Reversion to the Mean
James Simons, President of Renaissance Technologies, offered in a roundtable forum:
“I heard this story and I think it’s true. Anyway, it’s a pretty good story. It’s about how the Air Force trains pilots. When a trainee made a good landing, he would be praised. When a trainee made a bad landing, he would be ridiculed. Well, it was perfectly clear to the general that the first approach was lousy and the second approach was good. He had statistics demonstrating that when you praised a pilot who made a perfect landing, his next landing was not likely to be as good. Whereas, if you berated a pilot who made a bad landing, his next landing was likely to be much better. However, if you think about it, it doesn’t matter what you do, because landings are most likely to be average. If a pilot had an exceptional landing, his next landing was likely to be average. If he had a poor landing, his next landing was likely to be average, also. By slicing the data and only looking at what follows good landings and praise, you only see part of the picture. You must consider how data was selected before you can draw conclusions. This example is closer to home. We interview a lot of managers, because we do some asset allocations. Although I haven’t compiled careful statistics on this, it frequently seems that a manager with a marvelous record does not perform as well after I invest with him. Why is that? Well, do managers who lost 35% in the last three years show you their records? No, those guys aren’t showing anyone their records. You are seeing a sample of the best managers, a sample of “good landings.” Going forward, some people do better and some people do worse, but reversion to the mean is probably a persistent phenomenon in both managing money and landing airplanes.”
