PDF : Jensen_2013_Estimating_Player_1.pdf
Estimating Player Contribution in Hockey with Regularized Logistic Regression
Robert B. Gramacy, Matthew A. Taddy, Shane T. Jensen
(Submitted on 22 Sep 2012 (v1), last revised 12 Jan 2013 (this version, v2))
PRNewswire story that links to a release from U of Chicago:
http://www.prnewswire.com/news-rele...w-research-from-chicago-booth-210979841.html?
U of Chicago article:
http://www.chicagobooth.edu/about/newsroom/news/2013/2013-02-13-hockey
Estimating Player Contribution in Hockey with Regularized Logistic Regression
Robert B. Gramacy, Matthew A. Taddy, Shane T. Jensen
(Submitted on 22 Sep 2012 (v1), last revised 12 Jan 2013 (this version, v2))
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.
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An exception is Pavel Datsyuk, who stands out as the league's very best, having a coefficient that is unmoved even after considering the strong team effect of his Red Wings.
PRNewswire story that links to a release from U of Chicago:
http://www.prnewswire.com/news-rele...w-research-from-chicago-booth-210979841.html?
U of Chicago article:
http://www.chicagobooth.edu/about/newsroom/news/2013/2013-02-13-hockey
While baseball has been transformed by statisticians, hockey remains less affected. That is partly due to the fact that baseball generates more data than hockey does. Moreover in hockey, it’s far more difficult to isolate individual performance.
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While its simple formulation is appealing, the plus-minus statistic has important flaws, according to the researchers. A key weakness is that a player’s plus-minus score depends partly on the performance of his teammates and opponents, which makes evaluating a player’s performance based on his own abilities more challenging.
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Through new techniques developed in the study, Gramacy, Jensen, and Taddy were able to come up with a more precise measure of performance—one that can isolate each player’s unique contribution to a goal. Using a type of statistical analysis called regularized logistic regression, which can estimate the credit or blame that should be apportioned to each player every time a goal is scored, they drew conclusions about player performance that were markedly different from traditional plus-minus figures. When the authors applied this new performance measure to data from four regular NHL seasons (2007 to 2011), they found that far fewer players stood out from their team’s average performance, and they were able to identify overvalued and undervalued players.
For example, the Pittsburgh Penguins’ Sidney Crosby is considered by many to be the best player in the NHL. But using the more precise measure shows that he made a much smaller contribution to goals than his plus-minus rating suggests. The same was true of Alex Ovechkin of the Washington Capitals, who had the largest plus-minus statistic of the league. Evgeni Malkin of the Pittsburgh Penguins and Tampa Bay Lightning’s Vincent Lecavalier both received huge salaries, but the authors’ estimates show that these players did not make significant contributions to goals after taking team effects into account.