Abhijit Brahme | Searcharxiv

arXiv2026

Who Blocks Whom? Probabilistic Pass-Blocking Assignments for Evaluating Blockers and Pass Rushers in American Football

Historically, statistical analysis of offensive lineman has been hindered by the lack of easily measurable quantities. More recently, with the introduction of player tracking data new methodological advances are now possible. Using high-dimensional spatio-temporal data, we adapt the defensive-matchup hidden Markov model of \cite{franks2015characterizing} from basketball to football pass protection, producing frame-by-frame probabilistic assignments of each pass blocker to the rushers. We show how this probabilistic assignment is a usable modeling artifact that augments existing player-evaluation frameworks. We directly quantify the attention a rusher commands, upgrade adjusted plus-minus \citep{Macdonald+2012} from all-or-nothing stints to partial, continuous blocking credit in continuous time, yield block-shedding survival metrics, and measure the space a rusher generates for his teammates. Fit to the first eight weeks of the 2021 NFL season, the resulting metrics recover widely-recognized elite rushers and pass protectors and align with independent charting.

stat.AP↗

arXiv2026

Concave Processes for Multi-Task Career Trajectories: Evaluating Aging Across Multiple Measures of NBA Performance

NBA athlete performance tends to increase through early career as athletes develop and acclimate to the league, followed by decline due to age-related deterioration in athleticism. While this general pattern persists, the precise shape of this trajectory varies by athlete and across different measures of performance. To model performance increase and decline, we introduce the concave process prior, a novel nonparametric prior over concave functions. We then use a latent variable model to characterize dependence in aging profiles across player-metrics, embedding each player in a shared low-dimensional latent space so that players with similar profiles learn similar trajectory shapes, peak ages, and peak values. Posterior analysis of the learned embedding supports latent-space nearest-neighbor retrieval of career-comparable players and informed projections of young players. We apply our model to data across over a dozen performance metrics for over two thousand players in seasons ranging from 1997 to 2026. Our results show that jointly modeling all metrics improves held-out predictive performance over single-metric alternatives, and that the concavity constraint itself improves prediction. We find that athleticism-driven metrics such as blocks and offensive rebounds peak in a player's early twenties, while skill-based shooting metrics peak in the mid-twenties or later.

stat.AP↗