Monte Carlo Pass Search: Using Trajectory Generatio... | AI Research

Monte Carlo Pass Search (MCPS) is a new framework designed to evaluate football passes by treating them as a distribution of possible outcomes rather than a single, fixed event. By combining a world model that simulates future player movements with a value model that measures scoring potential, the system can analyze how a pass might have unfolded under different conditions. This allows researchers and analysts to separate a player's decision-making from the physical execution of the pass, providing a clearer picture of both the quality of the choice and the robustness of the attempt.

Evaluating Passes as Distributions

Traditional football analytics often rely on "point estimates," which score a pass based solely on what actually happened on the pitch. MCPS moves beyond this by using a Monte Carlo approach to simulate hundreds of variations for every pass. These variations fall into two categories: "local" variants, which test how small changes in kick speed or direction affect the outcome (execution sensitivity), and "global" variants, which test entirely different passing options (alternative decision-making). By generating these counterfactual scenarios, the system creates a distribution of potential value, revealing whether a pass was a high-risk gamble or a reliable, high-reward play.

How the System Works

The framework functions like a simulation engine. First, it uses a solver to infer the specific kick parameters of an observed pass. Next, it employs a "world model"—a trajectory generator adapted from autonomous driving technology—to predict how players and the ball will move in the short term following the kick. Finally, a "possession value" model scores these simulated futures based on the likelihood of the team creating a scoring opportunity. By comparing the actual pass to these simulated alternatives, the system calculates two key metrics: a mean-difference score, which shows how much better or worse the chosen pass was compared to the average, and a percentile score, which ranks the pass within the distribution of all possible variations.

Key Findings and Performance

When tested on Bundesliga tracking data, the MCPS framework demonstrated a strong ability to forecast player and ball trajectories, outperforming standard baselines in accuracy. The researchers found that this approach effectively highlights passes that are robust to execution noise, as well as situations where a player may have missed a better passing option. The results suggest that by simulating "what-if" scenarios, teams can gain deeper insights into player performance that simple outcome-based statistics might miss.

Important Considerations

While the framework offers a sophisticated way to analyze football, it is important to note that the system is constrained by the quality and availability of tracking data. The authors emphasize that their model is a conservative tool; because it relies on generating hypothetical futures, it is subject to the inherent uncertainty of human movement. Furthermore, the evaluation is most reliable when the initial kick parameters can be inferred with high precision. The researchers have released their code and model checkpoints to encourage further development and reproducibility in the sports analytics community.