Sports Streaks

Probability · Axiom Academy

The "hot hand" phenomenon: Is it skill or just randomness? "He's on fire!" Sports commentators love to describe players having a "hot hand"—moments when a player seems unstoppable, making shot after shot. But is this a real phenomenon, or is our brain just finding patterns in randomness? This question has fascinated psychologists, statisticians, and sports fans for decades. The answer lies in understanding the geometric distribution and how streaks naturally emerge from random sequences. A player takes 100 shots with a 45% success rate. Watch for streaks! Notice how streaks of 3, 4, or even 5+ made shots appear naturally, even though each shot has the same independent 45% probability! When we ask "How long until the next miss?" or "How long will this streak last?", we're dealing with a geometric distribution . It models the number of trials until the first success (or failure). where X is the number of trials until first success, and p is the probability of success Mean = 1/p: Average number of shots until a make Memoryless: Past results don't affect future probabilities Variance = (1-p)/p²: Measures spread of streak lengths Decreasing probabilities: Longer streaks become exponentially rarer In 1985, psychologists Thomas Gilovich, Robert Vallone, and Amos Tversky published a landmark study analyzing NBA shooting data. Their conclusion shocked the sports world: the hot hand doesn't exist .

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