Due for a make?

Question

A basketball player's free throws are independent, each made with probability 45%. She has just missed five in a row and feels she is "due" to make the next one.

What is the probability that she makes her next free throw?

Accepted Answer

Under the stated assumption that her free throws are independent, the five misses do not build up any pressure toward a make. Each attempt stands alone at her true rate, so the next one is made with probability 45\% = 0.45. The sense of being "due" is the gambler's fallacy applied to a skill: treating independent attempts as if a run of failures must be repaid by a success. Nothing in an independent process stores up a correction. Her long-run make rate settles near 45% simply because many future shots outnumber this short streak, not because misses are refunded. (Real debates about a "hot ha…

Due for a make?

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