Rather than being signs of non-randomness, they are actually signs of randomness. Their use of optional starting and stopping is based on the presumption of psychic variation and an apparent ignorance of the probabilities of random events. Combining the clustering illusion with confirmation bias is a formula for self-deception and delusion. A detailed analysis was done of the Philadelphia 76ers shooters during the 1980-81 season. It failed to show that players hit or miss shots in clusters at anything other than what would be expected by chance.
Basketball players do shoot in streaks, but within the bounds of chance.
It is an illusion that players are 'hot' or 'cold'. In epidemiology, the clustering illusion is known as the Texas-sharpshooter fallacy . In logic, this fallacy is known as the fallacy of division , assuming that the parts must be exactly like the whole.