When they hear about reversion to the mean, most people nod their heads knowingly, Michael Mauboussin says:
But if you observe people, you see case after case where they fail to account for reversion to the mean in their behavior.
Here’s an example. It turns out that investors earn dollar-weighted returns that are less than the average return of mutual funds. Over the last 20 years through 2011, for instance, the S&P 500 has returned about 8 percent annually, the average mutual fund about 6 to 7 percent (fees and other costs represent the difference), but the average investor has earned less than 5 percent. At first blush it seems hard to see how investors can do worse than the funds they invest in. The insight is that investors tend to buy after the market has gone up — ignoring reversion to the mean — and sell after the market has gone down — again, ignoring reversion to the mean. The practice of buying high and selling low is what drives the dollar-weighted returns to be less than the average returns. This pattern is so well documented that academics call it the “dumb money effect.”
I should add that any time results from period to period aren’t perfectly correlated, you will have reversion to the mean. Saying it differently, any time luck contributes to outcomes, you will have reversion to the mean. This is a statistical point that our minds grapple with.
Reversion to the mean creates some illusions that trip us up. One is the illusion of causality. The trick is you don’t need causality to explain reversion to the mean, it simply happens when results are not perfectly correlated. A famous example is the stature of fathers and sons. Tall fathers have tall sons, but the sons have heights that are closer to the average of all sons than their fathers do. Likewise, short fathers have short sons, but again the sons have stature closer to average than that of their fathers. Few people are surprised when they hear this.
But since reversion to the mean simply reflects results that are not perfectly correlated, the arrow of time doesn’t matter. So tall sons have tall fathers, but the height of the fathers is closer to the average height of all fathers. It is abundantly clear that sons can’t cause fathers, but the statement of reversion to the mean is still true.
I guess the main point is that there is nothing so special about reversion to the mean, but our minds are quick to create a story that reflects some causality.
Reversion to the mean also creates the illusion of feedback:
Let’s accept that your daughter’s results on her math test reflect skill plus luck. Now say she comes home with an excellent grade, reflecting good skill and very good luck. What would be your natural reaction? You’d probably give her praise — after all, her outcome was commendable. But what is likely to happen on the next test? Well, on average her luck will be neutral and she will have a lower score.
Now your mind is going to naturally associate your positive feedback with a negative result. Perhaps your comments encouraged her to slack off, you’ll say to yourself. But the most parsimonious explanation is simply that reversion to the mean did its job and your feedback didn’t do much.
The same happens with negative feedback. Should your daughter come home with a poor grade reflecting bad luck, you might chide her and punish her by limiting her time on the computer. Her next test will likely produce a better grade, irrespective of your sermon and punishment.
The main thing to remember is that reversion to the mean happens solely as the result of randomness, and that attaching causes to random outcomes does not make sense.