Do NHL teams get a boost after killing a two-man advantage?

In an OHL game I was watching the other day, one of the teams had a two-man advantage and didn't score. The announcer was disappointed that the shorthanded team to get a boost from having killed off the penalties, as conventional wisdom says they should.

Is conventional wisdom right? Now that I have access to a database of NHL games (thanks again to the Hockey Summary Project), I was able to check.

This study is basically the same format as the study I did on fights a few weeks back. I found all games from 1967-68 to 1984-85 where one team killed off a two-man advantage (of any length). Then, I found a random control game, which matched the score differential and the relative quality of the home and road teams. When I was done, I had two pools, each comprised of 1,703 games.

The teams that killed the penalties scored an average 0.26 more goals than their opponents from that point to the end of the game (actually, to the 17:00 mark of the third period). On the other hand, the control team scored only 0.12 more goals then their opponents.

That's statistically significant, at almost exactly 2 SDs.

I'll put that in chart form to make it easier to read, along with the SD. I use the term "killing teams" to mean the ones that actually killed off the two-man advantage.

Killing teams .... +0.26 goals (+/- 0.05)
Control teams .... +0.12 goals (+/- 0.05)
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Difference ....... +0.14 goals (+/- 0.07)

At six goals per win, you'd have expected the extra goals to have resulted in around 40 extra wins. They actually resulted in 32 extra wins. Actually, 36 extra wins, minus 8 fewer ties:

Killing teams .... 836-604-263
Control teams .... 806-626-271
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Difference ....... +36 wins, -8 ties

So, should we conclude that killing off a two-man advantage causes a psychological boost? Well, not so fast. Because, after you take two consecutive penalties, the referee is very likely to try to even things up by giving future penalties to the other team.

The difference of +0.14 goals is almost exactly what you'd get from a single power play. So, if the result of surviving a two-man advantage is that you get one extra "free" power play in the remainder of the game, that would explain the results exactly.

As it turns out, it's not quite that high. It's only half that high. On average, the teams that survived being shorthanded two men got about half an extra power play in the remainder of the game:

Killing teams ... +.346 power plays rest of game
Control teams ... -.130 power plays rest of game
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Difference ...... +.476 power plays rest of game

That leaves about 0.07 goals per game as the unexplained difference. It's only 1 SD, which is no longer statistically significant. It's about the effect of half a power play. Or, with an average save percentage of .900, it works out to 7/10 of an additional shot on goal.

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We can also handle the penalty issue another way. We can insist that when we choose a control game for the real game, we make sure the control team was the lone who took the last penalty. That way, we'd expect some of the referee "evening up" difference to disappear. Perhaps not all of it, because a two-man advantage isn't the same as a one-man advantage -- but at least part of it.

The additional restriction reduced the sample size to 1,662 games; for the remaining 41 games, I couldn't find a suitable control.

As it turns out, the goal difference stays about the same, even though the penalty difference is significantly reduced:

Killing teams ... +0.25 goals (+/- 0.05)
Control teams ... +0.08 goals (+/- 0.05)
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Difference ...... +0.17 goals (+/- 0.07)

Killing teams ... +.340 power plays rest of game
Control teams ... +.032 power plays rest of game
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Difference ...... +.308 power plays rest of game

The difference of .308 power plays accounts for around .04 goals of the observed .17 difference. That leaves .13, which is a little less than 2 SD from zero. Not statistically significant, but close. (Technically, it's even less than that, because the control games aren't completely independent. Also, when I ran the study a second time, I got +0.10 goals instead of +0.08, which lowers the difference. So think of the 1.9 SD as probably a bit too high.)

Strangely, though, there wasn't as much difference in game results; only the equivalent of 13.5 wins:

Killing teams ... 815-591-256
Control teams ... 807-610-245
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Difference: +8 wins, +11 ties

Again at six goals per win, you'd expect 47 wins, not 13.5. What happened?

Well, it turns out that the "killing" teams spent a lot of their goals winning blowouts. For instance, in games won by six goals or more, they were 81-34. The control group was only 73-51.

In those games, the difference was 12.5 wins. That normally "costs" 75 goals, but, for these games, the difference was really around 150 goals. So, that accounts for 75 of the 282 goal difference right there.

The "killing" group also "wasted" goals in the 3- and 4-goal games. That was offset by the opposite effect in five-goal games, but not by much.

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If you recall, we found the same effect when we looked at fighting: teams that started a fight appeared to score more goals, but not necessarily win more games.

What connects the two studies is ... penalties. It could be that teams that get penalized a lot win a lot of blowouts. Not necessarily because of cause-and-effect, but because it just so happened that, between 1967 and 1984, certain teams just happened to be high in both categories.

Or, it could be coincidence. Or, it could be something else.

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For my bottom line, I'd say: after killing off a two-man advantage, teams did appear to benefit by about 1/7 of a goal. Half of that can be traced to referees calling fewer penalties against them in the remainder of the game.

The other half is unknown. It's not statistically significant, so you have to give serious consideration to the idea that it's just coincidence ... but the teams *did* appear to benefit, by around 0.07 goals.

Historically, the average size of the "boost" in a team's play after a two-man kill has been small: the equivalent of less than a single shot on goal over the remainder of the game.