grid at the player's measured coordinates, so the surface loss trains the per-player encoder end to end. Those systems adopt an interface; this paper measures one. On 53,628 passes from the 2022 World Cup, painting improves selection likelihood over the same core fed rasters alone by about a quarter of a nat: in every match of an eight-fold cross-validation, with every arm tuned over five seeds, and after retraining on seven Bundesliga and 2. Bundesliga matches from another provider. Thirteen pre-specified studies locate the gain: painting the nine raw player features with no encoder carries three quarters of it, and the learned encoder and message passing add a smaller, resolved increment. Painting also helps the original SoccerMap and a canonical U-Net, whereas offset channels, a finer raster, an attention painter and a raster-free decoder do not. Frozen across the provider boundary the likelihood advantage is lost; injected tracking error compresses it. These results concern observed-endpoint prediction, not calibrated evaluation of hypothetical passes.
The process of decision-making in football is characterized by a complex interplay between spatial positioning, opponent pressure, and player intent. This work introduces a Graph Neural Network (GNN) framework designed to predict Receiver Selection, the optimal passing target, by modeling on-field interactions as dynamic graphs. Each player is represented as a node with positional and contextual features, while potential passing lines form weighted edges characterized by distance, angle, and pressure metrics. A Message-Passing Neural Network (MPNN) has been developed and trained using a combination of tracking data and event data from professional matches, synchronized through a robust pipeline based on an optimized version of the Needleman-Wunsch Algorithm. The model achieves competitive accuracy in identifying the actual chosen receiver and state-of-the-art accuracy within its top three suggestions. Our model further offers quantification of each option's likelihood, threat, and creativity, enabling performance analysts to evaluate over 1,000 passes in seconds.
Gabriel Masella, Giuseppe Alessio D'Inverno, Max Goldsmith +1