Monday, November 24, 2008

One Jump Ahead of the Breadline

The NY Times had a very good piece last week about the phenomenon of offensive players grunting, moaning, yelling, or otherwise vocalizing when they put up a shot near the basket. This is apparently the offensive counterpart to flopping. Presumably, players do this because it works (or at least, they think it works): it increases their probability of receiving a favorable foul call, effectuating the beloved “and one” scenario.

I am slightly saddened (though I shouldn’t be) that referees are apparently so easily swayed by these antics. Whether you call this bounded rationality or cue awareness or sensory limitation, it’s obvious that referees, as humans, cannot shut out their various biases when calling fouls. That includes biases as to the reputations of individual players, biases as to the appropriateness of fouls in various game situations (hence the original “Jordan pushed off” problem), and biases as to the propriety of a big man slamming a small. Perhaps some of these biases are normatively desirable as a way of guiding refs to a decision that is likelier to be correct, in a setting where no human could possibly follow all the action occuring at close range between world-class athletes at breakneck speeds. It reminds me of some recent unfortunate luck when I was forced to sit in the front-most row of a packed theater to watch the latest James Bond film. When Daniel Craig stood in one place, I could follow the scene, but the chases across the rooftops of Haiti were a bit much for my eyeballs.

I would like to quickly think through the league-wide implications of this yelling strategy.

I. Let’s assume first that making these perorations is costless: that is, it is neither painful nor tiring nor shot-altering to yell out a cry of pain as you release the ball. If that’s the case, and screaming increases your chance of getting a foul call, we would expect everyone to do it. … But if that is so, referees presumably would recognize that they are getting “played” by cheap talk; I assume that referees have some ability to deliberately and consciously counteract their biases. Ultimately propensities of foul calls would be exactly the same as if nobody was doing it. That is not a very interesting equilibrium. On the other hand, if referees were differentially affected by the screams of different players — probably they would be more sympathetic to little guys — then we might see more fouls called for the benefit of little men and fewer fouls called for the benefit of bigs. And if that were the case, we might then see little guys with the temerity to drive to the hole even more than before; and, perhaps, we might see some bigs with shooting touch slightly more willing to put up a J from the perimeter, which might reduce referees’ propensity or willingness to blow their whistle for the little guys. You can’t be blowing your whistle on every play. That, in turn, could bring the equilibrium back somewhat closer to the no-whining scenario, though we might still see more drives by little guys and more fouls called for their benefit.

(I should note that I’m assuming that referees want to keep the total number of fouls called in a game fairly constant, so as not to slow the game down and cause more foul-out disqualifications. I would be curious to see data on how the average number of fouls per game has varied over time. Retrospective accounts hold that the 1990s NBA of Jackson’s Bulls, Riley’s Knicks, and Riley’s Heat was particularly thuggish and slow, but was that really so?)

II. Let’s assume next that yelling has a cost. Let us first assume that yelling is equally costly for everyone. If that is so, then if the cost is low enough, the benefit of yelling could exceed the cost, and everyone would do it, as in the above discussion. If the cost is too high, nobody would do it.

What if there is a differential cost of yelling across different players? I will assume that yelling is more difficult for big men than for little men: Big men have bigger lungs to fill to produce those exhortations, and big men typically have poorer long-run stamina than little guys. A regular habit of screaming during every shot attempt would be more deleterious to power players than to wiry guards.

There are a few possibilities under that broad rubric. First, it could be that even with the differential cost, the costs are just generally too high for everyone to justify doing it; thus, nobody would do it. Second, it could be that the costs for everyone are so still low that everyone wants to do it, so everyone increases their frequency of going hard to the hoop. This would resemble my discussion in I. above, but now little guys would be more emboldened (relative to bigs) to drive and cry out, compared to the scenario described in I. If refs are equally affected viscerally by the cries of bigs and smalls, and they are able to notice that smalls are whining more than bigs are, they might consciously call fouls for the benefit of little guys with lower propensity, so as to maintain the overall number of fouls called. Thus, the whining of a Wade or Iverson would be counterproductive. (It could even reduce the value of whining for munchkins so much that in the equilibrium, smalls would whine with equal frequency to bigs.)

Third, we could have a scenario where the cost of grunting was so high for big men (compared to the perceived benefit) that they chose not to do it, but low enough for smalls that they find it worthwhile. Then only smalls would be grunting, and the smalls would, at least at first, find themselves receiving beneficial foul calls with higher propensity than before. Referees could adjust to this by consciously reducing their propensity of foul calls equally, regardless of height of the beneficiary (in which case big men would receive fewer foul calls in the equilibrium, compared to the world without whining); or perhaps they might realize that smalls are causing the uptick in fouls with their whining, and decide to be less kind to the little guys.

There’s a lot of moving parts in this analysis and I know there are issues that I’ve not thought carefully about, but that’s my first cut.

No comments: