Why punishment seems to work

Before I explain anything, I want you to run a flight school.

Eight trainee pilots fly a difficult manoeuvre every day, scored out of 100. Your job, after each day's flights, is the standard doctrine of instructors everywhere: praise the best pilot, chew out the worst. Then watch what your feedback does to their next flight.

Play the six days — it takes about a minute. And don't worry about keeping track of what your feedback does: your instructor's log will keep score for you.

This trap is not hypothetical. In the 1960s the psychologist Daniel Kahneman — later a Nobel laureate — was lecturing Israeli Air Force flight instructors on the evidence that reward works better than punishment. A seasoned instructor objected: on many occasions he had praised cadets for a cleanly executed manoeuvre, and they usually did worse on the next try; he had screamed at cadets for botched ones, and they generally did better. So with respect — please don't tell us that reward works and punishment doesn't, because the opposite is the case. And he wasn't making it up. That really is what he had watched happen, over and over, for years.¹

The instructor's observations were correct. His inference was completely wrong — and Kahneman later wrote that grasping why was one of the most important insights of his career:

“I had stumbled onto a significant fact of the human condition: the feedback to which life exposes us is perverse. Because we tend to be nice to other people when they please us and nasty when they do not, we are statistically punished for being nice and rewarded for being nasty.”

Sit with that for a second. Life itself is rigged to teach every parent, teacher, coach and boss the same false lesson, every day, forever: kindness fails; cruelty works. Not because it's true, but because of when we choose to be kind.

Statisticians call what you just experienced regression to the mean — the mean is simply the average — and the name is a small disaster. It sounds like a force. A rubber band. Gravity for luck. Things stretched too far from average get pulled back. People who learn the phrase usually walk away with a new piece of invisible physics in their heads: extremeness, left alone, gets corrected.

That mental model is wrong, and it is why the idea never sticks. So before anything else:

Nothing regresses. No force pulls anyone back. The pattern is real — and it comes entirely from how you picked.

No force acted on your pilots; there were no pilots. The dice were not "correcting" anything; dice can't remember what they rolled yesterday. The only thing that happened was this: you picked the extremes, and extremes are where the luck is.

Here is the actual mechanism, and it fits in a paragraph.

Every score you will ever care about — a test result, a sales quarter, a blood-pressure reading, a child's behaviour on a given Tuesday — is a blend of two ingredients: things that persist (ability, habits, the underlying condition) and things that don't (mood, sleep, weather, which questions came up, measurement error — call it all luck).

An extreme score is almost never the persistent part alone. The best performance in any group usually belongs to someone genuinely good who also got a good bounce that day. The worst usually belongs to someone weaker who also got unlucky. So when you select the extremes — the star, the disaster, the record quarter, the worst flare-up of your back pain — you have silently selected for extreme luck too.

Then tomorrow comes. The persistent part shows up again, faithfully. But the luck is re-rolled from scratch — and a fresh roll is typical, not extreme. So the group you picked drifts back toward ordinary. Nothing pushed it. You just stopped selecting for luck, because you can only select on yesterday.

Skill carries over. Luck doesn't. Extremes are part luck. That's the whole phenomenon.

Kahneman's shorthand for it: “Success = talent + luck. Great success = a little more talent + a lot of luck.”

And this gives you something better than a definition — it gives you an instrument. How much an extreme group falls back measures how much of the score doesn't persist — which, over a short gap in a stable game, is mostly luck. Try it:

Notice three things as you play:

At 0% luck, nothing regresses. Drag the slider all the way down — a game even purer than chess — and the top players in Round 1 are the top players in Round 2. Regression to the mean is not a law of nature that applies to everything — it applies exactly as far as luck does.

At 100% luck, everything regresses completely. The "top" coin-flippers fall all the way back to average, because their selection was nothing but luck. This is your flight school again.

In between is where life happens. The selected group keeps the skill part of its edge and loses the luck part. The fall-back you observe is a readout of how much of the game fails to carry over — which is why statisticians can look at how hard fund managers regress and put a ceiling on how much of stock-picking can possibly be skill. (Spoiler, from decades of persistence data: very little survives the re-roll.²)

Here is the most elegant test in this whole subject, and almost nobody teaches it.

Athletes who appear on the cover of Sports Illustrated tend to decline afterwards — the famous "SI jinx". The magazine once audited its own first 2,456 covers and found that misfortune had followed 37% of the time. The causal stories write themselves: pressure, complacency, overexposure. But ask one strange question: what were these stars doing in the season before the one that earned the cover?

The economist Gary Smith ran that test with baseball's batting leaders. The five best averages of 2014: all five hit worse in 2015, just as the jinx predicts — and all five had hit worse in 2013, too.³ The career year was the aberration; the seasons on either side of it were just the player. No jinx, no pressure, no complacency can reach backwards in time. Selection can: you get the cover for a career year, a career year is part luck, so the seasons on both sides of it sit closer to your true level.

That's the test. A causal story can only explain the after. Selection explains the before and the after. So when the decline shows up running time backwards too, the curse isn't so much disproved as made redundant — selection alone produces the whole pattern. Better still, the comparison tells you how much room is left for a real effect: only the part of the after-decline that exceeds the before-rise can belong to causation. For Smith's batting leaders, the backward decline sat right there alongside the forward one, leaving the jinx nothing to explain. At the speed-camera sites you'll meet below, by contrast, the fall after installation exceeds what selection and trend can account for — and that excess, about a fifth of the observed drop, is the cameras. (Flip the time toggle in the lab above and watch the arrow swing sideways: the same fall-back, run the other way in time.)

This test has a distinguished history of embarrassing smart people. Francis Galton, who discovered the phenomenon in the 1880s, measured parents and children and found that exceptionally tall parents had children less tall than themselves — closer to average. It would be easy to conclude that heredity dilutes, that humanity is converging on uniformity. But Galton noticed the mirror image: exceptionally tall children had parents less tall than themselves, too.⁴ Height can't dilute in both directions at once. The spread of heights wasn't shrinking at all — the extremes just don't line up across generations, because each generation's extremes get there partly on the luck of the draw.

Fifty years later a statistics professor named Horace Secrist did not notice. He and his assistants spent a decade tracking the fortunes of American businesses, found that the most exceptional firms kept drifting toward averageness, and in 1933 published a 468-page book about it — The Triumph of Mediocrity in Business — concluding that competition itself grinds excellence down. The statistician Harold Hotelling pointed out the fatal flaw: sort the very same firms by how they finished rather than how they started, and now the middling firms appear to climb toward excellence. The pattern ran backwards just as well — “from the same data one may demonstrate stability or instability according to taste.” When Secrist protested, Hotelling compared the decade of labour to “proving the multiplication table by arranging elephants in rows and columns, and then doing the same for numerous other kinds of animals”.⁵

The trap has one signature: something was selected because it was extreme, and then it was measured again. Any time you see that shape, regression to the mean is already in the room. A field guide:

Half of understanding this idea is refusing its evil twins. Regression to the mean does not mean any of the following:

You cannot see this illusion coming — it looks exactly like causation from the inside, which is why the flight instructor was so sure. But one question dissolves it:

“Compared to what? What would have happened anyway?”

Any before/after story that starts at an extreme is unreliable by construction — the bounce was already loaded into the selection before the intervention ever arrived. This is not a small academic worry; it is the reason controlled trials exist. Give a treatment to people selected for being at their worst and most will improve. Give a sugar pill to identical people selected the same way and most of them improve too. Both groups bounce; only the difference between the groups is the treatment. A control group is civilisation's instrument for subtracting regression to the mean. (Donald Campbell, the great methodologist of policy evaluation, rated regression artifacts “probably the most recurrent form of self-deception in the experimental social reform literature”.⁹)

For daily life, four rules cover most of it:

1. Distrust any intervention launched at rock bottom. The consultant hired in the crisis, the remedy taken at the symptom's peak, the policy passed after the freak disaster — all will "work". Wait for the second data point, or ask what happened to comparable cases that did nothing.

2. Never pay full price for a career year. You met this one in the field guide: select the extreme and you have bought the luck at skill prices. Budget for it to leave.

3. Judge people on averages, not on their most vivid moment. One brilliant interview, one disastrous shift, one terrible Tuesday — the extreme moments are the least repeatable ones. More observations, less regression. The vivid moment is precisely the least representative one.

4. When kindness seems to fail and harshness seems to work, remember the flight school. The dice manufacture that exact pattern out of nothing, every time. You now know something the instructor didn't — the evidence of your own eyes has a systematic bias in favour of cruelty, and it is lying.

There is one more thing this idea gives you, and it is oddly gentle.

Your most humiliating day — the botched talk, the failed exam, the shift where everything went wrong — overstated your flaws by exactly the same mechanism that your finest hour overstated your gifts. Both were real performances by the real you; both were also extreme draws, selected by memory precisely because they were extreme. The extremes are where the luck lives. The average is where you live.

So: be a little suspicious of your triumphs, a little gentle with your disasters, and extend both courtesies to everyone else. The world will keep handing you vivid before-and-after stories that begin at an extreme — the miracle cure, the turnaround CEO, the scolding that worked. You now know what's inside them: a re-rolled die, dressed up as a moral.