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Regression to the Mean

Regression to the mean is a technical term in probability and statistics. It means that, left to themselves, things tend to return to normal, whatever that is.

It applies to random performance: if you roll an ordinary die, and it comes up 5, the odds are that the next roll will be lower. It applies to things that indicate other things: if a man is seven feet tall, his son is likely to be tall, but not nearly seven feet tall. The first application is the most important, since it is the one we mostly get wrong.

Suppose we are teaching a complicated task to someone, and our student has learned the basics but is still uncertain. He sometimes does well, and sometimes badly, because he knows what to do but does not yet have it ingrained.

When he does it well, this is partly because he was lucky, and therefore he will probably do less well the next time. When he does it poorly, this is partly because he was unlucky, and he will probably do better the next time. This is going to happen no matter what else happens, including what we do as teacher.

Suppose, for example, that we praise the student when he does well, and scold him when he does poorly. We will see that when we praise the student, he performs worse, and conversely when we scold him he will do better. If we are observant, we will probably conclude that scolding does better than praise in motivating students. In fact, praise tends to be more motivating, but we wouldn't observe that unless we varied our teaching style and took careful notes.

Professional athletes and sportswriters sometimes refer to the "Sports Illustrated" jinx, in which bad things happen with a player right after he is featured on the cover of the magazine. Now, a player appears on the cover for spectacular performance, particularly unexpected spectacular performance. In the early 90s, an outfielder hitting almost as well as Barry Bonds would be more likely to be featured than Bonds, since SI wanted some variety in its covers. Now, a player who is performing unexpectedly well is probably being lucky, and his luck is not going to last long. When the SI cover is announced, the player's run of luck is probably over, and his performance lapses back to his norm. (The same thing is true of All-Stars, who are frequently selected for being hot in the first half.)

Regression is also valuable for indicators. If Joe has an I.Q. of 130, your best guess for his daughter's IQ, if you know nothing further, is 115, which is 130 averaged with 100. Oddly enough, the same thing is true in reverse: if Betsy's IQ is 130, your best guess (knowing nothing else) for her father's IQ is 115. The reason is that there are many more people with IQ of 115 than 130, and so IQ 130s tend to stand out in their families.