The Wharton School professor whose study started a controversy about possible racial bias in foul calls in the NBA has now seen the NBA's own data about its officiating, and is more convinced than ever that he's right.
"Their own study agrees with our conclusion: A referee is more likely to blow the whistle and call a foul against a player of another race," Justin Wolfers said after he reviewed the information in work done by an NBA contractor.
The league initially had refused to allow Wolfers to examine its study, but finally sent it to him last week after a series of blistering criticisms of Wolfers and his work.
Responding to Wolfers' conclusions that officials were guilty of "own-race bias" in enough foul calls to affect the outcomes of games, a league spokesman said that Wolfers was "wrong," that he was "disingenuous" and that his work was "sloppy and ludicrous." Commissioner David Stern and league president Joel Litvin attacked Wolfers in numerous broadcast appearances.
"After refusing my requests for weeks, the NBA was unexpectedly gracious enough to share its material with me," Wolfers said. "And I am now able to say that their critical statements are contradicted by the league consultant's own statistical output."
Why did the NBA suddenly give Wolfers its study?
"I believe they were tired of the criticism that they had not given it to us," he said. "And I don't think they really knew what their study said."
An independent analysis of the two conflicting studies requested by ESPN.com confirms Wolfers' findings that referees favor their own race when they blow their whistles. Thomas Miles, who has a Ph. D. in economics from the University of Chicago and is a graduate of Harvard Law School, dissected the massive study completed by Wolfers, and compared it with the smaller study by an NBA consultant.
"I believe [Wolfers] has the better points," said Miles, a professor at the University of Chicago Law School. "His study focused on the interactions of the race of the referee and the race of the player. The NBA was more concerned with the number of fouls called on black players and comparisons with the number of fouls called on white players."
Miles reviewed Wolfers' study of more than 600,000 foul calls made in regular-season games between 1991 and 2004, along with an additional study of the last three seasons, the NBA's analysis of 148,000 calls made in the last three seasons, and Wolfers' own look at the NBA study.
An NBA spokesman declined to respond to Miles' observations.
"It's done. It's over. We have nothing to add to what we have said already," the spokesman said.
Wolfers' study was made public in a front-page New York Times article in early May. The Times also submitted the data from both studies to independent experts, who found the Wolfers study to be more credible than the NBA's analysis. Miles' examination of the two studies supports Wolfers' contention that the NBA's numbers actually support rather than contradict his results.
"It is remarkable how [Wolfers] was able to use the NBA's own data set and show that it supported what he said at the beginning," Miles said. Wolfers used the NBA's own categories of minutes played in his response to the NBA's study, and showed that there is evidence of discrimination even with the NBA's own data.
The most significant gap in Wolfers' study is that he was unable to identify the race of the specific referee who made each call. The NBA refused to give him that information, so he used the racial makeup of each three-official crew and put it through rigorous and complex statistical tests.
Some critics of Wolfers' work have asserted that the impact of the bias affects only a microscopic number of foul calls. But the study also describes a measurable effect on the outcomes of games from the bias his statistics revealed. Wolfers compared the real outcomes of games against a standard in which the racial makeup of the officiating crews matches the racial makeup of players in the league (approximately 80 percent black and 20 percent white). He found that 1.8 percent of the games would have different outcomes. That would be two games per team in a regular season of 82 games.
"We also studied the impact of a single-race crew of officials -- an all-white crew or an all-black crew," Wolfers said. "With a crew of a single race, own-race bias would produce a difference in game outcomes of 3.4 percent."
That's a difference of three games per team in a regular season. An impact on the outcomes of two or three games per team in a season would be between 30 and 45 games, league-wide.
"Own-race bias" is a social science term for decisions made in favor of one's own race, unconscious decisions made without the malice of intentional bigotry.
The study provided by the NBA didn't address any impact on outcomes.
"You can easily imagine why they would not ask that question," Wolfers said.
The NBA study, performed by the Segal Company, used 148,000 foul calls over three seasons beginning in 2003 to answer 14 questions called "models," reworking the data in response to each question.
"Only four of their models addressed our question," Wolfers said. "The others determine things like whether black players earn more fouls than white players or whether black referees blow the whistle more often for fouls than white officials. They also compared the number of fouls playing at home or on the road. Our question is whether there is 'own-race bias' among NBA officials when they call fouls."
Wolfers said that three of the four NBA models that address the bias issue yield statistically significant estimates of own-race bias.
The fourth model, Wolfers said, does not produce any conclusions that meet the basic tests of statistical validity.
The NBA's statisticians also didn't consider important variables, according to Wolfers, such as the time in a game when fouls were called.
"A starter who accumulates fouls early in the game plays differently later in the game," he said. "We are able to account for this variable. The NBA did not."
After the NBA attacked his findings, Wolfers added the last three seasons of calls to his database and concluded that "all of our findings are statistically significant."
"It is always difficult to present these studies in the media, but the flaws in the NBA study cause its analysts to draw incorrect inferences from their data," he said.
Lester Munson is a Chicago journalist and lawyer who has been reporting on investigative and legal issues in the sports industry for 18 years.