Score Effects and Minor Penalties

The playing to the score effect has received a fair amount of coverage from the more statistically inclined members of the hockey blogosphere over the last two years or so (see here, here and here for some good overviews on the subject). In short, playing from behind tends to have a favourable effect on a team’s shot ratio, whereas playing with the lead tends to have the opposite result. The effect increases linearly as a function of goal margin, and is exaggerated in the third period.

The majority of analysis conducted in relation to the subject thus far has focused on the effect of game score on shot ratio. Little, if anything, appears to have been done in the way of determining the extent to which the effect operates in other aspects of the game. It’s conceivable, for example, that game score could have an analogous effect on team penalty percentage (defined as minor penalties drawn / ( minor penalties drawn + minor penalties taken).

In order to answer the above question, I looked at the NHL.com play-by-play data from the 2007-08 and 2008-09 seasons and created a script on excel to determine how many penalties each team drew and took during that period. However, because I was only interested in penalties that provided one of the teams with a manpower advantage (relative to the situation that existed prior to the penalty was called), I only counted “unique” penalties. I defined a unique penalty as a penalty not accompanied by the calling of any other penalty at that specific point in time. This obviously fails to account for situations where multiple penalties are called and one team emerges with a powerplay, but such situations are rare enough so as to not affect the data materially.

I then determined the goal state prevailing at the time that the penalty occurred – in other words, whether the team that drew/took the penalty was trailing, leading or tied at the time that the penalty was called. Here are the combined results for the two seasons, broken down at the team level.

Evidently, the trailing team does significantly better in terms of penalty ratio than does the leading team. During the period in question, every single team did better in terms of penalty percentage when trailing than when leading. In aggregate, the trailing team drew roughly 54.5% of all penalties, making the magnitude of the effect similar to that observed with respect to shot percentage (the trailing team had an aggregate Corsi percentage of 55.2 during the same timeframe).

One final question remains – does the trailing team earn its penalty advantage on merit, or is it a product of referee bias? Given that the trailing team also enjoys an advantage in terms of Corsi, and therefore spends more time in the opponent’s end than its own (an area of the rink in which a disproportionate percentage of penalties are drawn), one might be inclined to favour the former explanation. However, as demonstrated in the table below, there isn’t much of a relationship between Corsi percentage and Penalty percentage when the score margin is other than zero.

In other words, while the trailing team tends to both outshoot and “outdraw” the leading team, teams that outshoot the opposition by a large margin when playing from behind don’t do significantly better with respect to (trailing) penalty ratio than teams that outshoot the opposition to a lesser extent.

As alluded to above, the second possibility is that the penalty advantage accruing to the trailing team is the result of referee bias. If this explanation is correct, then the team-to-team variation in both leading and trailing penalty percentage would be the product of both randomness and team ability differences in drawing more penalties than the opposition. To test this hypothesis, the following experiment can be performed:

• taking each team’s penalty percentage with the score tied over the two seasons in question and regressing each value 60% to the mean. The resulting values provide an estimate of each team’s underlying ability to draw more penalties than the opposition. The regression is necessary given that approximately 60% of the team-to-team variation in penalty percentage with the score tied (in the sample of question) can be attributed to luck

• simulating the two seasons such that every “unique” penalty that occurred when each team was trailing constitutes an individual trial

• designate the probability of drawing any given penalty as that team’s “true ability” penalty percentage (as determined above) plus 0.045 (0.045 being the magnitude of the referee bias)

• calculate the average team-to-team spread (standard deviation) in penalty percentage after conducting a sufficiently large number of simulations

• compare the predicted standard deviation to the actual value

• repeat the above with respect to all penalties that occurred when each team was leading

The results:

The essentially confirms the above hypothesis in that the predicted standard deviations are virtually identical to the actual values. As such, an analogy can be drawn between the trailing team advantage in penalty percentage and home ice advantage. The probability of a team winning any given game is approximately 5% higher on home ice relative to neutral ice, but all teams benefit from the effect equally (that is, the team-to-team variation in home vs. road winning percentage is entirely random). Similarly, the referee bias in favour of the trailing team appears to be even across the board.