?Across all of these specifications,? they write, ?we find that black players receive around 0.12-0.20 more fouls per 48 minutes played (an increase of 2 ?-4 ? percent) when the number of white referees officiating a game increases from zero to three.?
Mr. Wolfers and Mr. Price also report a statistically significant correlation with decreases in points, rebounds and assists, and a rise in turnovers, when players performed before primarily opposite-race officials.
?Player-performance appears to deteriorate at every margin when officiated by a larger fraction of opposite-race referees,? they write. The paper later notes no change in free-throw percentage. ?We emphasize this result because this is the one on-court behavior that we expect to be unaffected by referee behavior.?
Mr. Wolfers and Mr. Price claim that these changes are enough to affect game outcomes. Their results suggested that for each additional black starter a team had, relative to its opponent, a team?s chance of winning would decline from a theoretical 50 percent to 49 percent and so on, a concept mirrored by the game evidence: the team with the greater share of playing time by black players during those 13 years won 48.6 percent of games ? a difference of about two victories in an 82-game season.