I was flipping through the student newspaper today and ran across an AP-derived report about a study of NCAA basketball referees which claims to show that refs are biased, mainly toward evening out the game to make it a closer match in the end. Key findings include:
- They call more fouls on the team in the lead.
- More fouls are called on the visiting team.*
- The bigger the difference in the foul count between the two teams, the more likely it is that the next foul would be called against the team with fewer fouls.
This might all be true, but they've neglected one potentially critical factor--the base rate.** In this case, they're only analyzing the CALLS the referees make. In order to know if the referees are biased, we also have to know what ACTUALLY happened. Suppose, for some reason, that the team in the lead ACTUALLY COMMITS more fouls than the team that is trailing. Then, a perfectly fair referee would have to call more fouls on the leading team--merely as a function of that base rate.
Before decrying the refs then, perhaps we should back up and think this through a little bit more. Without correcting for that (unknown) base rate, we have to assume that both teams are committing fouls at the same rate, whether they are at home or away, whether they are leading or trailing, and no matter how many team fouls have been committed. There are good reasons to suspect that all of those things are not the case.
For example, the authors illustrate their case with a Final Four game in which one team committed the first 7 fouls--but as the game continued, the foul count evened out to 13-12. This illustrates the third finding mentioned above. But let's stop and think about this for a second. If your basketball team fouls seven times in a row, isn't it possible (even HIGHLY likely) that you will change your behavior on the court? That growing foul count is bad for your team and chances are, after seven in a row, players are going to back off and play a little more carefully in order to avoid adding to that count. So, after 7 consecutive fouls, of course it is more likely that the other team is going to commit the next foul--And that has nothing to do with referee bias.
This dynamic is reinforced as teams approach the number of team fouls necessary to put them in the penalty. They will try like heck to avoid the final foul that will put them in the penalty, while the team that has fewer can foul with relative impunity. Who do we think is more likely to commit the next foul in those circumstances? Obviously, it's the one with fewer fouls--again, this has nothign to do with the refs.
Another of the scenarios: Is there a reason teams in the lead might actually commit more fouls than teams that are behind? Well, maybe. One thing is for sure, if a game is close and the lead keeps changing hands, it is almost inevitable that the team in the lead will foul more. At the moment a lead change occurs, the team that is ahead will have just scored, and therefore will immediately be on defense--and there are far more defensive fouls committed than offensive fouls. Further, as in the situation with fouls counts above, the team that is ahead is simply more willing and able to absorb some foul calls--whereas the team that is trying to catch up is probably less willing to send someone to the foul line.
I'm not sure these are enough to account for all of the differences the authors report, but ignoring these factors hopelessly biases the study. The analysis must correct for the base rate somehow or the results are never going to be worth a damn.
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* This isn't consistent with the "evening it out" logic, I'd also note...
** Truth in Advertising: I say all this without actually reading the study--I wasn't able to access it electronically and our library doesn't carry the journal. I just read the AP and newspaper reports--which might not tell the whole story. With that disclaimer, here's the citation so you can track it down yourself, and if so inspired, can inform me that I've got something wrong.
Anderson, K. & Pierce, D. (2009). Officiating bias: The effect of foul differential on the subsequent fouls in NCAA basketball. Journal of Sport Sciences, 27(7), 687-694.