From Daniel Kahneman “Thinking, fast and slow”
What is Regression to the Mean?
Outcomes are a combination of skill and luck. If someone performs unusually well, it was due to luck. So next time they perform, they will do a lot worse. If someone performs unusually bad, it was due to bad luck. So next time they perform, they will do much better.
“This is why the pattern is called regression to the mean. The more extreme the original score, the more regression we expect, because an extremely good score suggests a very lucky day.” (p. 178)
Often someone will make up a causal story to explain why something did much better or much worse. The story may sound reasonable, but that person is probably deluding himself. Sometimes the simple reason something did better or worse is Regression to the Mean. If that person believes in his own story, it’s a dangerous thing because he will act on his beliefs in the future expecting the same results.
“our mind is strongly biased toward causal explanations and does not deal well with “mere statistics.” (p.182)
Regression to the Mean is a tricky subject and fools even many well respected researchers.
Examples of Regression to the Mean.
- A flight instructor explains to Kahneman why rewarding flight cadets when they do really well is a bad idea. He also explains why scolding flight cadets after they do really bad is a good idea.
“On many occasions I have praised flight cadets for clean execution of some aerobatic maneuver. The next time they try the same maneuver they usually do worse. On the other hand, I have often screamed into a cadet’s earphone for bad execution, and in general he does better on his next try. “(p. 175)
Kahneman explains to the flight instructor when a cadet performed much better than average the first time and then performed much worse the second time, It had nothing to do with what the flight instructor told him. It was simply Regression to the Mean.
Kahneman said, “he praised only a cadet whose performance was far better than average. But the cadet was probably just lucky on that particular attempt and therefore likely to deteriorate regardless of whether or not he was praised. Similarly, the instructor would shout into a cadet’s earphones only when the cadet’s performance was unusually bad and therefore likely to improve regardless of what the instructor did. The instructor had attached a causal interpretation to the inevitable fluctuations of a random process.”
- Daniel Kahneman was watching the Olympic’s ski jumping competition on TV.
Each athlete gets two jumps. If an athlete had a really good first jump, the announcer would say, “Norway had a great first jump; he will be tense, hoping to protect his lead and will probably do worse”
If an athlete had a bad first jump, the announcer will say, “Sweden had a bad first jump and now he knows he has nothing to lose and will be relaxed, which should help him do better.”
“The story itself could even be true. Perhaps if we measured the athletes’ pulse before each jump we might find that they are indeed more relaxed after a bad first jump. And perhaps not. The point to remember is that the change from the first to the second jump does not need a causal explanation. It is a mathematically inevitable consequence of the fact that luck played a role in the outcome of the first jump. Not a very satisfactory story—we would all prefer a causal account—but that is all there is.” (p.179)
- There is a well know “Sports Illustrated jinx.” If an athlete was on the cover of Sports Illustrated (because he had an outstanding year), he will often do poorly the next season. People like to give causal explanations, like he had too much pressure or overconfidence. He simply did worse because of Regression to the Mean. He had one lucky year, so naturally he will go back to his baseline performance.
- A study of Fortune’s “Most Admired Companies” finds that over a twenty-year period, the firms with the worst ratings went on to earn much higher stock returns than the most admired firms.” (p.207)
You might make a casual explanation like the most admired companies got complacent, or the worst companies worked harder.
No, the simple reason companies improved or worsened many years later is Regression to the Mean. The companies that had the worst ratings had bad luck. Bad luck will go away and the companies will go back to their baseline performance. The companies with the best ratings were lucky. Luck runs out so these companies regressed back to their baseline performance.
Other Good Quotes About Regression to the Mean.
“The statistician Howard Wainer has drawn up a long list of eminent researchers who have made the same mistake—confusing mere correlation with causation. Regression effects are a common source of trouble in research, and experienced scientists develop a healthy fear of the trap of unwarranted causal inference.” (p. 183).
“Stories of how businesses rise and fall strike a chord with readers by offering what the human mind needs: a simple message of triumph and failure that identifies clear causes and ignores the determinative power of luck and the inevitability of regression. These stories induce and maintain an illusion of understanding, imparting lessons of little enduring value to readers who are all too eager to believe them.” (p. 207)
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