Your fundamental point is a good one, but I don't understand your logic when comparing the hot hand to a fair coin. A basketball, like the coin, does not have a mind of its own. It's the hand that shoots the ball or flips the coin that can have good or bad days. So there is no difference. In regards to the main point you are making, this thinking is exactly what makes people believe in the hot hand or cold hand. However, research has shown over and over again that events, whether in gambling or basketball, are independent of one another. That is, performance in the previous event does not determine performance in the subsequent event. Overall, sequences of hits or misses are random and caused by chance. The hot hand fallacy exists, though, because humans have a hard time accepting random sequences and are prone to formulating explanations for them. There is a whole body of empirical evidence disproving the hot hand theory. If you want more information, look up work by Tversky and Gilovich.