Regression to the Mean Across a Season

Regression to the mean is a statement about noisy measurements. When a performance is far above a person's usual level, the performance probably mixed skill with a favorable sample. The next measurement tends to sit closer to the usual level, because the favorable sample is unlikely to repeat at the same size. This is not the claim that the sport owes someone a failure. The distinction is the whole lesson.

A free-throw illustration

A player who usually makes about 75 percent of free throws makes 8 of 10 in one game. That is 80 percent on a small count. The next game is more likely to land nearer 75 percent than to repeat 80 percent or to climb further, if the skill has not actually changed. The 8-of-10 contained some makes that a 75 percent shooter will not always get. The next ten throws are a new sample from a similar skill, not a bill that must be paid in misses.

If you say the player is due to miss, you have switched to the gambler's fallacy. Each throw can still be around 75 percent. Regression describes where a new sample tends to sit relative to an extreme one. It does not reach into the ball and schedule a miss.

Why extremes are fragile

Any process that is skill plus noise will produce a best week and a worst week. The best week is a biased sample of the process: you selected it because it was the best. Of course the following week, which you did not select that way, tends to look more ordinary. Why small samples mislead is the selection problem in plainer clothes. Regression is what that selection looks like across a season.

The same pattern runs downward. A dreadful week for a solid player is often followed by something less dreadful. Predicting a miracle recovery because of a mystical bounce is unnecessary. Predicting that a terrible small sample was partly noise is enough, and it leaves room for the possibility that the player is injured or has actually declined. Regression is a tendency, not a guarantee you can schedule.

What has to stay stable

The idea assumes the underlying skill is fairly stable and the measurement is noisy. If the skill changed, the mean you are regressing toward is the wrong mean. A player in a new role, a team that traded its best passer, a pitcher coming back from a layoff: the old average is a poor target. Check whether the process that produced the old number is the process in front of you.

Injuries are the clean way the assumption fails. A hot team average that included a healthy star does not regress toward that average after the star sits. It moves to the average of the team that remains. Look at the roster before you announce a statistical destiny.

Use it as a brake on stories

When a headline says a player has figured it out after two weeks, regression is the brake. Two weeks are a noisy measurement. The usual level is still the best first guess, updated a little, not replaced. When a headline says a star is finished after a bad fortnight, the same brake applies. Brakes are not picks. This article does not price games and does not suggest a wager. It suggests you demand a longer count before you rewrite a person.

Readers under the legal gambling age can use the brake for free. It is a reading skill. It does not require an account.

Frequently asked questions

Is regression to the mean the same as being due for the opposite result?

No. Being due claims the next trial must compensate. Regression says a new sample of a stable skill tends to be less extreme than a sample you selected for being extreme.

Does a hot start have to cool off?

Not on a schedule. If the hot start was a small, noisy sample, the next stretch is likely to be closer to the player's usual level. Injury or a real change in skill can override that.

Can I bet the cooling-off?

This article is not a wagering method. A tendency in noisy data is not a price, and it is not a recommendation.