Surprised by the Hot Hand Fallacy? A Truth in the Law of Small Numbers
This is an interesting paper that I am still working through.
So far, I’ve been unable to validate the hot hand fallacy reversal using a Monte Carlo simulation. Admittedly, the sim utilizes the usual statistical property assumption (i.e.: iid) which maybe part of the problem, see below. With that said, I cannot seem to support the hot hand fallacy reversal even using standard statistics. I need to spend more time with the paper….
To me, the hot hand fallacy reversal would have an intuitive explanation. Statistical analysis assumes independence and identically distributed random variables. (iid) That is, every shot is independent of earlier shots and the kind of shots taken have the same environment (re: how the defense plays). As I wrote in "Training and the interaction between left and right hemispheres" the athlete can reach a "flow state" where the speed of reaction and ability to execute is at its highest. I would expect this is a hot hand state. As such, this would invalidate the independence assumption. As such, neuroscience maybe the explanation for the lack of independence. Defense is a metaphor for entropy enforcement. A hot hand represents a low entropy state. The defense and fatigue of the hot hand player introduce factors that move players to the expected level of performance…e.g., higher entropy and reversion to the mean.