Using Statistical Evidence to Catch Crooked Refs A Tough Task

From the Numbers Guy in the WSJ. The article also mentions a possible non-public information trading opportunity:

Certainly refs, like any group of people, have natural tendencies, and the betting market can't adjust for those because the NBA doesn't announce officiating assignments in advance. But not all behavior is predictive. A clutch-hitter in baseball one season is no more likely than his teammates to hit well in tight spots the next season. The same may well be true about refs who officiate over unexpectedly high-scoring games in one season.

Just look at the 10 top officials who were found most likely to referee games in the 2005-2006 season in which scoring exceeded the predicted total, and who then returned the next season. Four of the 10 were no longer in even the top half of all refs for the over bet. Mr. Donaghy himself wasn't consistent, even before the period of suspicion. The over bettors won just 44% of his games in the two-season period ended in 2005. But in the three years before that, these bets won in 60% of his games.
...
Brigham Young University statistician Shane Reese demonstrated how such a system might work by examining all referees last season to see whether any of their results on over-under bets were outside normal variation. No refs would have tripped the switch on this warning system -- not even Mr. Donaghy. "There's nothing suggesting he was an outlier," says Prof. Reese.