Adjusted Plus-Minus for NHL Players using Ridge Regression with Goals, Shots, Fenwick, and Corsi

TL;DR

This paper introduces a ridge regression approach to calculate adjusted plus-minus statistics for NHL players using goals, shots, Fenwick, and Corsi data, providing more reliable estimates of individual contributions.

Contribution

It applies ridge regression to hockey data, incorporating multiple metrics to improve the accuracy and stability of player contribution estimates compared to traditional methods.

Findings

Ridge regression reduces error bounds in player contribution estimates.

Using shot-based metrics increases data availability and estimate precision.

The model provides independent offensive and defensive contributions during various game situations.

Abstract

Regression-based adjusted plus-minus statistics were developed in basketball and have recently come to hockey. The purpose of these statistics is to provide an estimate of each player's contribution to his team, independent of the strength of his teammates, the strength of his opponents, and other variables that are out of his control. One of the main downsides of the ordinary least squares regression models is that the estimates have large error bounds. Since certain pairs of teammates play together frequently, collinearity is present in the data and is one reason for the large errors. In hockey, the relative lack of scoring compared to basketball is another reason. To deal with these issues, we use ridge regression, a method that is commonly used in lieu of ordinary least squares regression when collinearity is present in the data. We also create models that use not only goals, but also shots, Fenwick rating (shots plus missed shots), and Corsi rating (shots, missed shots, and blocked shots). One benefit of using these statistics is that there are roughly ten times as many shots as goals, so there is much more data when using these statistics and the resulting estimates have smaller error bounds. The results of our ridge regression models are estimates of the offensive and defensive contributions of forwards and defensemen during even strength, power play, and short handed situations, in terms of goals per 60 minutes. The estimates are independent of strength of teammates, strength of opponents, and the zone in which a player's shift begins.