Estimating Player Contribution in Hockey with Regularized Logistic Regression

• Activity Number: 1
• Type: Invited
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Journal of Quantitative Analysis in Sports
• Author(s): Robert B. Gramacy*+ and Matt Taddy and Shane Jensen
• Companies: University of Chicago and University of Chicago and University of Pennsylvania
• Keywords: logistic regression ; regularization ; lasso ; Bayesian shrinkage ; sports analytics

Abstract

We present a regularized logistic regression model for evaluating player contributions in hockey. The traditional metric for this purpose is the plus-minus statistic, which allocates a single unit of credit (for or against) to each player on the ice for a goal. However, plus-minus scores measure only the marginal effect of players, do not account for sample size, and provide a very noisy estimate of performance. We investigate a related regression problem: what does each player on the ice contribute, beyond aggregate team performance and other factors, to the odds that a given goal was scored by their team? Due to the large-p (number of players) and imbalanced design setting, a major part of our contribution is a careful treatment of prior shrinkage in model estimation. We showcase two recently developed techniques - for posterior maximization or simulation - that make such analysis feasible. Each approach is accompanied by publicly available software. The simple R commands we use, full scripting of data scraping from nhl.com, and graphical summaries of weekly updated player ability metrics are made publicly available via a blog and GitHub page for full transparency.