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Calculating the value of football player’s on-field performance has been limited to scouting methods while data-driven methods are mostly limited to quarterbacks. A popular method to calculate player value in other sports are Adjusted Plus–Minus (APM) and Regularized Adjusted Plus–Minus (RAPM) models. These models have been used in other sports, most notably basketball (Rosenbaum, D. T. 2004.  Measuring How NBA Players Help Their Teams Win .  http://www.82games.com/comm30.htm#_ftn1 ; Kubatko, J., D. Oliver, K. Pelton, and D. T. Rosenbaum. 2007. “A Starting Point for Analyzing Basketball Statistics.”  Journal of Quantitative Analysis in Sports  3 (3); Winston, W. 2009.  Player and Lineup Analysis in the NBA . Cambridge, Massachusetts; Sill, J. 2010. “Improved NBA Adjusted +/− Using Regularization and Out-Of-Sample Testing.” In  Proceedings of the 2010 MIT Sloan Sports Analytics Conference ) to estimate each player’s value by accounting for those in the game at the same time. Football is less amenable to APM models due to its few scoring events, few lineup changes, restrictive positioning, and small quantity of games relative to the number of teams. More recent methods have found ways to incorporate plus–minus models in other sports such as Hockey (Macdonald, B. 2011. “A Regression-Based Adjusted Plus-Minus Statistic for NHL players.”  Journal of Quantitative Analysis in Sports  7 (3)) and Soccer (Schultze, S. R., and C.-M. Wellbrock. 2018. “A Weighted Plus/Minus Metric for Individual Soccer Player Performance.”  Journal of Sports Analytics  4 (2): 121–31 and Matano, F., L. F. Richardson, T. Pospisil, C. Eubanks, and J. Qin (2018).  Augmenting Adjusted Plus-Minus in Soccer with Fifa Ratings . arXiv preprint arXiv:1810.08032). These models are useful in coming up with results-oriented estimation of each player’s value. In American football, many positions such as offensive lineman have no recorded statistics which hinders the ability to estimate a player’s value. I provide a fully hierarchical Bayesian plus–minus (HBPM) model framework that extends RAPM to include position-specific penalization that solves many of the shortcomings of APM and RAPM models in American football. Cross-validated results show the HBPM to be more predictive out of sample than RAPM or APM models. Results for the HBPM models are provided for both Collegiate and NFL football players as well as deeper insights into positional value and position-specific age curves.

Estimating player value in American football using plus–minus models