Is "superstar bias" caused by Bayesian referees?

Would you rather have referees be more accurate, or less biased in favor of superstars?

In the NBA, a foul is called when the player with the ball makes significant contact with a defender while he's moving to take a shot. But which player is charged with the foul? Is it an illegal charge on the offensive player (running into a defender who's set and immobile), or is it an illegal block by the defensive player (who illegally gets in the way of a player in the act of shooting)?

It's a hard one to call, because it depends on the sequence of events. As this Sports Illustrated article says,

"... the often-fractional difference between a charge and a block call is decided by a referee who has to determine, in a split second: a) were the defender's feet set, b) was he outside the court's semicircle, c) who initiated contact, and d) does the contact merit a call at all?"

It seems reasonable to assume that, in a lot of cases, the referee doesn't know for sure, and has to make an uncertain call. Maybe he's 80% sure it's a charge, or 70% sure it's a block, and makes the call according to that best guess. (Not that the ref necessarily thinks in terms of those numbers, but he might have an idea in his mind of what the chances are.)

Now, suppose there's a case where, to the referee's eyes, he sees a 60% chance it was a charge, and only a 40% chance it was a block. He's about to call the charge. But, now, he notices who the players are. Defensive player B ("bad guy") is known as a reckless defender, and gets called for blocks all the time. Offensive player G ("good guy") is known to be a very careful player with his head in the game, who doesn't charge very often at all.

Knowing the characteristics of the two players, the referee now guesses there's an 80% chance it's really a block. Instead of 60/40, the chance is now 20/80.

What should the ref do? Should he call the charge, as he originally would have if he hadn't known who the players were? Or should he take into account that G doesn't foul often, while B is a repeat offender, and call the block instead?

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If the ref calls the foul on player B, he'll be right a lot more often than if he calls it on G. When the NBA office reviews referees on how accurate their calls are, he'll wind up looking pretty good. But, B gets the short end of the stick. He'll be called for a lot more fouls than he actually commits, because, any time there's enough doubt, he gets the blame.

On the other hand, if the ref calls the foul on G, he'll be wrong more often. But, at least there's no "profiling." G doesn't get credit for his clean reputation, and there's no prejudice against B because of his criminal past.

Still, one player gets the short end of the stick, either way. The first way, B gets called for too many fouls. The second way, G gets called for too many fouls. Either way, one group of players gets the shaft. Do we want it to be the good guys, or the bad guys?

Maybe you think it's better that the bad guys, the reckless players, get the unfair calls. If you do, you shouldn't be complaining about "superstar bias," the idea that the best players get favorable calls from referees. Because, I'd guess, superstars are more likely to be Gs than Bs. Tell me if I'm wrong, but here's my logic.

First, they're better players, so they can be effective without fouling, and probably are better at avoiding fouls. Second, because they're in the play so much more than their teammates, they have more opportunities to foul. If they were Bs, they'd foul out of games all the time; this gives them a strong incentive to be Gs. And, third, a superstar fouling out costs his team a lot more than a marginal player fouling out. So superstars have even more incentive to play clean.

So if superstar bias exists, it might not be subconscious, irrational bias on the part of referees. The refs might be completely rational. They might be deciding that, in the face of imperfect information on what happened, they're going to make the call that's most likely to be correct, given the identities and predilections of the players involved. And that happens to benefit the stars.

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When I started writing this, I thought of it as a tradeoff: the ref can be as accurate as possible, or he can be unbiased -- but not both. But, now, as I write this, I see the referee *can't* be unbiased. If there's any doubt in his mind on any play, his choices are: act in a way in which there will be a bias against the Bs; or act in a way in which there will be a bias against the Gs.

Is there something wrong with my logic? If not, then I have two questions:

1. Which is more fair? Should the ref be as Bayesian as possible, and profile players to increase overall accuracy at the expense of the Bs? Or should the referee ignore the "profiling" information, and reduce his overall accuracy, at the expense of the Gs?

2. For you guys who actually follow basketball -- what do you think refs actually do in this situation?