One Last NBA Point

Blog reader Peter Bergman tells me that John Hollinger has an interesting analysis of the NBA racial bias piece at, although you have to be a subscriber to read the whole thing. I haven’t actually read it because I’m not a subscriber, but Hollinger apparently does a nice job of putting the magnitude of the bias into perspective: The coefficient estimates imply that if LeBron James faced only white refs the whole season relative to having only black refs the whole season, he would be expected to run up an extra 11 or 12 fouls over the course of the season and score about .3 fewer points per game. These results are derived from Table 5 of the original paper.

These are not very big numbers. Table 7 of the original paper, which focuses on team level outcomes instead of individual level measures, seems to generate much bigger effects, but is also much less precisely estimated. Most of the discussion in the original paper of magnitudes is based on the larger numbers in Table 7. My advice to Price and Wolfers would be to be cautious on this point. My guess is that the individual level results in Table 5 are more believable and will be more robust than the larger numbers they rely on in doing their analysis.


How many b-ball games are won by one point? Couldn't it be said that for every three games, LeBron James could tie that one point game? It seems that 0.3 ppg could be quite important.


Here is something I just thought of -

If white and black players tend to play different position in basketball then may it be true that white and black refs tended to play different positions.

Perhaps, there is a position bias that is not specified and is correlated with race.


In considering bias on an individual level there are a number of other factors that need to be controlled. Primarily popularity and reputation. In other words, less popular or less reputable players are probably more likely to earn borderline penalties than those that are more popular/reputable. This is less a function of race than of skill and PR. You could use salary as a proxy or an artificial market index akin to the Hollywood Stock Exchange


Who the hell cares? My guess is that it is people that don't actually watch or attend games and only super analytical people that have nothing better to do with their time.

If anyone watched any type of coverage since the paper came out then you would know that the majority of those involved in the game said it was complete garbage.

Most of the players that I heard talk about it or comment on it said that they felt it was a complete and utter waste of time and (especially the black players) said that they do not believe or care about what it said.

According to Charles Barkley, he said at least 70% of the players in the NBA are black and those on the court are probably 90% black so of course there are going to be more fouls called on them. He then went on to say that throughout his life and career the bball court was the only place that he felt that people saw each other as equals. He then concluded by saying that the people who wrote the letter were "Jackasses."

I agree.

Watch and enjoy the game for what it is.



An issue which I've only seen addressed in a most informal way is that adding points does not translate into the flow of how an actual game is played and how the outcome is determined. Many NBA games look closer than they actually are; one team gets up by a large amount and then gives back some of that lead, playing well only when the other team gets within a certain point spread. Other scenarios are harder to describe but the gist remains: a game involves a flow of action and teams and players change their strategies depending on the relative score. Since every player has individual characteristics, with some being favored more than others, it appears the game already has a strategy for handling relatively gross disparities in how fouls are called. If coaches are aware of the ebb and flow - as they are - then they would sensibly adjust their team's style of play to compensate for even the slightest apprehension on their part that the game is slightly uneven.

If we assume the study's numbers are correct, how many games would actually be affected if:

a. the actual final point spread of the game is too gross a simplification of the ebb and flow;
b. if players and coaches take into account dynamically any very slight bias in foul calling.

These thoughts do not challenge the basic idea that there is unconscious bias, but I do doubt the effective conclusion about the effect of this bias on outcomes. It appears that section of the paper overly simplifies the dynamics of an actual contest.



Even should some discrepancy exist in the way certain races call fouls against other races, which in my opinion is likely not the case, why is it that whites are taking most of the rap? It is the media's portrayal of these "statistics" that is the biggest foul of all. I have yet to hear a newscaster point out that perhaps blacks are giving less penalties to black players and that is why such a difference may exist. Or perhaps they blacks favor blacks and whites favor whites, in which case, they probably balance out. Or perhaps the difference is so negligible that it really doesn't matter at all and simply ballooning another minor racial issue into a mountain of frustration does a greater damage to race relations than simply not mentioning it at all.


Its funny to me that sports fans, who use "statistics" all the time to argue points, have a hostile reaction when academics or sabermetricians analyze their beloved sports.

People should read the study, but a couple of small points: (1) the authors only consider the racial makeup of crews not individual referees but this should bias their results against (not for) their hypothesis.

(2) they control for position, starter / bench, playing time among a whole bunch of other factors.

(3) the study shows that that, as a whole, white players get called for more fouls on average per 48-minutes than black players. So arguments about white players having a "less aggressive style" don't hold water (forget the irony that people who make this point are using a racist premise to dispute a finding of racism).

I'm fascinated by the disconnect between the careful wording in the study and the public outcry. As the authors clearly note, it could be that players play more aggressively in front of refereeing crews of a different race.



This whole NBA study has the correct data, but the wrong conclusions. Suppose the NBA is 80% black. Then of course, the ref will call more fouls on black players than on white players; regardless of whether the ref is black or white. Therefore, the controversy surrounding white refs calling more fouls on black players than on white players is just wrong; it should BE that way, precisely because if one calls fouls objectively, then in the end, refs will call fouls on more black players than one ones. The real controversy I see is the other half of the study, that black refs call more fouls on white players. How is it possible that black refs can, in the aggregate, end up calling more fouls on only 25% of the league? Because they are calling fouls subjectively, unlike their white counterparts.


i meant to say 20% of the league (white).


slim--Read the paper. The factors you pointed out are taken into account. The authors don't look at total fouls, they look at fouls per minute played for a theoretical white player and black player. Also, they focus on differentials between white and black players, referees, and player/referee combinations. Statistically, it's pretty solid work, though I think the conclusions are incorrect.


re comment 10:

good point. Essentially the results of the paper are:

white players are penalised more than black players;

the above is true when the crew is black;

when the crew is white, black players get penalized about the same, and white players get penalized less than when the crew was black (but still more than black players; see Table 3).

A perfectly logical explanation is that white crews call the game fairly, but black crews are biased against white players.

I'm not saying this is true, but it does explain the findings. It's interesting that this possibility gets so little attention.

The interpretation of the results depends entirely on what you think the "correct" disparity between fouls on white and black players should be (because of the other factors mentioned in the paper such as white guys being heavier etc. on page 7)


First of all, the information in the box score is insufficient to make any conclusions. Secondly, even if detailed information was available, it could indicate that black referees are biased against whites! Amazing how that is hardly mentioned as a possibility. Afterall, we all know the NBA is racist against whites, just look at the disparity in black v whites players versus % of population. Numbers don't lie . . .