Regression To The Mean: Most Things Average Out

In statistics, regression to the mean is the tendency of any given variable to move towards the average value. This variable can be random and extreme. In most cases, the more you pick out results, the closer they will regress to the average. Its a useful concept to consider when trying to understand any scientific experiment, test, or data analysis, and keeps us from jumping to false conclusions about extreme events. They can be genuine extreme events or meaningless statistical noise.

Take the simple example of a class of students taking a test. Suppose they all choose randomly on all questions. Each item has a yes and no answer, giving them a 50 percent chance of getting it right. Some score substantially above 50 others significantly below 50 just by chance. So it does not matter whether you select the top scoring 10 percent or the bottom scoring 10 percent and give them a second test where they again choose randomly. The mean score would still be expected close to 50.

Let’s take it up a notch. Say it’s a non-random exam. They are a combination of skill and luck. In this case, some students might score high due to great skill and some luck, together with those who had little skill and extreme luck. If you retest them, the regression to the mean would be: the lucky but unskilled students would get a low score, since it is unlikely they will repeat their lucky break; the skilled but less lucky will get more consistent scoring and perhaps a higher score if luck is on their side. This happens since student scores are in part determined by ability and by chance. Same goes for business: if an organization has a highly profitable quarter due to sheer luck of publication but its real performance is unchanged, it will do less well the next quarter.

Regression to the mean is a significant consideration for anyone designing or trying to comprehend experiments. You can even use it for better snap judgments. The hottest place in the country today is more likely to be cooler tomorrow. The best performing mutual fund over the last five years is more likely to see a relative performance decline than improvement over the next five years. The most successful actor in Hollywood is likely to be paid less, not more, for their next movie. Regression to the mean is one of the explanations to why rebukes improve performance but praise backfires

Real-life examples of regression to the mean:

• Education: a student achieves a record high score on a difficult exam. This performance does not last. The next exam score will be closer to their average performance, as the high score was partly due to favorable conditions and/or luck. Educators and students have to understand that exceptional performance isn’t always sustainable.

• Sports: a basketball player makes an unusually high number of three-pointers in a game. In subsequent games, their shooting percentage will regress toward their career average. Coaches and analysts must use this understanding to temper their expectations and keep training stable.

• Finance and Investing: a stock experiences an unusually high return in one quarter due to a market anomaly. In the following quarters, the stock’s return moves closer to its long-term average. Investors have to be cautious about assuming that short-term wins will persist. This can keep them from overinvesting based on transient highs.

• Health and Medicine Research: a patient shows an unusually high response to a new treatment during an initial trial. Later tests show the treatment’s effect regresses to a typical level of improvement. Medical professionals use the regression model to interpret treatment effects accurately and avoid premature conclusions.

How you can use regression to the mean as a mental model: (1) avoid overreacting — when you see an exceptionally good or bad outcome, consider that its a random one-off and will probably return to the average; (2) expect reality — understand that extraordinary performance normalizes over time and use historical averages as benchmarks for predictions, not one-off leaps; (3) be extremely careful — before you attribute success or failure to something in particular, examine whether the intervention can be repeated or if its a one-time effect; (4) consequences of consequences — use both the short-term result and long-term trend as a gauge for decision-making; (5) dirty some graphing paper — check the statistics of a given variable to see whether extreme results are significant or just noise that is prone to regression.