A jab to the right, then Carmelo steps back behind the three-point line and launches a shot. It clanks off the back of the rim. How likely is he to be the next person on his team to attempt a shot? And what are the odds that his follow-up shot will come from behind the arc?
NBA players are paid enormous sums of money to make good decisions on the basketball court. To thrive in the league, they learn to pick their spots. Some players know they should avoid three-pointers at all costs, some only take such shots when they are wide open and can set their feet, and others (Steph Curry being a great example) have a green light to toss up three-pointers just about whenever they desire.
But what happens when an NBA player misses a shot? How does such a failure influence the distance and timing of his next shot?
Psychologists have known for a while now that sports enthusiasts believe too strongly in the idea of the “hot hand” – that once a basketball player makes one or two fifteen-footers, he has proven himself to be hot and should, therefore, be fed the ball more often so he can continue his hot shooting. This hot hand theory has been shown to be fallacious, with research establishing that the likelihood of making an NBA shot has, at most, only a slight correlation to the success or failure that same player experienced with his previous shot. The majority of studies in the academic literature have shown that the outcome of the previous shot has no correlation with that of the subsequent shot, once you adjust for the average field goal percentage of the player from the distance in question. Some studies show a small correlation, but even these studies do not dispel the fallaciousness of the hot hand theory, because most of us perceive the correlation – the hot hand – to be much greater than it is.
So fans and sports casters believe too strongly in the hot hand. We perceive that once Carmelo hits one three-pointer, he is likely to hit some more. But what about players? When they hit a shot, or miss one, does belief in a hot hand influence their next shot? Or are they so finely calibrated to their performance, because of the strong financial incentive to perform optimally, that they have found a way to avoid this psychological bias?
Rationally speaking, if players recognized that the correlation between the success of successive shots is tiny, they would not let a rim clanker change where they took their next shot from. But a study in Psychological Science shows that when players miss, say, fifteen-foot shots, their next shots are likely to come from ten feet or less. Whereas if they make fifteen-footers, their next shots are more likely to come from twelve or thirteen feet:
Why do both groups shoot from a shorter range on the next shot? Because the average NBA shot is less than fifteen feet, so there is a bit of a regression to the mean going on here.
The researchers found another interesting phenomenon. When a player makes a shot, he is more likely to be the next player on the same team to take the next shot. In fact, if he makes a three-pointer there is a one in four chance that he will take the next shot for the team (with slightly less than one in five being the norm, since they might be even taken out of the game.) By contrast, if a player misses a three-pointer, he has only a one in six chance of taking the next shot:
What these data show is that even professional athletes are biased by perceptions of having hot or cold hands. If you want your team to win basketball games, you should hope that its players do not respond too strongly to the success or failure of their last three-point attempts.
***Previously Posted in Forbes***