The Hot Hand: Do Basketball Players Get Streaky?
Commentators talk about a player 'being hot' after a run of makes, as if a made shot raises the chance of the next one going in. Real shot-by-shot data lets you test whether streaks in basketball happen more often than chance alone would produce.
Introduction
In 1985, Gilovich, Vallone and Tversky analysed real NBA shooting data and found no evidence of hot streaks: makes and misses looked statistically independent, like coin flips. Decades later, Miller and Sanjurjo (2018) showed the original analysis had a subtle bias: the natural way of counting 'shots following a hot streak' underestimates the true conditional probability, even for a sequence of independent coin flips. This exploration works through both sides using real or simulated shot data: does streakiness look real, and does the counting method itself distort the answer?
Guiding Questions
- Find or record a sequence of makes and misses for one player over several games. What proportion of shots after a streak of two or more makes go in, compared with the player's overall shooting percentage?
- Model each shot as an independent trial with a fixed success probability. Simulate a long sequence and count streaks the same way you counted them in the real data.
- Compare the real streak-shooting percentage with the simulated one. Is the difference large enough to suggest real streakiness, or within the range chance alone produces?
- Miller and Sanjurjo showed that averaging 'percentage made after a hot streak' across short sequences underestimates the true conditional probability, even when shots are independent by construction. Reproduce this bias in your own simulation and explain where it comes from.
- After correcting for that bias, does the evidence for a real hot hand change?