It's fun to go to the track and bet on a hundred-to-one longshot: You can put down two bucks and dream of walking away with $200. But as it turns out, the odds on longshots aren't long enough.
Even with those high odds, people who bet on longshots over an extended period lose way more money than those who pick randomly or bet the favorite every time.
Economists have known for a long time that the payoff on longshots is too low, but they haven't known why. A couple economists who crunched data from millions of horse races think they've figured it out.
In a working paper, Erik Snowberg and Justin Wolfers start with two common hypotheses.
One is "risk love." According to this idea, gamblers know that longshots aren't long enough, but they bet on them anyway. It's more exciting to take a flier on a hundred-to-one horse than to put a few bucks on some three-to-five favorite with a small payoff.
Another possibility is "risk misperception." Bettors just don't know that, despite the long odds, longshots are a bad deal.
Using data from millions of horse races held in America between 1992 and 2001, Snowberg and Wolfers test models of both hypotheses. Their conclusion: People just don't know that longshots are a really bad deal.
There's lots of math, and lots of tests, in how they come to this conclusion. Wolfers and Snowberg talked me through an example using the exacta — a bet that requires a bettor to pick the horses that finish first and second in a race.
If risk-love were the main driver, any exacta that had a one in 100 probability should have roughly the same payoff. But that's not the case, they found.
Instead, a one-in-100 exacta made up of two one-in-10 horses tends to have a better payoff than a one-in-100 exacta made up of a one-in-two horse and a one-in-50 horse.
That example — and lots of others like it — suggest that bettors are overestimating the chances of the one-in-50 horse and other longshots.
Overall, the rate of return on longshots with odds of 100-to-one or more is -61%. For favorites, the rate of return is -5% for favorites, the authors found.
Wolfers said the economic literature has shown pretty clearly that people overestimate the probability of very rare events. "We're dreadful at perceiving the difference between a tiny probability and a small probability," he said.
There was a baby crying in the background when we talked. When I asked Wolfers about whether he's observed risk misperception in his own behavior, he told me he's a new father, and newly worried about all the one-in-a-million things every parent worries about.