>>The studies in question asked: Given a successful shot N,
does the probability of success for shot (N+1) increase,
decrease, or stay the same?

>>The answer is "stays the same" in any sufficiently large
sample set. This isn't in the realm of opinion-- it's a
simple observation of real data. (That paper has since been
expanded to larger studies in multiple sports, as I mention
above.)

> As I said, there is more than just probability in succesful shots.
When you flip a coin then yes, those studies would be applicable.
As an ultimate example: you would never train if your consequent shot has the same probability of success.
But, nevertheless, people become better with shots as they are training hard.
Or become worse as they stop training, getting old or tired.

> These "studies" operate with average hit percentage, but that percentage already includes hitting streaks of different players.
A "hot hand" player makes a succesful shot not because his previous shot was successful, but because he's feeling good and unstopable today (which includes a number of factors).
And a "cold hand" player misses his shot because it is not his day, not because he missed his previous shot (he is sick today, for example).
The trick is that the average hit ratio of that player already includes his good or bad streaks and thus will certainly "confirm" that their streaks are nothing and are within the probability based on their average hit ratio.

Without having read the studies, I dare guess that Valg simplified it a bit. The reasonable way to study something like that would be to analyze a large sample of shots and see if the hits/misses on a per-game basis match a normal distribution... I.e. that hot-hand days and cold-hand days would just be statistical fluctuations.