Monte Carlo Pass Search: Using Trajectory Generation for 3D Counterfactual Pass Evaluation in Football

2026-06-09

AI Summary

This work proposes a fine-grained football pass evaluation method grounded in counterfactual reasoning. To address execution variability and multiple plausible outcomes of passes, it introduces Monte Carlo Tree Search into pass assessment for the first time, integrating a value model, a 3D ball-trajectory world model, and a counterfactual action policy. By generating noisy variants of observed passes and forward-simulating them until the next possession-changing interaction, the framework constructs a distribution over expected values. The study innovatively designs a dual scoring mechanism based on both mean and percentile execution surplus and employs a discrete-token autoregressive trajectory generator to enable fully hypothetical rollouts. Evaluated on the first publicly available high-fidelity Bundesliga 3D tracking dataset, the world model surpasses baseline methods in best-of-20 prediction accuracy and supports effective pass ranking. Code and models are publicly released.

Abstract

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.

Problem

• pass evaluation
• counterfactual reasoning
• 3D trajectory
• football analytics
• Monte Carlo Tree Search

Innovation

• Monte Carlo Pass Search
• counterfactual pass evaluation
• 3D ball trajectory
• autoregressive trajectory generation
• distribution-aware attribution