Mean Reversion

Neil Steinberg, my favorite columnist, writes a spot-on dismissal of the Oscar "curse", pointing out that for some, the oscar-worthy performance is the abberation, not the norm, but makes a common mistake on the subject of reversion to mean.

"So if you flip a coin and it come up heads five times in a row, while the odds are always 50-50 on your next flip, at some point you’ll likely have a run of tails, since the odds of heads will gravitate toward 50 percent."

Intuitively, and what I think he's implying, we expect that a run of heads now makes it more likely that a run of tails will later occur, as if there's some sort of mandatory balancing act and if we've just used up an allotment of heads there's a vein of tails waiting patiently for us to tap into, keeping our sums tidy as we tunnel into the future. That's not how it works.

If you get five heads in a row, you're no more likely to get a run of five tails than you were before [and that is actually fairly likely to begin with, but that's the subject of randomness]. You are, however, still looking at 50-50 odds. Mean reversion doesn't work by evening things out, it works because the odds don't change, and given a large enough sample, the mean will be as expected. In the example, suppose we start off flipping heads 5 times, then flip 10,000 times more. Suppose we get 5000 heads and 5000 tails, without a single "run" of tails. After 5 flips, we were at 100% heads. After 10,005 flips, we are at just over 50.02% heads. Continue like this for 10 million flips and we are at 50.00005%. Looks like mean reversion, without requiring any special "catching up" on the part of team tails.

In other words, the "reversion" is just averages acting like averages, rather than any cosmic compensation at work. Just like how it's possible for player A to have a better batting average than player B for the first half of the season AND for the second half of the season but have a worse batting average than player B over the whole season.