Loose Ends - Part II: Score Effects and Minor Penalties

Back in November of last year, I looked at whether there were any score effects in relation to minor penalties. The conclusion? Playing from behind has a significant positive effect on powerplay differential. That is, teams tend to be much better at drawing penalties when trailing, as compared to when leading or when the game is tied.

While my initial article only looked at data from the 2007-08 and 2008-09 seasons, I've since ran the numbers for 2009-10 as well. Here are the aggregate numbers for all three years:

[PD=penalties drawn; PT; penalties taken; P % = penalties drawn/(penalties drawn + penalties taken)]

I should include a reminder that only penalties that were not accompanied by the calling of another penalty at the same point in time were included in the above totals.

In the original post, I asserted that trailing team's penalty advantage was not owing to its superior play, but was instead caused by favorable officiating. In support of this, I noted that actual team-to-team distributions in trailing and leading penalty percentage were roughly what one would expect them to be if the putative bias affected all teams equally.

Although I remain confident that my assertion was correct, I suspect that others may have found my explanation to be less than convincing. And in turning my attention to the subject for a second time, I think that there's a better way in which I can illustrate my point.

In determining whether the trailing team's penalty advantage is the product of bias or earned on merit, it becomes necessary to ask what result we would expect to observe, based on what we know about what causes some teams to be better at drawing penalties than others.

One of those causes is even strength outshooting. If we look at the relationship between EV tied Corsi and tied penalty differential over the last three seasons, each unit increment in the latter equates to 0.027 in the former.

It's well established that the average team does much better in terms of Corsi when playing from behind. Over the three years in question, trailing teams had a collective Corsi percentage of 0.552 (107706 For, 87079 Against). Given the positive relationship that exists between outshooting and penalty differential when the score is tied, the trailing team's advantage in Corsi may be able to account for it's advantage in penalty percentage.

However, upon performing the required calculations, it becomes clear that this factor can only explain part of the difference.


In other words, only about one third of the gap can be attributed to outshooting.

Not only that, but it's clear that the shot statistics flatter the trailing team, given that playing from behind encourages a team to take more risks and play more desperately. For example, during the period in question, trailing teams only scored 51.9% of all non-empty net even strength goals (4623 For, 4292 Against), despite, as mentioned above, generating 55.2% of all Corsi events. It's more than arguable that goal differential, and not Corsi differential, provides the best measure of how well the trailing team actually performs.

As with outshooting, there is a positive relationship between even strength goal differential and penalty differential when the score is tied. Based on data from the three seasons in question, each net goal is worth 0.26 in net penalties drawn. We're able to use this figure to determine what kind of penalty advantage we'd expect the trailing team to have, based on its goal differential.


As the table indicates, we would expect the trailing team to do only slightly better than the leading team in terms of penalty differential on the basis of its advantage in even strength goal differential. Thus, however which way you approach it, referee bias must account for a substantial part - and probably almost all - of the penalty gap.