# Praise, Punishment, & Regression to the Mean

Regression to the mean is seriously underrated. In sports, stock market funds, and biological trends like generational height differences, regression to the mean is a powerful, yet misunderstood phenomenon. A rookie athlete may have a standout first year, only to perform less spectacularly the following year. An index fund may outperform all others one year, only to see other funds catch up the next year. And a tall man may have a son who is shorter. In each instance, regression to the mean is at play, but since we underrate it, we assume there is some causal factor causing our athlete to play worse (it went to his head!), causing our fund to earn less (they didn’t rebalance the portfolio correctly!), and causing our son to be shorter (his father must have married a short woman).

In Thinking Fast and Slow Daniel Kahneman looks at the consequences that arise when we fail to understand regression to the mean and attempt to create causal connections between events when we shouldn’t. Kahneman describes an experiment he conducted with Air Force cadets, asking them to flip a coin backwards over their head and try to hit a spot on the floor. Those who had a good first shot typically did worse on their second shot. Those who did poor on their first shot, usually did better the next time. There wasn’t any skill involved, the outcome was mostly just luck and random chance, so if someone was close one time, you might expect their next shot to be a little further out, just by random chance. This is regression to the mean in an easy to understand example.

But what happens when we don’t recognize regression to the mean in a random and simplified experiment? Kahneman used the cadets to demonstrate how random performance deviations from the mean during flight maneuvers translates into praise or punishments for the cadets. Those who performed well were often praised, only to regress to  the mean on their next flight and perform worse. Those who performed poorly also regressed to the mean, but in an upward direction, improving on the next flight. Those whose initial performance was poor received punishment (perhaps just a verbal reprimand) between their initial poor effort and follow-up improvement (regression).  Kahneman describes the take-away from the experiment this way:

“The feedback to which life exposes us is perverse. Because we tend to be nice to other people when they please us and nasty when they do not, we are statistically punished for being nice and rewarded for being nasty.”

Praise a cadet who performed well, and they will then perform worse. Criticize a cadet who performed poorly, and they will do better. Our minds overfit patterns and start to see a causal link between praise and subsequent poor performance and castigation and subsequent improvement. All that is really happening is that we are misunderstanding regression to the mean, and creating a causal model where we should not.

If we better understood regression to the mean, we wouldn’t be so shocked when a standout rookie sports star appears to have a sophomore slump. We wouldn’t jump on the bandwagon when an index fund had an exceptional year, and we wouldn’t be surprised by phenotypical regression to the mean from one generation to the next. Our brains are phenomenal pattern recognizing machines, but sometimes they see the wrong pattern, and sometimes that gives us perverse incentives for how we behave and interact with each other. The solution is to step back from individual cases and try to look at an average over time. By gathering more data and looking for longer lasting trends we can better identify regression to the mean versus real trends in performance over time.

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