an a Bad Economist Watches a Hockey Game
"Despite increasing public unease over violence in hockey, a statistical analysis of NHL data by university professors shows that on-ice fighting is a good strategy for team success."Well, isn't that interesting. And contradictory to current consensus.
At first sniff, it doesn't pass the BS test. While it's possible that instigating a fight may 'spark' one's team to a better performance, how do you distinguish which team is 'sparked?' If the fighting majors are coincidental, shouldn't both teams receive the same benefit? I just had to take a closer look. The paper is available here.
To summarize, Ordinary Least Squares is used to determine which variables contribute positively and negatively to team points and team goals against. Here are their equations:
PTS = a0 +a1(GA) + a2(A) + a3(TFW) + a4(TFL) + a5(PIM) +
a6(MAJORS) + a7(ESG) + a8(PPG) + a9(SHG) +
a10(G/SHOTS) + a11(PLSMIN) + a12(SAV) + a13(YEAR) + e
GA = a0 + a1LOG(TFW) + a2LOG(TFL) + a3LOG(PIM) +
a4LOG(G) + a5LOG(SAVPCT) + a6LOG(SHOTS) +
a7LOG(MAJORS) + a8LOG(YEAR) + e
The logs are used in the GA model "due to increased fit."
Right away, one glaring mistake stands out. To get useful results out of a regression analysis, you have to have independent variables (PIM, ESG, MAJORS etc.) that correlate highly with your dependent variable (PTS) but correlate minimally with each other. See caveat #5 here (pdf).
I.e. in hockey, it would be unwise to include, say, both 'total team salary' *and* 'team average age' as separate variables. One will surely be correllated with the other.
Your independent variables should not depend on one another. That's why they're called independent. Wikipedia calls this Multicollinearity. Multicollinearity is the source of "correlation, but not causation" effects. Other bloggers and hockey analysis websites have addressed this topic, but I'm too lazy to go looking for them.
Given that, how anyone could describe face-offs won and face-offs lost as separate, independent variables is beyond me. The authors of this paper do just that, and conclude that winning face-offs has a greater absolute effect than losing them:
"Thus, although TFW keeps an opposing team from scoring goals, TFL doesn’t necessarily imply a great chance for the opponent to score."So, winning a face off is better than not losing a face-off. Impeccable logic. We're headed for the age of the high-event face-off man, who wins *and* loses more than 50% of his draws.
Of course, I picked out the most obviously interdependent variables to pick on but I think I made my point. Fighting majors could also correlate with one of the other variables. Other analyses have been done (again, too lazy to go look for them) that isolate the fighting majors and show that losing teams accumulate more of them than winning teams.
Reading the paper wasn't a complete waste of time. The most interesting line was in reference to a prior study by someone else whose results "...show that teams with unusually high or low numbers of French-Canadians tend to be less efficient." Unfortunately, that paper appears to be unavailable.