Is hitting important in the NHL? A study and a puzzle
Do hits – in the sense of players physically checking other players' bodies -- contribute to winning hockey games?
Here's a study from "On the Forecheck" that finds that they do. For the teams in the 2005-06 NHL, blogger "The Forechecker" ran a regression on hits inflicted vs. goals for and against, and found close to zero correlation. But then, he considered hits taken, this time regressing the ratio of hits inflicted divided by hits taken, on the ratio of goals for/goals against. This time, the correlation was significant, at -0.4. In chart form:
Hits inflicted vs. Goals For: .............. –0.03
Hits inflicted vs. Goals Against: .......... +0.05
Hits inflicted/taken vs. Goals for/against . -0.40 (p=.03)
The more a team gets hit, the better it turns out to be. The more a team hits, the worse it turns out to be.
Why would this happen? A commenter on Forechecker's post suggested that because a player can be legally hit only when in possession of the puck, a low hit ratio may be implying a high possession ratio, which in turn implies a good team.
That makes sense, and I'd bet he/she was right. Except that, if hits inflicted have nothing to do with goals, but hit ratio does, it must be hits taken that makes the difference. Using Forechecker's data, I ran a couple more regressions:
Hits taken vs. Goals For: ............... +.31 (p=.10)
Hits taken vs. Goals Against: ........... -.28 (p=.13)
Hits inflicted/taken vs. Goals For: ..... -.35 (p=.06)
Hits inflicted/taken vs. Goals Against: . +.34 (p=.07)
So the bottom line appears to be that hits taken is very important, but hits inflicted is only a tiny bit important.
Why would that be? Obviously, a hit taken by team A is a hit inflicted by team B, so there's a symmetry there. If team A somehow wins games in connection with being hit by team B, shouldn't team B lose games in connection with team A being hit?
The SD of hits taken is almost the same as the SD of hits inflicted, so it can't be compression of the data.
Could it just be coincidence? Any other ideas?