Concept/Probability and Statistics/No. 0830

Regression to the Mean

Regression to the mean is a statistical pattern in which extreme scores tend to be less extreme when measured again. Named by Francis Galton, it occurs when repeat measurements are imperfectly correlated and can make a rebound look like a treatment effect.

Also called Regression Toward the Mean · Regression Towards the Mean

a concept: name it

Evidence: Well established
Read: 6 min
Links: 12 connections
Useful when: Evaluating a claim · Judging people and hiring · Reading data and statistics · Complex systems and policy

01You've seen this when…

in life
After your worst night of sleep this month, you try a new pillow. The next night is better, and the pillow gets the credit.
at work
A support team has its slowest week all quarter. The manager introduces a new workflow on Monday, and the following week’s faster replies seem to prove it works.
out in the world
A city adds warning signs at intersections with last year’s highest crash counts. The next report shows fewer crashes, and officials credit the signs.

02The idea

A terrible week is often a mixture of an ongoing problem and unusually bad luck. If you pick that week as your starting point, the next one will often look better even if you change nothing. The same works in reverse: an exceptional performance is often followed by a less exceptional one.

This is regression to the mean. When repeated measurements only partly predict one another, cases selected for extreme first scores tend to have less extreme later scores, on average.

The selection matters. Choosing the worst week works the same way as choosing the best performer or patients with the highest readings. That choice collects cases whose first measurement probably contains an unusually large temporary contribution.

Skill and territory shape a sales total, for example, while the result also depends on which customers happen to sign that month. Skill may persist. The unusual timing probably won’t.

A result can move closer to average on its own because the temporary circumstances need not repeat. The prediction is about a group average, not a promise that every extreme case will move inward. Some will become even more extreme.

03Why it matters

We often intervene precisely when a result becomes extreme. A struggling employee gets coaching. A high medical reading prompts further testing or treatment. A dangerous-looking junction gets redesigned. That makes regression to the mean a frequent impostor for improvement caused by the intervention.

It can also make helpful actions look harmful. Someone’s performance may worsen after praise for their best result and improve after criticism for their worst. Without a comparison, you can conclude that praise hurts and criticism helps—even if neither caused the change.

A before-and-after chart shows the sequence of events. To establish whether something works, you also need a comparison with what would have happened without the intervention. A suitable control group helps supply that missing comparison.

This statistical pattern has consequences for people and interventions. Misreading a rebound can lead you to punish a capable employee or stick with an ineffective intervention by preserving a program or continuing to buy a remedy that does nothing.

04A worked example

Consider an invented sales-training trial. A company has 200 representatives and offers coaching to the 40 with the fewest deals last month. It randomly assigns 20 to start immediately and 20 to wait a month. In this example, both groups averaged eight deals in the selection month.

The following month, the coached group averages 12 deals. The waiting group averages 11.

What it looks like Coaching raises sales from eight deals to 12—a 50% improvement. A manager looking only at the coached group has an impressive result to present.

What’s actually going on The uncoached group rebounds too. Both groups were selected after unusually poor results, so some improvement without coaching was plausible. Better market conditions could also lift both groups. Subtracting the waiting group’s change from the coached group’s four-deal increase gives an estimated coaching benefit of one extra deal per representative. Even that estimate has uncertainty; these are small groups.

What would have helped The randomized waiting group makes the comparison possible. Reviewing several earlier months would also help distinguish persistent underperformance from one unusually bad month. Without those checks, the company could mistake the timing of its intervention for evidence of its effectiveness.

The comparison leaves open how much of the untreated rebound comes from regression to the mean. It shows why crediting the whole treated rebound to coaching would overstate the evidence.

05Where people trip up

They start the clock at the extreme. Comparing this month with the worst month in three years almost guarantees a flattering baseline. Check how the starting point was chosen, and inspect several earlier measurements.
They confuse sequence with cause. A change following treatment can have other causes. Crediting the treatment based on timing alone is a common route to the post hoc fallacy. Compare with similarly selected cases that didn’t receive the treatment, ideally through a randomized experiment.
They think a reversal is owed. Expecting bad luck to be repaid with good luck is the gambler’s fallacy. Regression allows an ordinary night after a terrible night of sleep; the repayment belief calls for an exceptionally good one.
They expect everyone to reach the overall average. For an unusually high reading from an elite runner, the relevant average can differ from the average for all adults. Use a relevant reference group, and allow for differences between people.
They treat every fluctuation as a verdict on ability. One excellent or awful result mixes lasting differences with temporary circumstances and measurement error. Look for consistency across repeated observations before changing someone’s role, pay, or reputation.

06When it isn’t regression to the mean

An extreme result can reflect a lasting change. A broken machine may stay slow until repaired. A salesperson who loses a major territory may keep selling less. An intervention may also cause improvement. Regression to the mean is a competing explanation to investigate as you assess whether an intervention helped.

It matters most when the initial result helped select the cases and contains substantial temporary variation. Averaging several measurements generally reduces that variation. Highly repeatable measurements leave less room for regression.

The law of large numbers describes a separate statistical pattern: averages settle down as observations accumulate. Regression to the mean concerns what to expect after selecting an extreme observation.

07Roots

Francis Galton approached the problem by studying families. He compared parents’ heights with the heights of their adult children. To summarize a pair of parents, he adjusted for differences between male and female stature and combined their heights into a mid-parent measure.

Tall parents generally had tall children, but the children were, on average, less exceptionally tall. Short parents generally had short children, but their children were less exceptionally short. Galton described this in his 1886 paper Regression towards mediocrity in hereditary stature. Here, mediocrity was a value-neutral term for the middle of the height distribution. His interest in heredity was tied to his broader advocacy of eugenics.

The puzzle was how differences in height persisted across generations even with this movement toward the middle. The answer required keeping two things separate: the average height expected for children of a given parental height, and the variation among those children. Individual children still spread out around that expected height.

The term regression survived as statistics developed methods for predicting one measurement from another. The pattern traveled far beyond heredity. Whenever people select unusually high or low results and then measure again, Galton’s observation becomes relevant—from school scores to clinical readings to a manager’s monthly dashboard.

08How solid is this?

A well-established statistical pattern in repeated measurements, with a mathematical basis and extensive practical documentation. Whether it explains a particular rebound depends on selection, measurement variability, and what else changed.

09Connections

Often confused with Gambler’s Fallacy, Law of Large Numbers, Law of Small Numbers Bias, Peter Principle
Countered byRandomized Experiment, Control Group
Helps counterPost Hoc Fallacy
Can follow from Measurement Error
See also Dunning-Kruger Effect, Correlation, Selection Bias, Shrinkage

+ 2 more in the list

10Origin and sources

Francis Galton described and named the pattern in his 1886 paper on the relationship between parents’ and adult children’s heights.

Suggest an edit· Updated 2026-10-02