Thursday, May 03, 2007

Reffing it some more, or, rejecting the null 

The discussion of the NBA referee piece continues. The NBA players and league officials are actively downplaying the study. The response of one of the co-authors, Justin Wolfers, is that one is misunderstanding the study:

"This is not a view that one set of people hates another set of people. This is implicit, unconscious biases," said Wolfers, who conducted the study with Joseph Price, a graduate student in economics at Cornell.

"You see two players [collide] on the floor and you have to call a block or a charge. Does the skin color of the players somehow shape how you interpret the signals your brain gives you?"

Some economists on the private sports economics list dismiss the study as not being real economics. And true, there is no model in the paper that explains how it is referees would hold these unconscious biases. As I argued yesterday, it could be a style-of-play preference, something that can be influenced by how one calls fouls.

Referees have an interest in not being seen to be biased. There are clear calls that you cannot miss or else you will not keep your job as a referee. I researched many years ago the voting of sportswriters in the baseball Hall of Fame, and the behavior of arbitrators in deciding salaries for baseball players. In most cases there was no evidence of discrimination. However we did see some evidence in the HoF voting back in the 1970s and 1980s for discrimination against Latino players, and it appeared to be mostly for Latino middle infielders. Why? One explanation could have been that it was difficult for sportswriters to communicate with Latin ballplayers, and this changed their behavior only for the marginal cases. The marginal case is for the player whose batting stats are quite clearly below those of the big-time sluggers or base stealers, but are being considered because of fielding skills. Because the latter are more perception, subjective judgments could be made and not have them confront data. Likewise, the (secretly held) data on who calls fouls on whom in the NBA are not confronting the perception of no bias.

Steven Levitt raises another point that the size of these effects are not very large. He points to John Hollinger's calculation (subscribers link for ESPN Insider members) that the effect on Lebron James' total fouls if all his games were called by all-white officiating crews versus all-black crews would be 11 additional fouls over a season. His scoring average would be 0.3 points per game lower. Levitt doesn't mention another style of play factor that Hollinger picks up:

While we're talking about this study, one other item in it drew my attention: the finding that during the 13-year study period, teams with the greater share of playing time by black players won 48.6 percent of games. The authors seemed to imply some kind of mild institutional racism against black players by this result.

In fact, there's a much more obvious explanation -- the league imported a bunch of talent from Europe during the study period, almost all of it white, and the poorly run teams were the last ones to figure out there were good players on other continents. Thus, by default they ended up with more black players on their rosters.

And the poorer teams may commit more fouls as they play from behind; does this change the results? The study corrects for game effects which include the score, but I don't think I saw that it held constant the relative position of teams contesting for playoff spots, etc.

That doesn't make the Wolfers and Price paper incorrect. But I still would argue for additional tests to see if the age of the referee group matters (perhaps easily told, as far as I've been told, since each referee gets the next highest number on their jersey as they enter the league.) Rather than say this is evidence of bias, I'd look at their results and say "that is odd, doesn't really fit theory, what do you suppose explains that?" In statistical terms, the null hypothesis ALWAYS has to be "no discrimination" and rejecting the null doesn't mean you can accept the alternative.

UPDATE: Brian Goff makes some similar points.

UPDATE2: Phil Miller was inspiration for some of my comments, and he's greatly expanded on them here.

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