Hockey Player Performance via Regularized Logistic Regression

TL;DR

This paper introduces a regularized logistic regression approach to accurately estimate individual hockey players' contributions by modeling game situations and controlling for confounding factors, overcoming limitations of traditional plus-minus metrics.

Contribution

It presents a novel high-dimensional logistic regression model with regularization to infer individual player effects in hockey, accounting for complex game situations and interactions.

Findings

Effective estimation of player contributions in high-dimensional settings

Regularized logistic regression improves interpretability and stability

Software tools facilitate practical application of the methodology

Abstract

A hockey player's plus-minus measures the difference between goals scored by and against that player's team while the player was on the ice. This measures only a marginal effect, failing to account for the influence of the others he is playing with and against. A better approach would be to jointly model the effects of all players, and any other confounding information, in order to infer a partial effect for this individual: his influence on the box score regardless of who else is on the ice. This chapter describes and illustrates a simple algorithm for recovering such partial effects. There are two main ingredients. First, we provide a logistic regression model that can predict which team has scored a given goal as a function of who was on the ice, what teams were playing, and details of the game situation (e.g. full-strength or power-play). Since the resulting model is so high dimensional that standard maximum likelihood estimation techniques fail, our second ingredient is a scheme for regularized estimation. This adds a penalty to the objective that favors parsimonious models and stabilizes estimation. Such techniques have proven useful in fields from genetics to finance over the past two decades, and have demonstrated an impressive ability to gracefully handle large and highly imbalanced data sets. The latest software packages accompanying this new methodology -- which exploit parallel computing environments, sparse matrices, and other features of modern data structures -- are widely available and make it straightforward for interested analysts to explore their own models of player contribution.