Tuesday, January 02, 2007

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.


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9 Comments:

At Thursday, January 04, 2007 12:01:00 PM, Blogger Dackle said...

This appears to be the case in baseball as well, although a strategy of betting pure home dogs would still be unprofitable. For all baseball games from 1999 to 2004, the result of betting $100 on every home/road favourite/dog is --

gms Profit /game
Home fav 9916 -$35441 -$3.57
Home dog 4839 -4395 -0.91
Road fav 5317 -19299 -3.63
Road dog 9441 -9708 -1.03
TOTAL 29513 -68843 -2.33

Actually, while we're on the topic, on Tango's blog we talked about the record of a team following different 10-game sequences. Since the record in the past 10 has little to no predictive value, you might think a profitable strategy could be derived, since the general betting public likely overvalues a "hot" team. Well, not the case. Same dataset as above, but broken out into bets made based on the team's record in the past 10 games (ie betting $100 on every 9-1 team etc.).

Last 10 Gms Profit /game
10-0 66 $405 $6.14
9-1 473 -3077 -6.51
8-2 1535 -423 -0.28
7-3 3465 -8457 -2.44
6-4 5385 -871 -0.16
5-5 6215 -16771 -2.70
4-6 5167 -24448 -4.73
3-7 3362 -6152 -1.83
2-8 1542 -6695 -4.34
1-9 477 2538 5.32
0-10 47 -129 -2.74

(There are fewer total games in this table because the first possible bet occurs on the 11th game of each team's season.)

There could be something to betting teams on 10+game winning streaks, or teams 1-9 or worse, but those #s could be random chance and the betting opportunities would be few and far between.

 
At Thursday, January 04, 2007 2:12:00 PM, Blogger Phil Birnbaum said...

Wow! Great stuff, Dackle, thanks!

I guess we shouldn't be surprised to see that the market knows that streakiness is overrated ... but I'm impressed anyway.

 
At Tuesday, January 09, 2007 11:37:00 PM, Anonymous Jim A said...

FWIW, it has also been written that the home underdog effect in football is related to late-season weather.

See here and here

 
At Tuesday, January 09, 2007 11:39:00 PM, Blogger Phil Birnbaum said...

Awesome, thanks Jim! I'll look at those right away.

 
At Friday, January 19, 2007 5:34:00 PM, Blogger Webmeister said...

57.7% for home dogs and you have to win 55% of the time to break even. That's a 2.7% advantage over the house. That 2.7% is probably well within the standard error of the study, which would make it statistically irrelevant. I would like to know the sample size of this data and what the standard error is.
vr, Xei

 
At Friday, January 19, 2007 9:49:00 PM, Blogger Phil Birnbaum said...

Webmeister,

There were 2276 home underdogs, I think, so if 55% was the true probability, 57.7% would be 2.6 standard deviations away.

 
At Tuesday, February 06, 2007 2:23:00 PM, Anonymous Anonymous said...

Conventional wisdom is that HFA is worth 3 pts, but it's not that simple.

I looked at scores from 2005 recently. I noticed that the average winning score was about 24 pts regardless of being home or away. The average losing score was about 14 for visitors and 17 for home teams.

So when you lose at home you lose by less. That would explain why home underdogs are more likely to beat the spread.

 
At Thursday, April 12, 2007 5:44:00 AM, Anonymous Anonymous said...

Sorry webmeister but your maths needs some work. You need 52.4% to break even. If you hit 55% you enjoy roughly a 5% advantage over the book. 57.7% is roughly a 10% advantage.

 
At Monday, October 13, 2014 10:42:00 PM, Anonymous The Final Line said...

I know this is an older article, but I think the insights are still relevant - I do NFL handicapping and have noticed that home underdogs do seem to have lines that are a good value. Last week was an aberration - I think only 3/12 home teams won. I use teasers to increase the odds for teams, so I can sometimes get ridiculous odds for home teams. Thanks for the info!

 

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