Are more NHL penalties called in back-to-back games?

In a comment to one of the posts on "make-up" penalties, J.-P. Martel wrote,

"... blow-outs can easily lead to situations that get out of hand, so referees may call penalties on the leading team so that the trailing team still thinks it has a chance to come back, rather than resort to fighting to "prepare" the next game between the two teams.

Actually, you may want to check penalties in the second half of the third period when the teams' next game is (or may be, depending on outcome) against each other (particularly in the playoffs), as opposed to when it's not."

So I did. And, J.-P. is right, it looks like there's something there.

I found all cases from 1967-68 to 1984-85 where teams played back-to-back games (regular season only). Then, I formed three groups:

-- first game of back-to-back games
-- second game of back-to-back games
-- other games that year between those two teams

It turns out that, overall, there are more penalties than usual in the first game, and fewer penalties than usual in the second game:

First game .... 12.36
Second game ... 10.87
Other games ... 11.77

Broken down by periods:

-------------- Gm 1 --- Gm 2 --- Other
--------------------------------------
Period 1 ..... 4.78 ... 3.98 ... 4.37
Period 2 ..... 4.25 ... 3.75 ... 4.12
Period 3 ..... 3.32 ... 3.13 ... 3.26
--------------------------------------
Total ....... 12.36 .. 10.87 .. 11.77

So: there's 0.6 extra penalties in the first game, and 0.9 fewer penalties in the second game.

I thought the second game would be dirtier because the player are holding recent grudges from the previous game, but the numbers show the opposite. The players seem to be more aggressive early, rather than late. In fact, more than half the "first game" effect happens in the first period. By contrast, a large "second game" effect seems to last two periods rather than one.

Most of the differences are statistically significant, which suggests that they're all real. For those scoring at home, here are the standard errors:

-------------- Gm 1 --- Gm 2 --- Other
--------------------------------------
Period 1 ..... 0.16 ... 0.12 ... 0.06
Period 2 ..... 0.13 ... 0.11 ... 0.06
Period 3 ..... 0.15 ... 0.12 ... 0.07
--------------------------------------
Total ........ 0.30 ... 0.24 ... 0.13

Finally, coming back to J.-P.'s hypothesis about the second half of the third period of the first game, here are the numbers:

First game .... 1.76
Second game ... 1.63
Other games ... 1.67

So, yes, there's a small effect where, when the teams are going to meet again next game, the referee calls more penalties than normal in the last ten minutes of the third period. Whether that's because of the referee, or the players, we can't tell.

Taken alone, these differences aren't statistically significant. But, considering they match the pattern, and the broader picture is statistically significant, we can be fairly confident that this is a real effect we're seeing.

That's actually why I saved J.-P.'s scenario for last, so I could first show that the effect is probably real and not just random.

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UPDATE, 1/15/2012:

Technical note: the "other games" rows and columns are weighted by games, rather than matchups. Suppose teams A and B had back-to-back games, and so did C and D. But A and B met only 2 other times that year, while C and D met 4 other times. That means that C/D will be overrepresented in the "other games" column.

If I reweight that column so A/B and C/D get equal weight, the results change just a little bit. These are the revised "other" columns:

Overall ...... 11.48 (was 11.77)
1st period .... 4.24 (was 4.37)
2nd period .... 4.07 (was 4.12)
3rd period .... 3.15 (was 3.26)
Last 10 min ... 1.59 (was 1.67)