Night Build · 11 Oct 2026 · sports · experiment protocol

Is Your Hot Hand Real?

For 40 years, the "hot hand" was the textbook example of seeing patterns in noise. Then two economists found a small counting trap in how the test was scored. Guess first, then see the trap, re-score the original 1985 data, and plan a test of your own streaks.

Guess first

Flip a fair coin 100 times. Each time you get three heads in a row, write down the next flip. Work out what share of those next flips were heads. Do this for many 100-flip runs and average the shares.

What is that average?

50%

Read this first

Part 1 is pure maths: computed exactly, and checked against 200,000 simulated runs per point.
Part 2 rebuilds the 1985 Cornell test from the paper's printed table (rounded to two decimals), not the raw shot logs. The paper's Tables 4 and 5 disagree in five places (shooter M10's row does not add up; M10, F4, F5 and F10 differ by one hit between tables). Hit totals here come from Table 5; the result barely moves if M10 is dropped or Table 4's totals are used (see part 03).
Part 3 is for any streak you can log (free throws, darts, putts, puzzles). It is education, not coaching or betting advice.

01The trap: short runs eat their own streaks

Inside one finite run, a streak of three heads "uses up" heads. Where a streak sits near the end, there is no next flip to count. And if a heads follows the streak, it starts the next overlapping streak, so heads-after-streaks get spread across fewer, longer runs. Averaging each run's share therefore lands below 50%, even though every single flip is a fair 50/50. Pool all flips from all runs together and the bias disappears; it lives in the per-run average, which is exactly how the hot-hand studies scored each player.

Average share of heads right after k heads in a row, by run length

02Coin lab

Flip one run and see which flips get counted (ringed). Then run thousands and watch the average settle below the fair-coin line. Change the run length, the streak length or the coin itself.

Run length 100 Streak length k 3 Coin's true heads rate 50%

03Cornell, 1985, re-scored

Gilovich, Vallone and Tversky had 26 Cornell varsity players take about 100 shots each from a distance where they hit roughly half. Players hit about as often after three makes as after three misses, so the paper concluded there was no hot hand. But a 100-shot run is exactly where the trap bites: with no hot hand at all, each player's "after 3 makes minus after 3 misses" gap should come out about 9 points negative. Measured against what chance really predicts, the same numbers tell a different story.

10+ shots after both streaksTHIN: under 10 after one streak

Source: Gilovich, Vallone & Tversky (1985), Cognitive Psychology 17:295–314, Tables 4 and 5. 25 of 26 shooters (one had no shots after three makes). Chance line: 100,000 shuffles of each player's own hits and misses. Recomputed 11 Oct 2026.

Every shooter

Scroll the table sideways for all columns.

THIN: fewer than 10 shots after three makes or after three misses. A single THIN player proves nothing; the claim rests on all 25 together.

04Test your own streaks

Log any hit-or-miss sequence. The test shuffles your own record thousands of times, so it compares you with a version of you that has the same hit rate but no memory. That corrects for the trap automatically.

Or paste a sequence (H/M, 1/0, X/O or W/L):

How many shots do you need?

Chance of catching a shooter who really is better after three makes (permutation test, 5% one-sided), by total shots. 1,000 simulated shooters per point, 50% base rate.

Model: a shooter hits 50%, rising by the boost shown after three makes in a row. Simulated 11 Oct 2026.

A protocol you could actually run

05Evidence

Gilovich, T., Vallone, R. & Tversky, A. (1985). The hot hand in basketball: on the misperception of random sequences. Cognitive Psychology 17, 295–314. doi:10.1016/0010-0285(85)90010-6. Tables 4 and 5 are the data in part 03.
Miller, J. B. & Sanjurjo, A. (2018). Surprised by the hot hand fallacy? A truth in the law of small numbers. Econometrica 86(6), 2019–2047. doi:10.3982/ECTA14943. The streak-selection bias in parts 01–02, and their reanalysis of the Cornell data, which reverses the 1985 conclusion.
Miller, J. B. & Sanjurjo, A. (2021). Is it a fallacy to believe in the hot hand in the NBA three-point contest? European Economic Review. doi:10.1016/j.euroecorev.2021.103771. A second, larger shooting dataset (not used here).

What this does not show: that game-time hot streaks are big, or that you should pass to the player who just scored three. The Cornell estimate here is about +12 points (about +11 without the single streakiest shooter), and part 04 shows how hard an effect that size is to see in your own small samples. The same trap applies to any short record of wins and losses you read streaks from.