Gur Yaari writes:
Anyone who has ever watched a sports competition is familiar with expressions like “on fire”, “in the zone”, “on a roll”, “momentum” and so on. But what do these expressions really mean? In 1985 when Thomas Gilovich, Robert Vallone and Amos Tversky studied this phenomenon for the first time, they defined it as: “. . . these phrases express a belief that the performance of a player during a particular period is significantly better than expected on the basis of the player’s overall record”. Their conclusion was that what people tend to perceive as a “hot hand” is essentially a cognitive illusion caused by a misperception of random sequences. Until recently there was little, if any, evidence to rule out their conclusion. Increased computing power and new data availability from various sports now provide surprising evidence of this phenomenon, thus reigniting the debate.
Yaari goes on to some studies that have found time dependence in basketball, baseball, volleyball, and bowling.
Here are my quick thoughts:
1. The effects are certainly not zero. We are not machines, and anything that can affect our expectations (for example, our success in previous tries) should affect our performance.
2. The effects I’ve seen are small, on the order of 2 percentage points (for example, the probability of a success in some sports task might be 45% if you’re “hot” and 43% otherwise). Yaari presents his results in terms of p-values but I think it’s best to look at effect sizes directly in terms of probabilities.
3. There’s a huge amount of variation, not just between but also among players. Sometimes if you succeed you will stay relaxed and focused, other times you can succeed and get overconfidence.
4. Whatever the latest results on particular sports, I can’t see anyone overturning the basic finding of Gilovich, Vallone, and Tversky that players and spectators alike will perceive the hot hand even when it does not exist and dramatically overestimate the magnitude and consistency of any hot-hand phenomenon that does exist.
In summary, this is yet another problem where much is lost by going down the standard route of null hypothesis testing. Better, in my view, to start with the admission of variation in the effect and go from there.