# Regression to the Mean: Why Extreme Results Don’t Last Numbers · 6 min read · updated 2026-10-30 > Why the worst performers improve and the best slip back, with no cause at all. Regression to the mean, and how it fools us about praise, cures and luck. ## The short answer Regression to the mean is the tendency for an extreme result to be followed by one closer to average, simply because the extreme result was partly luck and luck doesn’t repeat. No cause is needed. It fools people whenever they pick out the best or worst and measure again, making treatments, punishments and policies look as though they worked when the change would have happened anyway. The pupils who score worst on a test get extra tutoring. On the next test, they do better. Did the tutoring work? Maybe. But they would probably have improved anyway, and the reason is one of the most important and least understood ideas in statistics. It explains why the cover of a sports magazine seems to be cursed, why so many alternative remedies seem to work, and why a manager who shouts at their worst performers is convinced that shouting gets results. ## Skill plus luck Most results are part skill and part luck. A pupil’s mark on a test depends on what they know, and also on whether they slept well, whether the questions happened to suit them, and a dozen other things that vary from day to day. Now pick out the pupils with the very lowest marks. That group is mostly made of people with lower skill *and* a bad day. Next time, their skill is the same, but their luck is probably more ordinary. So their scores move back towards the average, without any help at all. The same happens at the top. The best scorers on one test include people who had a good day. Many of them slip back a little next time. Not because they got worse, but because that particular good day doesn’t repeat. No cause is needed. Regression to the mean happens whenever you pick people, or anything else, *because* they were extreme, and then measure them again. The toy at the top shows it on made-up data: choose the bottom scorers on a first test and watch their average rise on the second, with no help given to anybody. ## Where the name came from In the 1880s, the Victorian scientist Francis Galton measured the heights of hundreds of parents and their grown-up children. He found that very tall parents tended to have tall children, but less extremely tall than themselves. Very short parents had short children, but less short. The children were pulled back towards the middle. Galton called this “regression towards mediocrity”. The name has stuck (minus the mediocrity), though it misleads in one way: it sounds like a force pulling people to the middle. It isn’t. Heights in the population don’t get less varied from generation to generation. It’s simply that the most extreme values in one measurement include some luck, and the luck doesn’t carry over. *(An interactive illustration belongs here. Try it on the page: https://cognosc.com/blog/regression-to-the-mean)* ## A flight instructor’s mistake Daniel Kahneman tells a story from teaching flight instructors in the Israeli Air Force about the psychology of effective training. He explained that rewarding good performance works better than punishing mistakes. One experienced instructor objected. When he praised a cadet for a superb manoeuvre, he said, the next attempt was usually worse. When he screamed at a cadet for a bad one, the next was usually better. So, he concluded, praise doesn’t work and shouting does. Kahneman realised the instructor was seeing regression to the mean. An exceptional landing is likely to be followed by a more ordinary one, whatever the instructor says, and so is a terrible one. Praise was being blamed for something it didn’t do, and shouting was getting credit for something it didn’t do either. *(An interactive illustration belongs here. Try it on the page: https://cognosc.com/blog/regression-to-the-mean)* It’s worth dwelling on why this is so dangerous. The instructor wasn’t careless. He was paying close attention, and what he saw was real: after praise, performance usually did drop. His mistake was in the explanation, and it’s an explanation the world offers us all the time. We act when things are extreme, and things that are extreme are likely to become less so, so whatever we did looks responsible. ## Where it fools us **Treatments.** People seek help when a problem is at its worst, like back pain, a cold or a dip in mood. Many of those problems ease on their own, so whatever they tried next looks like it worked. A large part of the apparent success of many remedies, conventional and alternative, is regression to the mean. This is one reason medical trials need a comparison group: in many trials the people given a placebo improve too, partly because they were enrolled at a bad moment. **Sport.** The “Sports Illustrated cover jinx” is the observation that athletes often have a worse spell after appearing on the magazine’s cover. They make the cover after an exceptional run, which usually includes some luck, and the next run tends to be more ordinary. American football has its own version: the “Madden curse”, said to strike the players chosen for the cover of a popular video game. **Policy.** Speed cameras are often installed at sites that had an unusually bad run of crashes. Next year, there are fewer crashes at those sites, partly because last year was unusually bad. Studies that adjusted for regression to the mean, such as one for the RAC Foundation, still found the cameras reduced serious crashes, but by less than the raw before-and-after figures suggested. **Business.** The worst-performing branch gets a new manager and improves; the best one slips back. Both changes may be mostly luck. Business books are prone to this: when the companies profiled in *In Search of Excellence* were followed up, a 1987 study found that most of them did worse than the stock market over the next few years. Excellence, partly, had been a good run, and a good run is exactly the thing you’d expect to fade once you’ve chosen companies for having one. **Schools and hospitals.** A school that comes bottom of a league table and gets special measures will often rise the next year. A hospital with a spike in deaths will often see the rate fall back. Both may be real improvements. Both may be regression. You can’t tell without a comparison. ## How to tell a real effect from regression 1. **Ask how the group was chosen.** If it was picked for being extreme, the best, the worst, the most ill, expect it to move back towards average on its own. 2. **Compare with a similar group that got nothing.** If the untutored worst scorers improve just as much as the tutored ones, the tutoring didn’t do much. This is exactly what a randomised trial does. 3. **Look at more than two measurements.** A real effect should persist over time. Regression is a one-off bounce after an unusual result. 4. **Measure the starting point twice.** If you pick people on one test and measure their “baseline” on a second, separate test before you do anything, much of the regression happens before your intervention starts, and you can see it. ## The mistake in the other direction Knowing about regression can make you over-correct. Not every improvement after a bad patch is luck; sometimes the tutoring really worked. And not every slip after a great season is regression; sometimes the athlete got injured. The point isn’t to explain away every change. It’s to stop automatically crediting your action with a change that would have happened anyway. A useful way to think about it: regression sets a baseline expectation. When you select something for being extreme, you should *expect* some of the extremeness to fade. Only the change beyond that expectation tells you anything about what you did. ## What to take from it Next time something improves after you acted, ask: was it at its worst when I acted? If the answer is yes, some of the improvement was coming anyway. And next time something gets worse after praise, a promotion or a magazine cover, consider that it may simply have been at its best. The tutoring question is in the free [statistics test](/test/statistics), and the [thinking traps test](/test/thinking) covers the related trap of assuming that what came first caused what came next. For the broader family of mistakes about cause, see [correlation versus causation](/blog/correlation-vs-causation). ## What to remember - Most results are part skill and part luck. When you pick out extremes, you pick out a lot of luck. - Measure the same people again and the luck mostly doesn’t repeat, so they drift back towards the average. - Whatever you did in between, praise, punishment or a new pill, will look like it worked or failed. - The only fix is a comparison group of similar extremes that got nothing. - The weaker the link between two measurements, the more they regress. ## Questions people ask ### What is regression to the mean in simple terms? If you pick something out because it was unusually high or low, it’s likely to be closer to average next time, because part of what made it extreme was luck that won’t repeat. A pupil’s worst test score is usually followed by a better one, with or without help. ### Does regression to the mean mean everyone becomes average? No. It only applies to the luck part of a result. Skill, talent and real differences persist, so a strong student stays strong. What fades is the extra boost or dent they had on one particular day, so they move partly towards average, not all the way. ### What is the Sports Illustrated cover jinx? The observation that athletes who appear on the cover of Sports Illustrated often have a worse spell afterwards. It’s regression to the mean: they made the cover because of an exceptional run, which usually includes some luck, and the next run tends to be more ordinary. ### How do you avoid being fooled by regression to the mean? Compare with a similar group that got no treatment. If the worst scorers who weren’t tutored improved just as much as those who were, the tutoring did little. Randomised trials do this automatically, which is one reason they’re trusted over before-and-after comparisons. ### Who discovered regression to the mean? Francis Galton, in the 1880s, studying the heights of parents and their grown-up children. Children of very tall parents tended to be tall, but less extremely so; children of very short parents tended to be short, but less so. He called it regression towards mediocrity. ## Sources and further reading - Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246–263. - Kahneman, D. (2011). Thinking, Fast and Slow. Farrar, Straus and Giroux. (Chapter 17, Regression to the Mean.) - Barnett, A. G., van der Pols, J. C. and Dobson, A. J. (2005). Regression to the mean: What it is and how to deal with it. International Journal of Epidemiology, 34(1), 215–220. - Allsop, R. (2013). Guidance on use of speed camera transparency data. RAC Foundation. - Clayman, M. (1987). In search of excellence: The investor’s viewpoint. Financial Analysts Journal, 43(3), 54–63. --- Canonical page: https://cognosc.com/blog/regression-to-the-mean From Cognosc (https://cognosc.com): free tests, articles and an AI tutor that has you reason things through.