Towards explainable sports analytics: A physics-based trajectory simulation model for predicting yards after catch in American football

Yards after catch (YAC) is one of the most consequential outcomes in American football, yet existing predictive models operate as opaque black boxes that cannot be interrogated by coaches or analysts. This study presents a physics-based trajectory simulation model that addresses this gap through three methodological contributions: a Monte Carlo path-optimisation framework that exhaustively evaluates 2197 candidate trajectory combinations per play, a momentum-based collision sub-model that predicts tackle-break probabilities and post-contact yards from conservation-of-momentum principles, and a tree-based search for the maximum-expected-gain trajectory. The model employs classical kinematics to simulate ball carrier and defender movement and incorporates empirically derived collision physics. Using NFL Next Gen Stats tracking data from the 17-week 2018 regular season (13,573 plays), our model achieves a Mean Absolute Error (MAE) of 3.19 ± 0.12 yards under 5-fold cross-validation at the game level. This performance matches that of gradient boosting machines (MAE: 3.25) and exceeds that of random forests (3.30), XGBoost regressors (3.53), and deep neural networks (3.73), all evaluated on identical folds. The model's inherent transparency allows analysts to deconstruct the factors influencing YAC, providing actionable insights for strategic decision-making without sacrificing predictive power.