Regression zum Mittelwert

Sometimes, people think that certain events are under personal control. For instance, they may assume that their favorite athlete will always perform at their best, and therefore, may be surprised when an amazing performance is followed by an average one.

Notably, this trend occurs for multiple variables with normal distributions. For example, when a physician takes the patient’s blood pressure, her diastolic value measures 95 mmHg. 

The doctor then enters and compares this number to that of all of his patients, and notes that—when graphed—these values demonstrate a normal, bell-shaped distribution.

Here, the woman’s result falls at the extreme end of the curve. Concerned, the doctor retests her blood pressure; surprisingly, he finds that the diastolic number decreased.

In other words, the previously observed “extreme” pressure regressed to the mean for all the patients. It’s rare for someone’s results to be far from the average repeatedly, even at the higher end.

This inclination is called regression toward the mean—the tendency for an extreme value, upon reassessment, to be followed by a less radical score, essentially moving nearer to the group mean.

Consequently, if a therapy only influences individuals with initially extreme results, it’s likely an ineffective strategy. However, if a treatment lowers a group’s average—like for blood pressure—this is strong evidence of its success.

Without awareness of this statistical phenomenon, the doctor might have distributed blood pressure medication when, in fact, his patient didn’t need treatment.

In the end, results based on outliers shouldn’t be taken too seriously.