A couple of thoughts regarding the hot hand fallacy fallacy

For many years we all believed the hot hand was a fallacy. It turns out we were all wrong. Fine. Such reversals happen.

Anyway, now that we know the score, we can reflect on some of the cognitive biases that led us to stick with the “hot hand fallacy” story for so long.

Jason Collins writes:

Apart from the fact that this statistical bias slipped past everyone’s attention for close to thirty years, I [Collins] find this result extraordinarily interesting for another reason. We have a body of research that suggests that even slight cues in the environment can change our actions. Words associated with old people can slow us down. Images of money can make us selfish. And so on. Yet why haven’t these same researchers been asking why a basketball player would not be influenced by their earlier shots – surely a more salient part of the environment than the word “Florida”? The desire to show one bias allowed them to overlook another.

Also I was thinking a bit more about the hot hand, in particular a flaw in the underlying logic of Gilovich etc (and also me, before Miller and Sanjurjo convinced me about the hot hand): The null model is that each player j has a probability p_j of making a given shot, and that p_j is constant for the player (considering only shots of some particular difficulty level). But where does p_j come from? Obviously players improve with practice, with game experience, with coaching, etc. So p_j isn’t really a constant. But if “p” varies among players, and “p” varies over the time scale of years or months for individual players, why shouldn’t “p” vary over shorter time scales too? In what sense is “constant probability” a sensible null model at all?

I can see that “constant probability for any given player during a one-year period” is a better model than “p varies wildly from 0.2 to 0.8 for any player during the game.” But that’s a different story. The more I think about the “there is no hot hand” model, the more I don’t like it as any sort of default.

In any case, it’s good to revisit our thinking about these theories in light of new arguments and new evidence.