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).
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.
I also used this as an example in the last five paragraphs of section 3 in this paper.