🏀Regression to the mean

When a measurement is partly skill and partly chance, an extreme result is likely to be followed by a less extreme one, with nobody doing anything. The extreme was selected for being extreme, and so it was selected for luck. The luck does not repeat.

Hale Winter opened the autumn module with it in 🎓 Lecture 11 - Regression to the mean and showed 📱 Regression to the mean with free throws: a player's best night, then his next. He asked what we would have concluded after the best night. I would have promoted him.

• It runs both ways: after the worst month, improvement is the default.
• It is a fact about selection, not a force pulling on anything.
• The less a result depends on skill, the stronger the drift.

Often confused with: the gambler's fallacy. Nothing is due. The next result is simply drawn from the ordinary distribution again.

Galton found it in the heights of parents and children in the 1880s, which is where the odd word regression comes from.

Where I have seen it

The carrier that looked terrible in one bad month. It gets called in, warned and put on a plan. Next month is better. The plan is declared a success. A carrier warned by nobody would probably have improved as well.

In the lecture room Adaeze Nwosu said the same of hospital wards: every ward with a terrible month gets an action plan and then recovers by itself.

It turned up on the final exam on 9 December, dressed as exactly that carrier.

What I concluded, and what I now refuse to do on one reading: 💎 Extreme results drift back toward the average on their own.