The bestselling book Moneyball by Michael Lewis tells the story of how in 2002 the Oakland Athletics, a Major League Baseball team with a budget of about one-third of the New York Yankees payroll, revamped its line-up and eventually went on one of baseball history’s longest winning streaks. Rigorous statistical analysis convinced the Oakland A’s that on-base and slugging percentages—qualities that weren’t highly valued by other teams—were actually better indicators of players’ offensive abilities. This new way of assessing player performance helped the Oakland A’s find the most undervalued players in the market.
If baseball can do it, what about ice hockey? With a deal between the National Hockey League (NHL) and its players in place after a long lockout, ice hockey team owners might use statistics to make sure they’re getting the best players for the money. Research by Chicago Booth professors Robert Gramacy and Matt Taddy, with professor Shane Jensen of Wharton, suggests a useful metric.
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.
Hockey’s most popular measure of individual performance, beyond goals and assists, is plus-minus value: players on the ice get a “plus” for every goal scored by their team and a “minus” for every goal scored by the opposition. A player could theoretically score lots of goals but still have a negative plus-minus value if the opposition scored more.
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.
For example, most people have never heard of Rob Brown, who in his first two seasons in the NHL, with the Pittsburgh Penguins, had 174 points and a +35 plus-minus rating. Brown spent those two years playing on a line with Mario Lemieux, one of hockey’s all-time greats, and to whom he owed thanks for his impressive statistics. When Brown was traded two years later, to the Lemieux-less Hartford Whalers, he had 73 points in two seasons, and his plus-minus dipped to -21. So how much did Brown’s plus-minus really have to do with his individual performance? As one of Wayne Gretzky’s coaches, Glen Sather, once quipped, “Even a fire hydrant could score playing with Gretzky.”
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.
And by the authors’ estimates, some other players stuck out as undervalued. The Detroit Red Wings’ Pavel Datsyuk was actually the league’s best player, by the new metric.
Goaltender Dwayne Roloson’s negative plus-minus statistic (plus-minus statistics are not generally calculated for goalies, but the principle is exactly the same) suggested that he hadn’t played very well in the NHL, but a closer look using the authors’ performance metric shows that he was actually among the league’s strongest players.
Other undervalued players: The Winnipeg Jets’ Al Montoya is a solid player. Brian Boucher of the Philadelphia Flyers emerges as the top pick for a low-budget line-up—given his performance and a salary of just $925,000 per year, the authors think that he is extremely valuable for the money. Before the start of 2011-2012 NHL season the average player salary was about $2.4 million per year.
The authors find that a team assembled with the most expensive players fares only slightly better than a team formed on a small budget. But league owners, take note: the research evaluates players specifically in terms of contributions to goals. Even if overvalued players score fewer goals, they may earn their keep if their names sell tickets and jerseys.
“Estimating Player Contribution in Hockey with Regularized Logistic Regression.” Robert Gramacy, Shane Jensen, and Matt Taddy. Working paper, September 2012.