A hockey fighting study

An academic study on hockey fights made the news in a couple of papers up here in Ottawa, a day or two after Marginal Revolution blogged it.

Here's the paper: "Blood Money: Incentives for Violence in NHL Hockey." It tries to figure out if fighting, and winning fights, helps teams win.

The study is a bit aggravating throughout, mostly because the authors don't seem to know hockey very well at all, and make some strange assumptions.

For instance, they equate fighting with "real" violence in hockey, not acknowledging that fighting is an accepted part of the game, and allowed by the rules (if you're willing to accept the five-minute penalty). The authors cite violent incidents like the J. P. Parise's aborted attack on referee Josef Kompalla in the eighth game of the 1972 Canada-Russia series, and Dino Ciccarelli's 1988 attack on Luke Richardson (video), and don't seem to understand that these are entirely different, in hockey culture, from a routine fight.

This leads them, in their conclusions, to recommend how much the NHL would have to fine players to give them incentives not to fight. I don't think that particular number is relevant, not just because of flaws in the study (which I'll get to), but because the NHL would have no trouble banning fighting if it really wanted to. The authors seem to imply that the league wants fighting to end, but doesn't know how much the fines have to be.

Also, judging from the middle paragraph of page 11, they seem to think that in individual scoring, a goal is worth two points (it's only worth one).

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Anyway, let me get to the meat of the study.

The authors run a bunch of regressions to predict team performance based on a few factors. For some reason, they regress on the probability of making various rounds of the playoffs, rather than regular season points. I'm not sure why they do this; obviously, this adds a lot of randomness.

It's a weird regression, too: the authors include games won, but also goals for and goals against, which aren't all that important once you have goals won. They also have a dummy variable for team, which doesn't make much sense either, since the Philadelphia Flyers of 1967-68 (when the study starts) have little in common with the Philadelphia Flyers of 2007-08.

However, the authors wind up with the statistically significant result that penalty minutes do lead to playoff success. All the coefficients for the probabilities (for simply making the playoffs, all the way up to winning the cup) are positive. Penalty minutes help teams make the various rounds of the playoffs with significance ranging from 1.76 SDs (making the finals) to 2.70 SDs (making the semi-finals).

For fights, the effect is even more extreme – all five categories show fights as statistically significant, except for winning the Stanley Cup. Fighting helps you win the first and second round of the playoffs with SDs of 4.37 and 4.62, respectively.

If I've done the math right, an extra 10 fights in the regular season (the average team in the last forty years had 73) improves your chances of making the quarter-finals from 26.7% to 32.5%, which seems like a lot.

I guess this confirms conventional wisdom, that, given two equal teams, the more aggressive one will do better in the playoffs, where checking is tighter and it's a more physical game.

Next, the authors try to predict a player's salary based on how often he fights. Some of their regressions include dummy variables for each player. That doesn't make sense to me. Effectively, those regressions compare a player's fights to the rest of his own career, and his salary is set long before he actually gets into those fights. So I'll ignore those.

Fortunately, some of the other regressions don't control for the player. According to those other regressions, every additional fight is worth $1606, (not statistically significant).

Even ignoring the insignificance, I'm not sure that figure is meaningful – instead of adjusting for salary inflation, the authors used year dummies. So $1606 is the average over 40 years of play, which means we don't really know what that is in today's dollars.

The authors also break down the fight bonus by position. A fight *costs* a winger $7120 in salary. It *costs* a centre $31129. But it *increases* a defenseman's salary by $47726 (significant at 7 SD). Again, this is kind of bizarre. Why would defensemen be rewarded, but not forwards?

Perhaps what's going on is this: the study controlled for games played, but not for ice time. For forwards, ice time is roughly proportional to points (which the study controlled for). But for defensemen, there are so many different styles that if a guy gets 30 points, you don't know if he's a part-time offensive defenseman or a full-time defensive defenseman. So maybe lots of fights, for a defenseman, is an indication of ice time, which is an additional indication of high salary.

The most interesting part of the study is where the authors look only at fights *won* (they got this information from various web sources, such as dropyourgloves.com). Compared to just plain fights, the coefficients for forwards stay roughly the same. But the bonus for defensemen is about double.

For fights "not won" (a loss or a no-decision), the numbers are almost the same as for fights won. This suggests that it doesn't really matter if the player wins the fight -- which shouldn't be a big surprise to most fans.

However, in the regression that included player dummy variables, the numbers for forwards came out double for winning than for not winning. The authors cite this in their conclusions, but I'm not convinced it means anything because of those inappropriate dummy variables. And why would it hold for wingers but not centers?

And I don't think too much of this stuff matters anyway, because I don't think the controls are strong enough that we can trust the results. I wouldn't be surprised if what's really happening is that players are being rewarded for being physical, for ice time, or for something else that correlates with fights. Only goals, assists, and games are otherwise controlled for, so there are a lot of other factors that could be correlated with fights.

Also, could it be that most or all of the effect is being caused by the presence of a few "goons," who are indeed paid to fight? Even if the "real" players' salaries were unaffected by fights, couldn't it be that the entire results of the regression are caused by the presence of enforcers, who we know are paid to fight?

The authors think so:

"We provide evidence for the proposition that observed low-ability wing players are paid a substantial wage premium to protect high-ability center players who can score goals. They do this by fighting with any other opposing player who threatens their star players, allowing the star player unfettered scoring possibilities. ... For this the wing players are paid a premium ..."

This is just weird. Did we really need more evidence that enforcers exist? Do the authors think this is new information? Isn't the best evidence for enforcers the fact that their existence is admitted to by every GM, coach, and player? And if you don't believe the hockey establishment, won't you believe their stat lines?

Did the authors of this study really do all this work just to prove that certain players are paid to fight?