Tuesday, October 21, 2008

Focal foul calls in biased refereeing

It is naive to assume that referees only want to make the correct calls. What they really want is for all players and spectators to think that they are unbiased. The typical optimization strategy is to appear unbiased, not to actually be unbiased. This explains why in so many games two teams will have the same number of fouls called although it is highly likely that one team is objectively fouling more.

Once you accept this model, one surprising prediction arises: it is actually beneficial in the long run if your team has a bad, focal call made against them. One horrible call probably won't mean much in terms of the overall score, but the referee will have to "make up" for that call for some time. The more focal the call, the more the referee will "make up" for in order to appear unbiased.

For example, last week I was playing a competitive 3 on 3 game of basketball and one of my opponents made an awful call (it was self-refereed but the same principle applies). He claimed that I had traveled when in fact I had clearly not moved my pivot foot. My teammates and some spectators went wild with indignation, but I was enthused about the call. When my opponent offered to reverse it, I insisted that the call stand, ostensibly out of honor but really because I knew it would help my team's cause.

Since that one focal call had been made against me, I was able to get away with a litany of small calls or noncalls in my favor. The very next play I drove to the basket and probably took one extra step as I scooped in the layup. No call. Buckets.