Regression to the Mean (in Statistics)
Why does last year's number-one fund become ordinary this year? Did the manager's skill suddenly vanish? Much of the answer lies in a statistical law discovered in a 'height study' over a century ago.
What Regression to the Mean Is
Regression to the mean is the statistical phenomenon in which, after a very extreme value is observed, the next observation moves closer to the average (becomes less extreme). It appears when the outcome contains random elements like 'luck.'
The core principle is this. If a performance was extremely good, it's likely that 'luck was also very good,' not just skill. But luck is unlikely to stay extremely good. Next time, luck becomes ordinary, so performance also comes down toward the average. Conversely, if it was extremely bad, the next tends to rise toward the average.
The important part is that this is not 'because the strength ran out' or 'because of punishment,' but a purely statistical phenomenon. It appears naturally anywhere the measurement contains luck.
Regression to the mean doesn't mean there's no skill. It's the statistical property that, when an outcome contains both skill and luck, the more extreme the result, the more likely luck's contribution was large.
Galton's Height Research
The person who first laid out this concept was Britain's Francis Galton. In 1886 he published a paper titled 'Regression towards Mediocrity in Hereditary Stature.'
Galton gathered height data from 1,078 families and compared parents' heights with their children's. The result: children of very tall parents tended to be shorter (toward the average) than their parents, and children of very short parents tended to be taller than their parents. Children's heights shrank to about two-thirds of how far the parents deviated from the average.
Children of tall parents were still taller than average, but not as extreme as their parents — this is exactly regression to the mean. The statistical term 'regression' itself came from this research.
Galton's 1886 paper (Journal of the Anthropological Institute) became the root of the name 'regression analysis' in today's statistics. He observed the tendency for extremes not to be inherited but to return toward the center.
Regression to the Mean in Investing: Skill or Luck?
Investment performance also mixes skill and luck together, so regression to the mean appears often.
A representative example is 'last year's number-one fund.' A fund that ranked first in returns one year surely had skill, but it's also likely that 'luck' was large — the market flow that year happened to suit its style especially well. The next year, as that luck becomes ordinary, performance tends to come down toward the average. So chasing in based on 'last year's top performance' often ends in disappointment.
This interlocks with recency bias, being overly drawn to recent performance. Chase a recently sparkling target too late and, thanks to regression to the mean, the risk of meeting ordinary or disappointing results in the next stretch grows.
Conversely, seeing an extremely bad performance and concluding 'this is ruined forever' can also be hasty. The part that was bad luck has room to return to the average.
The shorter the period, the larger the share of luck in extreme performance. So 'steadiness over several years' reveals skill better than 'being number one in a single year.'
Why You Should View It over a Long Horizon
The lesson of regression to the mean is clear: don't get overly excited or disheartened by a single extreme short-term result.
An extreme value over a short stretch may have been heavily driven by luck, and that luck soon becomes ordinary. So rather than chasing 'last year's number one,' it's far safer to look at the steady flow over a long period.
This is why The Return of Almost Everything tries to show not a single year's flash return but actual performance over a long period — and, at that, together with maximum drawdown and loss periods. Looking at the long picture of buying a good asset over a long, steady period makes it easier to judge in balance without being swayed by one year's extreme result. Extremes, after all, tend to return to the average.
This article does not predict the future of any particular target. Regression to the mean is merely a statistical warning to 'not plug an extreme short-term result straight into the future.'
Preguntas frecuentes
Q. If there's regression to the mean, does bad performance always improve?
You can't conclude that. Regression to the mean refers to 'the tendency for luck-mixed extreme values to return toward the average'; it's not a guarantee that a particular target will recover. If the bad performance had a real problem rather than luck, it may not recover. Regression is a statistical tendency, not a prediction.
Q. Why is it easy to be disappointed after buying last year's number-one fund?
Because an extreme result like being number one in a single year likely owed much not only to skill but to 'luck' — the market that year suiting that style especially well. The next year, as that luck becomes ordinary, performance tends to come down toward the average. So chasing in late based only on recent top performance often ends in disappointment.
Q. So how should I judge performance?
Rather than a single extreme result over a short period, it's better to look at the steady flow over several years. The longer the period, the more luck's influence averages out and the better skill shows. Looking at long-term performance that includes maximum drawdown and loss periods lets you judge in balance without being swayed by one year's extreme value.
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