Open Access
September 2013 Competing process hazard function models for player ratings in ice hockey
A. C. Thomas, Samuel L. Ventura, Shane T. Jensen, Stephen Ma
Ann. Appl. Stat. 7(3): 1497-1524 (September 2013). DOI: 10.1214/13-AOAS646


Evaluating the overall ability of players in the National Hockey League (NHL) is a difficult task. Existing methods such as the famous “plus/minus” statistic have many shortcomings. Standard linear regression methods work well when player substitutions are relatively uncommon and scoring events are relatively common, such as in basketball, but as neither of these conditions exists for hockey, we use an approach that embraces the unique characteristics of the sport. We model the scoring rate for each team as its own semi-Markov process, with hazard functions for each process that depend on the players on the ice. This method yields offensive and defensive player ability ratings which take into account quality of teammates and opponents, the game situation, and other desired factors, that themselves have a meaningful interpretation in terms of game outcomes. Additionally, since the number of parameters in this model can be quite large, we make use of two different shrinkage methods depending on the question of interest: full Bayesian hierarchical models that partially pool parameters according to player position, and penalized maximum likelihood estimation to select a smaller number of parameters that stand out as being substantially different from average. We apply the model to all five-on-five (full-strength) situations for games in five NHL seasons.


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A. C. Thomas. Samuel L. Ventura. Shane T. Jensen. Stephen Ma. "Competing process hazard function models for player ratings in ice hockey." Ann. Appl. Stat. 7 (3) 1497 - 1524, September 2013.


Published: September 2013
First available in Project Euclid: 3 October 2013

zbMATH: 1283.62245
MathSciNet: MR3127956
Digital Object Identifier: 10.1214/13-AOAS646

Keywords: Bayesian inference , Competing process models , Cox model , hierarchical models , ice hockey , player ratings

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.7 • No. 3 • September 2013
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