A winning strategy: bet home underdogs

This Steve Levitt study is more about gambling markets than the sports themselves, but it comes to a surprising conclusion – that it's possible to make money betting on football using a very simple strategy.

Conventional wisdom is that a bookie will deliberately set the point spread for a football game so that an equal amount of money is bet on each of the two teams. That way, and since bettors have to bet $110 to win $100, the bookie is guaranteed a fixed profit regardless of who wins. If bettors put $110,000 on each side, the bookie takes in $220,000 but pays out only $210,000 to the winners. He therefore assures himself a profit of $10,000 (which is a little less than 5% of the total amount bet).

That's the theory; is it true in practice? It's hard to check, because bookies are reluctant to give out this information. But Levitt was able to find some public data from an online betting tournament. He found that, contrary to expectation, there are unequal amounts bet on the two sides of the spread. Instead of about 50/50, a typical distribution is 60% on one side and 40% on the other. That's significantly different from what you would expect by chance.

What does this mean? It means that the consensus is wrong -- bookies do *not* successfully choose the point spread to equalize betting on both sides.

Is it because they're not smart enough to predict what the spread should be? No, that can't be the case, because the deviations aren't random. Levitt found that the effect is skewed towards favorites. That is, in the typical 60/40 split, the "60" is usually bet on the favorite. And, in fact, when the favorite is the visiting team, more money is bet on the road favorite than the home underdog about 90% of the time!

Clearly, there's something else going on. Otherwise, bookies would just bump the spread down a couple of points to move more action to the home underdog, thus evening out the betting. The fact that they don't do that suggests that they have a reason for not wanting to.

That reason: home underdogs don't make the bookie as much money. They beat the spread much more often than 50% of the time. That is, bettors are so biased towards road favorites that they're willing to bet on them even when their odds are below 50/50. Bookies are therefore happy to see extra bets on them, because, even though they'll lose money if the favorite comes through, in the long run they'll still make more profit.

(As an extreme example, think of it this way: suppose a thousand dumb people are willing to bet you $110 to $100 that the Raiders will win the Super Bowl next year. And suppose another thousand rational people are willing to bet you $110 to $100 that the Raiders won't win. In that case, if you take all the bets, you're guaranteed a profit of $10,000. But wouldn't you be tempted to move the odds a little bit to encourage more people to bet on the Raiders, and fewer to bet against them? Sure, if the Raiders win, you'll lose money, but the chances of that happening are very low, and so your expected profit will be significantly more than $10,000.)

This hypothesis needs data to support it, of course – and Levitt comes up with that data. It does indeed turn out that both requirements for the hypothesis are met – (a) favorites cover the spread less than 50% of the time, and (b) more than 50% of customers bet on the favorite anyway. A summary of the findings:

Home favorites attract 56.1% of the bets, which are won 49.1% of the time;
Home underdogs attract 31.8% of the bets, which are won 57.7% of the time;
Road favorites attract 68.2% of the bets, which are won 47.8% of the time; and
Road underdogs attract 43.9% of the bets, which are won 50.4% of the time.

If you do the arithmetic, as Levitt did, you find that the above results show that bettors, being unduly biased towards favorites, win only 49.45% of their bets, instead of 50%. The missing 0.55% goes to the bookie. That increases his profit from 5% to 6.1%, which is a 23% increase. In exchange, the bookie takes the risk that, over a given time period, favorites will hit a lucky streak, and he'll make less money (or even post a loss). Levitt argues that the risk is small compared to the 23% increase in earnings.

And so Levitt's conclusions are:

-- bettors consistently overestimate favorites;
-- bettors like to bet on favorites anyway;
-- bookies recognize this, and are willing to allow more bets on favorites to increase their expected profits (despite the extra risk).

Moreover, Levitt looked at all NFL spreads from 1980-2001. He found that home underdogs beat the spread 53.3% of the time – higher than the 52.4% success rate a bettor needs to overcome the "110-to-win-100" vigorish and break even. And so, the simple strategy of betting the home underdog can turn a profit. Not only that, but the bookie actually knows it, but is willing to put up with it to make more money from the favorite bettors.

(Levitt finds that in both NCAA and NBA basketball, home underdogs also cover in about 53% of cases.)

Bookies could go even further – skew the line even more towards the favorite – to try to make even more money (again, at higher risk). But at some point, the advantage to the underdog bettors becomes so great that they wind up betting much more than they would otherwise, and the bookie loses his advantage. Levitt thinks that line occurs when betting *all* underdogs, not just home underdogs, becomes a winning strategy. At that point, the wisdom of the "you can make money betting on underdogs" rule would become so well-known that the bookies would no longer be able to depend on customer ignorance.

The study was published almost three years ago. Has the market adjusted to the new information? Maybe, but Levitt thinks that home underdogs are still profitable.