People that are trying to say there is really no such thing as a 'hot hand' are just looking at this the wrong way.
Flipping a coin, or other events based purely on chance with no element of skill involved, have a certain distribution of expected results based on the odds of each possible outcome. For coin flipping, you expect 50% heads and 50% tails. But, we know that there can be long stretches of, say, heads within any string of experimental results. No matter how many heads you have flipped in a row, that has no impact on the expected outcome of the next flip - it is 50% heads and 50% tails. That is because there is no skill or human element that impacts the flip and the coin has no memory - that is, past flips have no impact on the next flip. When there are long stretches of one or the other result, which is against what the odds would tell you to expect, there is no 'reason' for that long stretch - it just happens.
With shooting a basketball, or any other skill-based activity, it is not like that at all. There is a statistical element to the expect result - that is, a 25% 3-point shooter would be expected to make around 25% of his shots, if he shoots enough to regress to the mean. But, there are reasons, human reasons, for deviations from the expected statistics. Like the coin, there may be stretches of shots that deviate from the expected percentage - either in a good way or a bad way. But, unlike the coin, the reason for the deviation is not just chance. The reasons are many and have been discussed here ad nauseum. Essentially, all shooters need stretches where they shoot higher than normal - a 40% shooter is not going to make 2, miss 3, make 2 miss 3, all the time. He is going to make 3 in a row or 5 in a row, then miss a few - whatever. He is going to get hot every once in a while and then he is going to go cold. It just seems so obvious that I am having a hard time understanding how people can say it is not real.
An important point is that, unlike the coin, the shooter has a memory - his last shot affects his next shot - that is a very fundamental difference from the purely statistical analogies people have tried to make.
Those of you that are saying there really isn't any such thing as a hot hand - would you also say there is no such thing as the opposite - a shooter going cold?
A final point is that a shooter's percentage is not set in stone - it can be going up or down, depending on how he is shooting lately.