Regression to the Mean

What Is the Regression to the Mean in Simple Terms?

Regression to the mean is the statistical tendency for unusually high or unusually low results to be followed by results that are closer to the average.

This happens because extreme outcomes are often partly due to random variation, not because anything special occurred.

Regression to the Mean in Real Life

1. A city intersection experienced an unusually high accident rate compared to previous years. In response, the mayor decided to install traffic cameras. The following year, the number of accidents decreased.
   
   This decrease could be due to the cameras, but it could also be partly explained by regression to the mean. If the original spike in accidents was unusually high because of random variation, accident rates would be expected to move closer to their long-term average even without the cameras.
   
   The mayor, however, attributes the entire reduction to the cameras.
2. A coach criticized athletes whose performance fell significantly below expectations while praising those who performed exceptionally well. In the next round, the criticized athletes performed better, while the praised athletes performed worse.
   
   Regression to the mean predicts that unusually poor performances are often followed by better ones, and unusually strong performances are often followed by weaker ones, simply because extreme results tend to move closer to average over time.
   
   The coach mistakenly concludes that criticism improves performance and praise makes performance worse.
3. A company had an unusually poor quarter, so the owner replaced the manager. Under the new manager, the company's performance improved and moved closer to its usual level. The owner concludes that the new manager is responsible for the improvement.
   
   However, the improvement may be partly or entirely explained by regression to the mean. After an unusually poor result, performance often moves closer to its long-term average even if nothing significant has changed.
   
   The same principle works in reverse, after an unusually successful quarter, the following quarter is likely to be less exceptional and closer to average.

Conclusion

Regression to the mean reminds us that extreme results are often followed by more typical ones.

Failing to consider this statistical phenomenon can lead us to incorrectly attribute changes to specific actions or events, especially when combined with the False Cause Fallacy