A key principle of skill training is that rewarding improvement works better than punishing mistakes. An experienced instructor doubted this, he stated that his students performed worse after receiving a compliment and did better after being shouted at. He was right and wrong. A praised performance is likely to be followed by a poor performance and punishment is normally followed by an improved performance. The conclusion he had drawn about the efficacy of punishment and reward was wrong. His observation is known as ‘regression to the mean’, which was due to random fluctuations in the performance quality. He praised only a student who performed much better than average, but that one performance was just a case of luck, which is why his next performance was of lower quality. The praise did not cause the poor performance. The mistake of the instructor was attaching a causal interpretation to random fluctuations.

Imagine two golf players competing in a tournament. One had a great performance on the first day, which makes you think he is more talented than the average competitor and that he had better luck than others. The other player performed poorly, so he must be less talented and unlucky. If you had to guess their scores on the second day, you would predict that the first player will score above average (he is still more talented) and the other player below average. Luck can change and is not predictable, so you expect it will be average. Conclusion: player 1 will perform well, but not as good as on the first day as he won’t be that lucky again and player 2 will perform below average but better than on the first day, as he won’t be that unlucky again. The difference between both players will shrink. The answer is that the performance on the second day will be more moderate: closer to the average than to the scores on the first day. This is another example of regression to the mean.

A famous example is the ‘Sports Illustrated jinx”. After gracing the cover of this magazine, a sportsperson is expected to perform worse in the next season. This is often explained by increased pressure or overconfidence. However, it is easier than that: a sportsperson that makes it on the cover has performed extremely well in the last season, most likely with the help of good luck and luck fluctuates. 

Conclusion: the difference between a first and a second performance does not need a causal explanation, it is a mathematically consequence of luck.

The notion of regression to the mean was introduced by Sir Galton, in the late 19^th century. He compared the height of children to the height of their parents and found that the size of the children was not similar to that of their parents but was more mediocre. Large parents: children were smaller, very small parents: children are larger. The study also demonstrated that the mean regression towards mediocrity was proportional to the parental deviation from it. Galton was surprised by the results, but regression effects are very common.

The ‘correlation coefficient’ between two measures is a measure of the relative weight of the shared factors and varies between 0 and 1. Regression and correlation are different perspectives on the same concept. An imperfect correlation between two scores means that there will be regression to the mean. The concept of regression is difficult, because our mind cannot handle mere statistics very well, it is biased towards causal explanations. Associative memory starts looking for a cause when an event caught our attention. This is problematic when regression to the mean is detected, because that does not have a cause. Both System 1 and System 2 struggle with regression. While System 1 searches for causal interpretations, System 2 finds the relation between regression and correlation hard to understand.

Imagine reading the headline “Depressed minors treated with ice cream improve significantly over a two-month-period”. While this is made up, it is true: if a group of depressed minors is treated with ice cream for months, they will show improvement. But depressed minors who spend 15 minutes a day walking backwards or petting a rabbit will also improve. Many readers will automatically draw the conclusion that ice cream or rabbit petting caused the improvement, which is unjustified. Depressed minors are an extreme group and extreme groups eventually regress to the mean. Depressed minors will improve over time, even without the ice cream and rabbits. Not only readers of newspapers are prone to wrong causal interpretations of regression effects, even researchers make this mistake. In order to prove whether a treatment is effective, a group of patients receiving the treatment must be compared to a control group (not receiving treatment or a placebo). The control group will improve by merely regression, will the treatment-group improve more than can be explained by regression?