In the culmination of a project I worked on during my Masters program at UMass with current Southern New Hampshire assistant professor Kevin Snyder, the International Journal of Sport Finance recently published our article, titled “Biased Impartiality Among National Hockey League Referees.”
The journal’s official link, which requires access, is here. For those without access, the version at SSRN is pretty accurate (link)
The article tries to measure if and at what level make-up calls exist in professional hockey. Kevin and I called this “biased impartiality,” where a contest, by ending with roughly an even number of penalty calls on each participating team, keeps fan bases happy and giving the referees the appearance of impartiality. The cost, of course, is that in game judgement’s tend to sway from one team to the other.
A few of my favorite points.
1) We found evidence that biased impartiality exists at the highest levels during games of higher importance – both highly attended regular season games and postseason games (in particular, game 7’s). Below lies a plot of average second period penalties per team, conditional on penalty outcomes at the end of the first period (more or less first period penalties).
In the postseason game 7’s in our sample, as an example, teams with more first period penalties finished with about half as many average second period penalties as the team with fewer first period penalties.
2) Of course, there could be several other factors (game score, most specifically) accounting for why teams with more penalties early in games end up with fewer penalties later in games. We accounted for several game and team factors to model penalty outcomes, and found that, roughly, each additional penalty in the first period of the game is worth about a 10% reduction in second period penalties.
3) Here’s my favorite part (we saved this until the article’s conclusion, and here I quote from the article):
In 25 of the 134 postseason overtime games since 2006, at least two total penalties were called. In 19 of the contests with multiple penalties (76%), the second power play was awarded to the team that was called for the first penalty. We would expect the second power play to be awarded to the opposite team 50% of the time… this sample proportion is significantly different from 0.5 (pvalue <0.01).
In other words, during the most critical portion of the most exciting NHL games – postseason OT – biased impartiality is at its peak; the team whistled for the first penalty is roughly 3 times as likely to receive the next power play.
StatsbyLopez 
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