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Newly-created metric measures NHL players’ actual value

February 05, 2014

Are the most valuable players on the U.S. Olympic Hockey Team?

With National Hockey League teams adjusting their budgets to follow new salary restrictions that resulted from the 2012-13 lockout, a new metric created by University of Chicago Booth School of Business Professors Robert Gramacy and Matt Taddy, together with Professor Shane Jensen of Wharton, could help owners determine which players are overvalued and undervalued, and how to best shape their teams cost effectively.

Published in a recent issue of the Journal of Quantitative Analysis and Sports, the study, titled "Estimating Player Contribution in Hockey with Regularized Logistic Regression," discusses a more precise assessment which isolates a player’s involvement in a goal by calculating the partial effect of each player. Those figures then determine the appropriate credit deserved to individual players.

In hockey, aside from goals and assists, the most important player statistic is a plus-minus value. Players are given a plus if they are on the ice when their own team scores, and a minus if the opposing team scores. The result is that players can have positive values even if they're never part of a key play, or they can hold negative values despite impressive contributions.

Because the current system doesn't account for the effect of other players on the ice, special teams and other factors, individual players can be severely overvalued or undervalued based on their teammates' and opposition's cumulative performance, according to the authors. As a result, they could be receiving inflated or deflated salaries that may not be in line with their abilities.

When that statistical analysis was applied to NHL players from four regular seasons (2007 to 2011), the authors found decidedly different data on player performance than traditional figures, and identified several overvalued and undervalued players in the league. The paper suggests the isolated contributions of regarded and well-paid players like Sidney Crosby, Jonathan Toews, and Zdeno Chara should be re-evaluated. According to the authors, a team made up of the league’s most expensive players wouldn't compete much better than a low-budget team.

To keep the analysis current and encourage discussion of what, in some cases, may be
controversial results, Gramacy and Taddy started this blog from which they link to weekly,
updated cumulative and current-season player ability estimates. The code then automates the analysis (including data scraping from for full transparency. As the season has developed they, and others, have drawn interesting comparisons between players and commented on high profile trades.

In anticipation of the Olympics, the authors in a recent blog post consider certain high profile omissions from Team USA's roster, especially as compared to the team composition in their silver medal run four years ago. As an example, their analysis suggests that Erik Johnson (on the previous team) and Bobby Ryan should both have claimed spots over several players who were chosen, but whose player ability estimates were far below the league average.