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Racial bias in basketball fouls

Yu-Sung and Jeff pointed me to a study by Joseph Price and Justin Wolfers on racial discrimination among NBA referees. Basically, black refs call more fouls on white players and vice-versa.

basketball.png

Here’s a news article (by Alan Schwarz), here’s the technical paper, and here’s the abstract (with my thoughts following):

The NBA provides an intriguing place to test for taste-based discrimination: referees and players are involved in repeated interactions in a high-pressure setting with referees making the type of split-second decisions that might allow implicit racial biases to become evident. Moreover, the referees receive constant monitoring, and feedback on their performance. (Commissioner Stern has claimed that NBA referees “are the most ranked, rated, reviewed, statistically analyzed and mentored group of employees of any company in any place in the world.”) The essentially arbitrary assignment of refereeing crews to basketball games, and the number of repeated interactions allow us to convincingly test for own-race preferences. We find that—even conditioning on player and referee fixed effects (and specific game fixed effects)—that more personal fouls are awarded against players when they are officiated by an opposite-race officiating crew than when officiated by an own-race refereeing crew. These biases are sufficiently large that we find appreciable differences in whether predominantly black teams are more likely to win or lose, according to the racial composition of the refereeing crew.

The estimated difference is 0.2 fouls per player on the court per game, which comes to 1 foul per game for a team with all black players. Also, teams give black players less playing time (on average) when the refs are white–this looks like it hurt them more than the foul calls.

Looking at the raw data, white players commit lots more fouls per minute than blacks, but much of this can be explained by whites being more likely to be centers (presumably a more physical position with fouls as part of the job) and benchwarmers. Which reminds me that the data show a familiar pattern also noted in historical baseball data by Bill James: the black players are, by most measures, better than the whites (more points scored, more points per minute, more minutes played, more likely to be starters), which is consistent with discrimination in hiring (picking good-but-not-great whites over good-but-not-great blacks).

Other comments: yes, I would replace all the tables by graphs. (Start with Table 1–that’s an easy time series plot. Table 2 could be shown in a way similar to the graph in page 202 of our new book. Etc.) Figure 2 wold be better without those ugly horizontal lines at the top and bottom of the error bars.

Finally, black referees call more fouls than white refs–lots more for white players, but slightly more for black players too. Price and Wolfers characterize this as bias in judging white players but not in judging black players, but another interpretation is that black referees are just tougher about calling fouls in general.

P.S. Wolfers is the coauthor of this excellent review article on the deterrent effect of the death penalty.

P.P.S. In case it wasn’t clear, I like the paper.

One more thing

The analysis leading to Figure 2 should be replaced by a multilevel model. Really. These standard errors are huge, a clear case for partial pooling! No question. Take a look:

basketball2.png

8 Comments

  1. Anonymous says:

    Andrew, may I ask what you make of the comments on this paper at Mahalonobis? I'm not well-versed in statistics, but I'd like
    to email the paper to friends who are. Before I do, I would like to get a sense of
    how well it holds up.

    Great blog, by the way. I've learned a lot.

    -wtp

  2. Andrew says:

    Wtp,

    The bias estimated by Price and Wolfers is relative: refs call more fouls (on average) on players of opposite race. I don't see that the paper claims that refs are biased against blacks, rather it's that they favor players of their own race.

    The other issue is that the commenter you cite doesn't buy the regression analysis. I defer to actual basketball experts here, but the regression analysis seems fine to me: it seems to makes sense that centers and benchwarmers have more fouls per minute. Further study is warranted etc. etc. but it it seems like a reasonable analysis to me.

  3. tof says:

    the worst part of this whole thing has been the commentary on the statistical analysis.

    i breathe a sigh of relief that charles barkley will never weigh in on my work. does the world really need to hear kiki vandeweghe telling us that he took statistics in college and that anyone can lie with statistics?

    the original work adside, this research has once again put a bright light on that great american anti-intellectual streak. i would have hoped that the great strides that bill james, baseball prospectus and the like have made in explaning aspects of baseball would have carried over to other domains by now and that espn/disney could find an economist or statistician to explain and/or criticize the findings.

  4. ed kupfer says:

    Basketball "expert" here. I was pleasantly surprised reading the paper's methodology — there were none of the mistakes economists frequently make when looking at sports performance metrics.

    The controversy — such as it is — boils down to the public confusion between statistical and practical significantce. The paper displays the latter, but the actual effect size in real-life terms is very small., on the order of one marginal personal foul per 15 games for a 30 minute per game black player facing an all-white officiating crew versus an all-black crew.

  5. bee says:

    Andrew-

    You raise an interesting point regarding the magnitude of the effect being discussed. The magnitude of the effect is very small. This raises a red flag for me as I review the paper (which I find interesting from a methodological perspective.

    The asymmetry of the findings also raises questions regarding the nature of the effect.

    While I will not take on the whether regression is appropriate, I think that there is merit to raising the question. From a DOE perspective the findings do not offer much to the underlying hypothesis of racism.

  6. Very cool blog. I've linked to you from mine.

    I see this study as an example of the connections between mathematics and social justice, as highlighted at the recent conference in Brooklyn, Creating Balance in an Unjust World sponsored by Radical Math and the ongoing work of Bob Moses' Algebra Project

  7. Chris P says:

    I heard a rebuttal of the story from the NBA on NPR saying that the league looked at more granular data that identified the ref who made the call and against which player it was made. They also review the games and judge if the calls were made accurately.

    The interviewer did not ask which type of sums of squares was used in the random effects model for this, but given the richness of the data, it would seem that one would need to have a fairly complex model to tease out the effects at the proper level.

  8. Sri Maddipati says:

    This is an interesting discussion. I had a question/comment if someone would like to address them. One question that comes up is "style" of play which the authors attributed to other statistics such as steals, assists, rebounds etc. but these don't translate to style. What stood out was the extent to which white players were foreign which didn't seem to be completely taken into consideration.