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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
of hockey analysis, 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 with publicly available software and we include the simple commands
used in our analysis. Our results show that most players do not stand out as measurably
strong (positive or negative) contributors. This allows the stars to really shine,
reveals diamonds in the rough overlooked by earlier analyses, and argues that some
of the highest paid players in the league are not making contributions worth their
expense.