The NHL has fired a referee who, during a game, was caught on a hot mic saying that he "wanted to get" a penalty on one of the teams, presumably as a make-up call. In the statement announcing the firing, the NHL stated: "Nothing is more important than insuring the integrity of our game."
I'm on the ref's side, sort of. The above graph, from FiveThirtyEight Blog, shows pretty convincingly that he's being fired just for acknowledging what everyone knows is true. I had to stare at it awhile before I comprehended the significance, so I'll point out that it simply plots what the likelihood is of the next penalty in an NHL game being called on the home team or the visitors, given how many penalties each team has incurred in the game so far. For example, if the home team has been whistled for two more penalties than the visitors, then there is about a 39 percent chance that the next penalty is called on them (and a 61 percent chance that the next penalty is on the visitors). If, however, the visitors have had two more penalties than the home team, then there is about a 58 percent chance that the next penalty is on the home team (and a 42 percent chance that the next penalty is on the visitors).
The referees like to keep the penalties roughly even. I don't think there's an alternative explanation. This is ten years worth of regular season data. According to the article—the graph is worth a lot of words but the accompanying article is also interesting—the tendency is even more pronounced in the playoffs. The explanation for that would be that the refs become more determined not to be the story when more is at stake. But, in trying not to be the story, they now have become the story. It's probably also worth noting that the home team has an advantage insofar as the next penalty is more likely to be called on the visitors if, as is the case at the start of every game, the teams so far have incurred the same number of penalties.
As for "the integrity of the game," the data suggest there is little or no reward for being disciplined, unthuggish, clean: you're going to get called for about the same number of penalties anyway. I suppose you could say that the sin of the fired referee was that he made a deliberate, conscious choice. It's different if a referee subconsciously prefers the team that is "owed a penalty." But once one ref has been caught on a hot mic it's harder to believe the stark data is explained wholly by the effect of subconscious preferences on a referee's judgment.
The issue of subconscious preferences, however, reminds us that referees are human. I'm more of a basketball fan and it's interesting to think of how the NHL data might apply to a different game. Suppose one basketball team is small but very quick and plays an aggressive person-to-person, chest-to-chest defense. Their opponents, comparatively huge and leaden-footed, sit back in a zone defense. You'd expect the one team to foul a lot more than the other, but the NHL data predict that the foul disparity will not be as great as the actual game play would warrant. The team that is constantly testing the referee's conception of what is a foul will get away with bumps and nudges that are called fouls against the more passive team. That would be the theory, and my impression, having watched ten jillion basketball games, is that in fact that's just what happens—although, since I'm watching, I probably want one team to win, and in that case I can't think of why you should trust my judgment over that of the referees I'm complaining about.
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