A Regression-Adjusted Hockey Plus-Minus Metric

• 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): Robert B Gramacy*+ and Shane T Jensen and Matthew A Taddy
• Companies: The University of Chicago and The Wharton School and The University of Chicago
• Keywords: logistic model ; regularization ; Bayesian ; data augmentation ; latent variable ; Gibbs sampling

Abstract

We present a logistic regression model for backing out player contributions when goals are scored in hockey. The traditional plus-minus statistic, which gives each player on the ice one unit of credit (for or against), has long been regarded as a poor (and noisy) metric for ranking players. Our approach takes a longer view by considering the aggregate of all matchups involved in each goal, as well as overall team contributions and other factors. The large-p large-n nature of the data requires the use of shrinkage priors. Inference in this context has, until recently, been cumbersome. Therefore, this paper acts as a fitting showcase of two new methods: a Gibbs sampler for fully Bayesian inference; and an EM-style algorithm for variable selection and MAP inference. The result of the analysis is that most players don't stand out as strong (positive or negative) contributors. This allows the stars to really shine, and brings to light a few surprising underperformers overlooked in earlier analyses.