Cobra Effect · Statistics and probability
The hot hand
Streaks are mostly chance, though not always entirely.
7 cards, read aloud in 2:32, with a test and sources.
He has scored three in a row. Everyone knows to pass to him.
Players believe it. Coaches believe it. The whole stand believes it. In 1985 three psychologists decided to go and check.
Gilovich, Vallone and Tversky went through the shooting records.
They took a full season from a professional team in Philadelphia, then free throws, then a controlled experiment with college players. A shot after a hit went in about as often as a shot after a miss. No streaks beyond what chance produces on its own.
So the hot hand was filed away as a trick of the mind.
People see patterns in randomness. Four hits in a row looks like meaning, and over a long season runs like that are certain to turn up. For thirty years this was the textbook case of a belief that feels obvious and is not true.
2018. Two economists find a counting error hiding inside the method.
Joshua Miller and Adam Sanjurjo looked hard at how you pick out the shots that follow a hit. Flip a fair coin four times, over and over. Look only at the flips that came straight after a heads. On average about 40% of those are heads, not half.
That small tilt was buried in the original test.
If a steady shooter should look worse after a streak, then looking the same after a streak is evidence of something real. Corrected, the old data shows a genuine hot hand. It is small, it appears in some players and not others, and it is clearest in repeated shots from one spot.
The tidy story about a foolish crowd was itself a little wrong.
The belief was exaggerated. The players were not simply imagining it. And the correction took 33 years, because the mistake sat in a method nobody thought to question.
Carry both halves of this one.
Your eye really does invent streaks in random data, so a run of good luck is not a sign. And a confident debunking is a claim like any other, resting on a method that can be wrong. When somebody tells you the crowd is deluded, ask to see the counting.
Sources
- Hot hand, Wikipedia. The 1985 paper by Gilovich, Vallone and Tversky, the 2018 reanalysis by Miller and Sanjurjo, and where the evidence stands now.
- Thinking, Fast and Slow, Daniel Kahneman, 2011. Written while the basketball result was still settled science, so read the streaks chapter alongside the later correction. Excellent on how people read randomness.
- Selection bias, Wikipedia. How choosing which cases to look at can decide the answer before any analysis begins. The general form of the trap that hid inside the basketball data.
Nearby ideas
- The gambler’s fallacy. Chance has no memory, so nothing is ever due.
- The law of small numbers. Small samples swing wildly, and the swings look like signals.
- Regression to the mean. Extreme results drift back towards normal, whatever you do.
- The law of large numbers. Averages settle down over many tries, but a run never gets corrected.
- Mean and median. Why the average can describe nobody at all.
- The Literary Digest poll. A small sample chosen well beats a huge one of the wrong people.
- The garden of forking paths. Choosing the analysis after seeing the data makes flukes look real.
- The Monty Hall problem. Why switching doors wins twice as often as staying put.