Do hockey fights lift a team's performance? Part II

The previous post was a study on NHL fights. It found that, generally, a fight doesn't help the team that it's sometimes said to help (the team that's behind in the game, for instance), but in one particular case, MAYBE it did. That was the case where:

(a) one team was behind in the game
(b) that team fought more regularly than the other team, and
(c) the player fighting also fought more often than the other team's fighter.

In that situation, that team appeared to benefit by around 0.13 goals, as compared to a similar team that didn't fight. That was about the same as one extra power play.

However, the result was not statistically significant, being only 1 SD away from zero. Still, I left it at least a little bit open whether the effect *might* be real.

Tom Tango is more skeptical than that:

It’s not monkeys at a typewriter creating Shakespeare, but it’s close.

Well, I have some more evidence that supports that point of view.

I repeated the study 27 times, to get a larger sample of random control games. (I didn't pick the number 27 beforehand; I just ran the thing over and over until I got sick of it.) Here's the average of those 27 runs:

Actual teams .... -0.18 goals
Control teams ... -0.29 goals
------------------------------
Difference ...... +0.11 goals

To remind you what this means: the fighting team meeting the conditions was outscored by its opponent by 0.18 goals over the rest of the game. On the other hand, the control teams, which were selected randomly from games which matched as closely as possible (except for the fight), got outscored by 0.29 goals.

So, it looks like the team that fought gained 0.11 goals per game. As I said, that result is not statistically significant.

But now, here's the new thing. Even though the fighting team gained 0.11 goals, it actually lost more games. Here are the records, in W-L-T format:

Actual teams .... 52-274-38
Control teams ... 49-267-48
----------------------------
Difference ...... -2 wins

So, even though the fighting teams did better on the scoreboard, they did worse in terms of winning games. Actually, they won three extra games, but they lost seven more and tied 10 fewer. That adds up to minus four points in the standings, which is why I write "-2 wins". (I'm ignoring the "pity point" for an overtime loss.)

You wouldn't expect this to happen, that you score more goals but lose more games. The better your goal differential, the better your outcomes should be. I think I saw Gabriel Desjardins write, somewhere, that six goals equals one win. The observed difference of +0.11 goals per game, over 364 games, equals around 40 goals, which is almost seven wins.

But instead of winning seven extra games, the fighting teams *lost* two extra games.

Why did this happen? I think it's just luck, well within the bounds of random error. I think the +0.11 goals per game is random chance, I think the -2 wins is random chance, and I think the discrepancy between the two results is also random chance.

In any case, if you don't like all this talk of significance levels and randomness, you can just summarize like this: overall, the teams that fought wound up very slightly better on the scoreboard, but very slightly worse in the standings.