Does everyone move toward the mean?

No. The concept concerns expected patterns under particular measurement relationships.

Does it mean an intervention had no effect?

No. It means a simple change score may not identify the effect.

Is it the same as linear regression?

No. It is related historically and mathematically, but the fallacy is an error in interpretation.

AI Glossary / AI and machine learning / Intermediate

Regression fallacy

Definition

The regression fallacy is the mistake of attributing a change after an unusually high or low observation entirely to an intervention while overlooking regression to the mean. Extreme measurements often become less extreme on a later occasion because temporary influences or measurement noise do not repeat in the same way.

What it means

An observed result can combine a relatively stable component with short-lived circumstances and random variation. Selecting people, teams or machines because they had an extreme result also selects cases affected by unusually favorable or unfavorable temporary influences.
On a later measurement, those influences may be less extreme. The selected group can therefore move closer to its typical level even if nothing effective was done. The fallacy occurs when that expected movement is treated as evidence that a subsequent action caused the change.
Regression to the mean is a statistical pattern, not a force that guarantees every exceptional result will reverse, and not proof that interventions never work.

How it works

First, a group is selected using an extreme initial measurement. That measurement is imperfectly predictive of a later one because circumstances, noise or other influences change. Conditional on the extreme initial value, the expected later value is often closer to the relevant population average.
If an intervention occurs between measurements, a simple before-and-after comparison mixes its possible effect with regression to the mean and other changes. A well-designed comparison group, repeated baseline measurements and an appropriate analysis can help distinguish explanations. The exact pattern depends on the measurement relationship; an assumption of automatic return to a universal average is itself an oversimplification.

Three practical examples

A manager credits a coaching session for improvement among employees selected after one unusually poor week.
A maintenance team attributes fewer breakdowns to a new procedure introduced only after an exceptionally bad month.
An analyst assumes that top-ranked model configurations became worse solely because a software change occurred, overlooking selection based on noisy initial scores.

Think of it this way

Think of choosing the wettest day of a month and then judging an umbrella campaign by whether the next day is drier. The selected day was unusual, so a less extreme following day is unsurprising. The analogy highlights selection, but real evaluation still needs a model of weather or performance rather than assuming every sequence behaves identically.

Worked example

Suppose an organization's standardized performance scores have mean 0 and standard deviation 1 on each of two occasions. In a simple bivariate normal model, assume the correlation between occasions is 0.6. A team selected because its first score is −2 has expected second score 0.6×(−2)=−1.2 without any intervention.
That is an expected improvement of 0.8 standard deviations relative to its initial score, even though the underlying model contains no treatment effect. If coaching occurs between observations and the second score is −1.2, crediting all of the improvement to coaching would be unjustified.
These numbers describe a hypothetical statistical model, not a universal correction formula. A real evaluation must examine the relevant population, selection process, measurement scales and comparison design. Individual teams can improve more, improve less or worsen.

Illustrative case study

Fictional case: Lakeside Service introduces extra supervision for the five teams with the lowest monthly satisfaction scores. All five improve the next month, and the initial report calls the program a success.
A reviewer notices that selection used one noisy month and that similarly low-scoring teams from earlier periods also tended to rebound. The organization plans a stronger evaluation with multiple baseline measurements and a suitable comparison strategy. It keeps the supervision program under review rather than declaring it useless. The case illustrates why improvement alone is not enough to estimate an intervention's effect; it does not assert that supervision helped or harmed the teams.

Common misconceptions and mistakes

Do not confuse regression to the mean with a deterministic reversal or the gambler's fallacy. Independent coin tosses do not become more likely to compensate for an earlier streak.
Regression to the mean does not prove that every observed improvement is an illusion. Real effects can coexist with it. The relevant mean may differ across populations, and changes in measurement or environment need separate attention. A comparison group must be chosen carefully; mismatched selection rules or baseline patterns can leave important biases unresolved.

Business use

The concept matters whenever organizations intervene after extreme performance: poor sales, high error rates, unusually strong campaigns or low test scores. Without recognizing the selection effect, teams may reward ineffective programs or blame useful ones.
Before acting on a before-and-after result, document why units were selected and how variable the original measurement is. Use repeated observations and, when feasible, randomized comparisons designed around the actual decision. Predefine outcomes and follow-up periods. Explain the range of plausible causes for a change rather than presenting a single convenient narrative. This improves evaluation without requiring managers to assume every rebound is meaningless.

Check your understanding

A school gives extra support only to pupils with exceptionally low scores on one test, and their next scores rise. Does the rise alone prove the support worked?

Answer: No. Regression to the mean, other changes and a genuine support effect are possible. A suitable evaluation design is needed to distinguish them.

Related terms

Regression to the mean
Selection bias
Measurement error
Causal inference
randomised experiment
comparison group
before-and-after study
gambler's fallacy

Learn next

Learn regression to the mean with repeated noisy measurements, then compare a selected group's change with an appropriately designed control condition. Focus on how selection occurred. This is often more informative than trying to explain an extreme result after the fact.

Regression to the mean

Sources

David A. Kenny, author overview of Campbell and Kenny, A Primer on Regression Artifacts, consulted for extreme-score selection, repeated-measure artifacts and evaluation design: https://davidakenny.net/Primer/primer.htm. Related primary research: https://pmc.ncbi.nlm.nih.gov/articles/PMC5486877/; browser verification blocked access to that full paper. The bivariate-normal conditional expectation and original numerical example were independently checked. The author overview supports the explanation without claiming full-book review.

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