Regularized Bayesian NHL Player Ability Estimates

• Activity Number: 438
• Type: Invited
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Sports
• Author(s): Samuel L Ventura*+ and Andrew C Thomas
• Companies: Carnegie Mellon University and Carnegie Mellon University
• Keywords: Semi-Markov Processes ; Hazard Functions ; Lasso ; Ratings ; Hockey

Abstract

Evaluating the overall ability of players in the National Hockey League 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 neither of these conditions exists for hockey.

We use an approach for hockey that embraces these characteristics. We model the scoring rate for each team as its own semi-Markov process, with hazard functions depending 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 factors. These ratings have a meaningful interpretation in terms of game outcomes.

Additionally, since the number of parameters in this model can be quite large, we use a variant on the Lasso method to select a smaller number of parameters that are "extreme," so that some player abilities cannot be distinguished from "average" and affect their teammates' and opponents' ratings.