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Streak

Check the arithmetic
For thirty years, science said the hot hand was an illusion. The proof measured shooting after streaks and found nothing special. Then two economists showed the measurement itself was rigged, by an innocent-looking step you can expose with three fair coins. This page flips them for you.

The claim to test

Flip a fair coin three times. Among the flips that come immediately after a heads, what fraction are heads? A coin has no memory, so intuition says one half. If the intuition is right, the number below should settle at 50 percent. Run it.

The experiment

 
avg heads after heads
0
three-flip rounds
Rounds with no flip after a heads (TTT, TTH) answer nothing and sit out, exactly as in the famous studies. Each remaining round reports its own fraction; the number above is the average of those reports, which is precisely how the 1985 analysis scored shooters.

Why it is not one half

Average the six scores: five twelfths, about 41.7 percent, from a coin that is perfectly fair. Selecting the flips that follow a heads is not a neutral selection: in a short sequence, the heads you condition on tends to use up the heads. The bias shrinks as sequences grow, and never quite vanishes; a hundred shots is still a short sequence. So a real shooter measured this way should come out below his true rate, and a shooter who merely matches his average, the very result reported as proving no hot hand, has actually beaten the rigged benchmark.
What this does and does not show. The demonstration above is the core of Miller and Sanjurjo's correction, published in Econometrica in 2018. Applied to the original 1985 data, it flips the verdict: in the cleanest controlled shooting, streaks were real, on the order of thirteen points. It does not mean streaks are destiny, or that the in-game effect is large; defenses adjust, shooters force shots, and the live-game evidence stays modest. And the gambler's fallacy is still a fallacy: this page's coin shows a bias in the measuring, not a memory in the coin. The lesson is smaller and sharper: a verdict is a measurement, measurements have instruments, and this instrument sat miscalibrated in plain sight for thirty years.

Where this practice came from

Everyone Knows

Flow 7: The Hot Hand · Episode 1 · the first of eight stories

The building knows before the scoreboard does.

A shooter hits one from the wing. Then a second, a step further out, the kind that goes in without touching anything on the way. Then a third, and the noise starts arriving a fraction before the ball does, because everyone in the arena has already decided how this one ends.

That scene is imagined, and only in its details. Some version of it has happened in every gym on earth, and everyone watching reads it the same way. He is hot. Feed him.

There is a belief in basketball so universal that it barely registers as a belief, the way water barely registers with fish. His teammates know it and change their passing. His coach knows it and changes the play. His defender knows it and presses closer.

The shooter knows it most of all. Ask him afterward and he will tell you about the rim looking wide as a barrel, about a stretch where he could not miss.

The hot hand is not a theory anyone argues for. It is a thing everyone has seen.

Beliefs that universal do not usually get measured. There is nothing to measure. Everyone already knows.

In 1985 three researchers measured it anyway. Thomas Gilovich, Robert Vallone and Amos Tversky surveyed basketball fans and asked them, in effect, to put a number on the obvious.

Ninety-one percent believed a player has a better chance of making a shot after hitting his last two or three than after missing his last two or three. Eighty-four percent believed it is important to pass the ball to a player who has just made several in a row.

The scenes around that survey are imagined: the forms, the tallying, the mild absurdity of asking grown people to rate a fact they can see with their own eyes. The numbers hardly needed collecting. They are the sport's common sense, and not only the fans': the players and coaches the belief describes hold it at least as firmly.

But one of the three was not asking idly.

Tversky was at that moment perhaps the most feared man in the study of common sense, one half of the partnership with Daniel Kahneman that had spent the 1970s demonstrating that human intuition about probability is systematically, predictably wrong.

That research program had a favorite specimen: people are terrible judges of randomness.

Show people truly random sequences and they refuse to believe them, because real chance is streakier than intuition expects. A fair coin flipped twenty times will routinely produce runs of four or five heads, and every human eye reads those runs as pattern, as momentum, as heat. The gambler at the roulette wheel who sees red come up four times and knows something is going on is the canonical sufferer.

So the three researchers asked the obvious, impertinent question.

Basketball players are people. Shot sequences are sequences. When everyone in the building sees that a man is hot, are they seeing a real change in the shooter, or are they doing what the roulette gambler does, reading meaning into the clumps that pure chance produces anyway?

The belief makes a testable claim: that a make is more likely after makes than after misses. Shooting records exist. You can simply check.

They checked. The paper they published in 1985, in the journal Cognitive Psychology, became one of the most famous in the field, and its verdict, delivered with the full authority of the era's best methodology, was that everyone is wrong.

There is no hot hand, the paper said. The fire in the shooter's chest is real as an experience and empty as a prediction. The streaks are the coin's streaks, and the whole sport is organized around a mirage.

That verdict ruled for thirty years.

This season is the story of its reign, and of the quiet arithmetic that ended it.

Wren

The record says this much; the scenes between are imagined. The rest of the season, and the sourcing behind it, runs a few times a week at Wren. One page for the whole practice: /practice/.