Bayesian multilevel step-and-turn models for evaluating player movement in American football

Abstract

In sports analytics, player tracking data have driven significant advancements in the task of player evaluation. We present a novel generative framework for evaluating the observed frame-by-frame player positioning against a distribution of hypothetical alternatives. We illustrate our approach by modeling the within-play movement of an individual ball carrier in the National Football League (NFL). Specifically, we develop Bayesian multilevel models for frame-level player movement based on two components: step length (distance between successive locations) and turn angle (change in direction between successive steps). Using the step-and-turn models, we perform posterior predictive simulation to generate hypothetical ball carrier steps at each frame during a play. This enables comparison of the observed player movement with a distribution of simulated alternatives using common valuation measures in American football. We apply our framework to tracking data from the first nine weeks of the 2022 NFL season and derive novel player performance metrics based on hypothetical evaluation.

Figures (12)

• Figure 1: Our framework for evaluating player movement in this paper. We start by characterizing player movement with tracking data features, before building generative movement models. This allows us to perform simulations of player movement, enabling hypothetical evaluation relative to simulated trajectories.
• Figure 2: Simulated steps for an example play. The black path denotes the observed ball carrier trajectory after the handoff. At each frame along this path, a distribution of hypothetical next steps is generated (gray segments), against which the observed player movement can be evaluated. The blue and gold vertical lines represent the line of scrimmage and first down marker, respectively.
• Figure 3: Illustration of two metrics for characterizing player movement: step length and turn angle. The coordinate axes correspond to standardized football field coordinates, where the horizontal axis represents the end zone direction and the vertical axis represents the sideline direction.
• Figure 4: Joint and marginal distributions of step length and turn angle for running backs on run plays during the first nine weeks of the 2022 NFL season.
• Figure 5: Posterior distributions of the turn angle concentration random effect $w_j$ for NFL running backs with at least 70 rush attempts on running plays over the first nine weeks of the 2022 regular season. For each player, the posterior mean and corresponding 95% credible interval are depicted.