>First of all, I've glanced through the links you pointed.
>But they don't have the studies themselves, they just refer to
>some "studies".

They do explain the real life application of those studies though. Specifically this portion:

"Of course Larry Bird, the great forward of the Boston Celtics, will have more sequences of five than Joe Airball—but not because he has greater will or gets in that magic rhythm more often. Larry has longer runs because his average success rate is so much higher, and random models predict more frequent and longer sequences. If Larry shoots field goals at 0.6 probability of success, he will get five in a row about once every thirteen sequences (0.65). If Joe, by contrast, shoots only 0.3, he will get his five straight only about once in 412 times. In other words, we need no special explanation for the apparent pattern of long runs. There is no ineffable "causality of circumstance" (if I may call it that), no definite reason born of the particulars that make for heroic myths—courage in the clinch, strength in adversity, etc. You only have to know a person's ordinary play in order to predict his sequences. (I rather suspect that we are convinced of the contrary not only because we need myths so badly, but also because we remember the successes and simply allow the failures to fade from memory. More on this later.) But how does this revisionist pessimism work for baseball?"

>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.

This is a logical fallacy. If you improve, your average (or field goal % or whatever) improves. The point is that if your average is already at a highly defined number, then your misses/makes and runs can be accurately guessed. You are right in that it is not a coin flip, but player skill is reflected in their averages.

>But, nevertheless, people become better with shots as they are
>training hard.
>Or become worse as they stop training, getting old or tired.

Of course they do, but their average also decreases or increases appropriately.

>These "studies" operate with average hit percentage, but that
>percentage already includes hitting streaks of different
>players.

Nope, just the player themselves. It includes *that* players hitting streaks, but those, again, can be predicted and fall in the expected realm.

>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).

What they are saying is that the cause and effect are the opposite of what you claim (I think). He feels unstoppable because he's on a streak, but the streak is basically a random occurance based upon his skill level.

>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).

I've always been under the impression I play better when I'm sick. Logically I know this probably isn't true, but the times when I wasn't feeling well and performed average or poorly aren't remembered like the times when I felt crappy and played extremely well.

>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.

This is some sort of circular logic. Thats like saying that because flipping a coin already includes streaks of heads or tails that the frequency and length of them are somehow independant of the fact that it is a 50/50 chance. What the study is saying is in the quoted block above.

>The good news is that if you can prove they're mistaken,
>you
>can probably get a cover article in a nice economics journal.
>
>It's not every day you get to shoot down a Nobelist in his
>primary field!
>
>I should find time and point that their studies are
>misguiding.
>However, the good thing is that real sport managers don't
>really use those studies in making their teams successful.

Real sports managers probably buy into the "hot hand" thing, but that mean it has any scientific basis. Real people buy into the earth being 6000 years old, but I bet you don't think they're smart to think that way because it isn't the way you think. This case is even more extreme since literally everyone thinks this way because of the way our brains are wired as a species.