Regression to the mean

Regression to the Mean (also known as regression toward the mean, reversion to the mean, or reversion to mediocrity) refers to the statistical phenomenon in which extreme values, whether unusually high or unusually low, are likely followed by values closer to the average on subsequent measurements. This occurs purely due to chance when there is any element of random variability in the system being measured.

Clarification: Regression to the mean does not imply that things “naturally return to normal” or that performance declines due to some inherent limitation. It is a predictable artifact of variability. When measurements include both a consistent signal (e.g., skill, fitness, strength) and a random component (e.g., fatigue, stress, luck), extreme values often reflect a combination of both. The next measurement is unlikely to repeat the same degree of extremity, simply because the random component is unlikely to be as extreme again in the same direction.

Applied Example: If an athlete records a personal best sprint time, significantly faster than usual, it’s likely that on their next attempt, they’ll run closer to their average. This doesn’t mean they’ve gotten slower; rather, it’s likely that their peak performance was aided by favorable random factors (e.g., wind, adrenaline, ideal timing). Similarly, an athlete who underperforms one day is likely to improve on their next attempt. This fluctuation is expected and does not require a causal explanation.

Why Averages Regress to the Mean: Regression to the mean is also the reason that averaging values smooths out extremes. The process of averaging ensures that random high values and random low values balance each other out, pulling the overall average closer to the center of the distribution. The more repeated measures you take (or the larger the sample size), the more the average reflects the underlying signal, and the less it is influenced by noise. In this way, regression to the mean is what guarantees that sample means “regress to the mean.”

Research and Assessment Implications:

Regression to the mean can create false impressions of improvement or decline in research, especially when:

• Participants are selected based on extreme scores (e.g., weakest, slowest, highest pain level).
• Pre- and post-testing is used without a control group.
• Small sample sizes increase variability.

For example, if you select only patients with the highest reported pain scores, their post-intervention scores are likely to decrease—even if the intervention had no effect—simply because their original scores were unusually high. Without a control group, this natural “return to average” could be mistaken for treatment efficacy.

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