Andrew Gelman has blogged and published about the "hot hand" phenomenon from a statistical perspective. His statistical perspective is probably fairly authoritative, and his psychological perspective, at least in being very inclusive, not implausible. His basic idea is the following:
- Previous wins are very unlikely to have no effect on future performance.
- Previous wins (or losses) are likely to have some, albeit probably small, effect.
- For example, a player's performance could decrease, maybe due to overconfidence
- A player's performance could increase, for example, due to increase confidence
- Rather than asking if there is any "hot hand" effect at all, the better question is: of what kind is this effect?
In the sense of the latter, the existing studies are actually fairly homogenous: they all argue for a small to marginal effect, on the order of a few percentage points or less. So the idea that the "hot hand" effect is a small and highly variable phenomenon is supported both by a priori reasoning, and by the bulk of the data.
Beyond that, Gilovich, Vallone, and Tversky (1985) have demonstrated that people reliably over detect "hot hands"; we see patterns in near-random variance that aren't really there. Moreover, combining what we know about our perception of the "hot hand", and our statistical knowledge about it, we can establish one more fact: very often, when you think you're observing a "hot hand", you're wrong. This is because the effect size for the "hot hand" appears very small, so small that it is statistically questionable, and if even repeated statistical analyses have trouble establishing its size, we can be sure that the naked eye will not be able to reliably identify it in an individual case.
All this is an example of the debate between null hypothesis testing versus parameter estimation statistics. From the perspective of null hypothesis testing, we consider plausible that the effect might be truly zero, or something else, and zero is our null hypotheses. From the perspective of parameter estimation, we are interested in what the effect actually is, and it being precisely zero is rather unlikely to begin with.
Thus, I believe it justified to say this about the "hot hand" effect:
- It exists, in some form or other.
- It is likely small, and highly variable (sometimes positive, sometimes close to zero, sometimes even negative).
- Whenever you think you see it, you probably don't.