Let’s say an NFL team starts the season 3-1. You have to bet on their overall record this season (16 games) without knowing any more information than this. Where do you put your money?
It’s easy to say 12-4. Extrapolating three wins and a loss over a 16-game season gives us 12 wins, four losses.
But if you said 12 wins, you’re making a big mistake that will cost you a lot of money in the long run. While plenty of teams start out 3-1, only a handful each year win 12 games or more.
If the team had been 4-0 to start the season, you probably wouldn’t have predicted them to go 16-0. But with anything less extreme than that, the temptation is to make the big mistake of extrapolating their record exactly into the future.
Now try this one
Every year, some baseball player starts out on a ridiculous tear for the first two weeks of the season, and we joke about how he’s on pace to hit 120 homeruns.
But if you had to make a futures bet on how many homeruns he would hit that year, what would be your best guess at the actual number?
Nobody in their right mind would say 120. Anything over 60 or 70 would be crazy. You’d probably expect him to have a very good season, but not a historical one. And you’d probably be right.
Reversion to the mean
The force at work here is known as reversion to the mean. It’s a property of independent random events which dictates that after the observation of an “extreme event,” the next event is more likely to be closer to the mean than farther away from it.
We want to make a guess at a football team’s true ability to win games, in terms of winning percentage. We’ll never know exactly what that number is; randomness in the outcomes of their games limits us to making only an educated guess at it.
To better understand reversion to the mean, let’s first look at a case where randomness is the only factor.
Coin flippers—an extreme example
Suppose we have 10,000 people flipping coins together. All flip at the same time. If someone flips heads, he advances to the next round. If someone flips tails, he’s eliminated from the game. What happens?
After the first round, about 5,000 people have flipped heads, so they’re still in the game. After the next round, only about 2,500 are left.
Fast forward ten rounds or so, and we’re left with just a couple lucky flippers who have gotten heads every single time.
If you want, you can call them expert coin flippers. But if we were to play again, would you expect those same guys to make it to end again?
Of course not. Their apparent ability to flip coins was an illusion, entirely due to luck. We’d give them the same chances as anyone else in the next game.
In other words, it’s far more likely that they’ll perform around the average next time than it is that they’ll do even better than their exceptional performance the first time. Because their performance was based on luck alone, they will revert to the mean.
Back to football
When a team starts out 3-1, we’re tempted to estimate their ability to win at 75%. But is it really that high?
We don’t know for sure. Part of what we’ve observed in their 3-1 record is due to skill, part is due to randomness. It’s impossible for us to say how big a role each factor played.
It’s possible that they’re only a 60%-winning team in the long run, but that luck has been on their side so far. By the same token, it’s possible they’re a great team, and that their only loss was due to a few bad bounces.
However (and this is a big however), we must suspect this team of being lucky. If you’ll admit that luck plays at least a small part in the outcome of a football game—and how can you not—then we have to view the teams that start off hot with some of the suspicion with which we viewed the lucky coin flippers.
In short: The fact that they’ve been successful makes it more likely that luck was on their side than that it was against them. Once you accept that, then the only logical conclusion about their future performance is that they’re more likely to perform worse than they are to perform better.
In a given NFL season, you might see six, seven, or eight teams start out 3-1. A few will finish the season at 12-4. A few (maybe) will finish even better than that, but most will finish worse. And that’s reversion to the mean at work.
(For the more mathematically inclined, here’s a more precise explanation of reversion to the mean. Warning: integrals!)
How you can use reversion to the mean
There was nothing specific to winning teams about the above discussion. Reversion to the mean also happens with bad teams. A team that starts off 1-3 or 0-4 has likely been on the receiving end of more bad luck than good, and we can expect them to improve in the future.
So if bad teams aren’t as bad as they look, and good teams aren’t as good as they look, the message is simple: take the underdog early in the season. Good handicappers won’t be fooled by the early appearance of good and bad teams, but most of the public might. And large numbers of people certainly have the ability to influence the line and give too many points to the underdog.
Similarly, when making futures bets on end-0f-season wins, homeruns, touchdowns, or whatever, remember that most things will end up less extreme than they start. The lines will already account for this to some extent, so they’re very temping bets if you don’t remember that teams and players will, in general, revert to the mean over time.
As shown by the example of the homerun hitter in baseball or the team that starts off undefeated, we tend to intuitively understand reversion to the mean in the most extreme cases. We don’t predict that anyone will hit 120 homeruns or that many teams will go undefeated, for example. For this reason, I suspect that there’s less value in betting on mean reversion in extreme cases, since everyone already has a good idea that it’s hard to continue such extreme performance.
I’ll leave you with a question.
Last post I wrote about the Gambler’s Fallacy, where we established why a roulette wheel that has landed on black several times is in no way “due” to hit red because of the streak of blacks. How does this reversion to the mean not contradict this?
Be the first to answer correctly and you win…the envy of the dozens (yes, DOZENS) of Thinking Bettor readers everywhere. Come on, what more could you ask for?