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A little over a year ago, Wharton School professor Justin Wolfers published a controversial study which he felt proved that there was a racial component to the calls that NBA referees made on the court. The study claimed that "during the 13 seasons from 1991 through 2004, white referees called fouls at a greater rate against black players than against white players." The impact was said to be that "the probability of a team winning is noticeably affected by the racial composition of the refereeing crew assigned to the game."

David Stern (predictably) was not amused, and did his own study using the NBA's database of foul calls, which specifies which official made which call, and came to the conclusion that there was no bias. Wolfers' response? To prove the accuracy of his study by heading to Vegas to bet on the side of his statistics. And according to him, he was able to make some cash:

The Wharton professor took his statistics to Las Vegas - virtually - and bet on them. He calculated what would happen if you placed money on the outcome of NBA games solely on the racial makeup of the players and the referees.

What would happen, Wolfers reports, is that you'd turn a profit.

"Our estimate is that the outcome of up to 3 percent of all games would have been different with a different refereeing crew," Wolfers says. "Some people feel that 3 percent's not a lot. Some feel outraged that even that many games could be affected by something so arbitrary. But when you talk to team owners, if you could guarantee them another 3 percent of wins, they will tell you directly that's worth millions of dollars to them."

To most teams, three percent of an 82-game schedule -- which comes out to 2.46 games -- would have little impact on their season-ending result. But what if those games were playoff games, where the first team to win four moves on, on the loser goes home? That's a pretty significant number, and one the Wolfers feels the NBA needs to look at if it wants to maintain its competitive balance.

Wolfers goes on to say (in an interview, which can be heard here) that the racial bias that his study found was no higher than would be found in your average workplace, so it's not like the NBA has a bunch of racially intolerant officials working its games. But the fact that it exists and is affecting the outcome of games at all is something the league should take a harder look at if they truly want to maintain their competitive balance.

One more note from the interview, for all of you degenerate gamblers out there: According to Wolfers and his study, when the Utah Jazz are playing in a game that's being officiated by an all white crew, that's the time to drop the hammer and put all your money on the Jazz. (Provided you're in a legal, Las Vegas casino at the time, of course.) Good luck on that though, because for other reasons involving referees' tendencies, the NBA does not give out any information on which officials will be calling which games ahead of time. Never mind that last part. Thanks to commenter Phil for pointing out that referee assignments are now posted here on game days.