Streaks and regression to the mean
Lesson 9 of 31 in the course “Brain Hacks”. Free, with animations and a quiz.
Randomness doesn’t look random
Flip a coin 6 times. Which is more likely: HHHTTT or HHTHTT? Most people think the second looks “more random” and the first looks suspicious. But both have the same chance: 1 in 64. Autopilot looks for patterns everywhere, because in nature that helped us survive. So streaks look like a signal: “something’s going on here”. Most of the time it’s just randomness, which honestly produces streaks far more often than we expect.
The law of small numbers
A study of kidney cancer across 3,141 US counties found the lowest rates were mostly in small rural counties. You immediately want an explanation: clean air, natural food. But the highest rates were also in small rural counties! The cause isn’t rural life; it’s size. Where few people live, a couple of cases swing the percentage a lot, producing extremes in both directions. Big samples stay closer to the average. A small sample is a noisy sample.
A $1.7 billion mistake
People noticed that many of the best schools are small. A large foundation invested about $1.7 billion in creating small schools, sometimes by splitting big ones. The explanation sounded nice: teachers closer to students, more attention. But anyone who looked at the worst schools would have seen they were also more often small. Small schools aren’t better; they just land at the extremes more often. A pretty cause was found for ordinary noise.
Regression to the mean
Flight instructors told a psychologist: “When we praise a cadet for a great manoeuvre, next time he does worse. When we yell at him for a terrible one, he does better afterwards. So praise hurts.” In fact, it’s regression to the mean. A result is skill plus luck. A great manoeuvre is usually skill plus a lot of luck, and next time the luck will most likely be ordinary. Yelling and praise have little to do with it: after an extreme, results drift back towards the average anyway.
The “cover jinx” and creators
There’s a sports superstition: an athlete who makes a magazine cover plays worse the next season. There’s no jinx. You make the cover after an outstanding season where skill met a lot of luck. And big luck rarely repeats right away. Same with creators: after a viral video, the next ones get fewer views, and the creator thinks “the algorithm broke” or they “lost their touch”. More often it’s just a return to their normal level.
Honestly: the “hot hand”
Basketball players believe in the “hot hand”: sink three in a row and you’re on fire. In 1985 researchers declared it an illusion, and for a long time that was a textbook example. But in 2018 other scientists found a subtle flaw in the maths, and after correcting it, a small streak effect did show up. So we mark it “disputed”. The honest takeaway: streaks sometimes mean something, but much less than the feeling suggests. Deciding based on one streak is still risky.
Hack: “how many tries was that?”
Danya closes trades in profit 5 days in a row and thinks: “I’ve got a system!” Three questions before a conclusion like that. How many tries in total? Five is very few. How often does this happen by chance? A streak of five wins at 50/50 odds comes up about once in 32 tries, and there are millions of traders. What comes after an extreme? Most likely, regression to the mean. So test any “system” on dozens or hundreds of trades, not one lucky week.
Try it: 20 flips
First, make up a sequence of 20 coin flips in your head and write it down. Then actually flip a coin 20 times and write that down too. Compare the longest streaks. In made-up sequences, people almost never put more than three of the same in a row: it feels like that “doesn’t happen”. But in 20 real flips, a streak of four or more shows up about 77% of the time, and five or more almost half the time. It’s the best vaccine against believing in “patterns” over short stretches.
Check yourself
- Which is more likely in 6 coin flips: HHHTTT or HHTHTT?
Correct answer: Equal: each has a 1 in 64 chance. Yes. Every specific sequence of 6 flips has a 1 in 64 chance. The “more random” feeling is autopilot looking for a pattern. - The lowest and the highest disease rates were both in small counties. Why?
Correct answer: Small samples swing more and produce extremes. Right. Where few people live, a couple of cases move the percentage a lot. Extremes in both directions are a sign of small-sample noise. - A coach praises a player after his best game, and the next one is worse. What most likely happened?
Correct answer: Regression to the mean: the best game included a lot of luck. Right. A result is skill plus luck. After a very lucky game, the next one is almost always closer to average, praise or no praise. - Danya has been in profit 5 days in a row and wants to put everything into “his system”. What’s smart?
Correct answer: Test the system over dozens or hundreds of trades. Right. Five days is noise: such a streak happens by chance about once in 32 tries. Only a large sample can show whether the system has an edge.