## 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.

Labels: , ,

At Thursday, January 04, 2007 12:01:00 PM,  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
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,  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 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,  Phil Birnbaum said...

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

At Friday, January 19, 2007 5:34:00 PM,  Xeifrank 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,  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 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 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 Tuesday, July 21, 2015 12:31:00 PM,  Ben said...

Interesting read. I actually did a similar analysis of NBA games, and found the exact OPPOSITE to be true. That is, Home Underdogs have the worst winning percentage ATS (46.48%), and Away Favorites have the best winning percentage (51.82%). You can read more about it on my blog if you wish: http://spsbets.com/homeaway-x-favoriteunderdog/

At Friday, September 25, 2015 1:51:00 PM,  MSUDersh said...

Webmeister,

The author looked at 20,000 hypothetical wagers placed by 285 "bettors" at a rate of five games per week in the 2001-02 NFL season (85 total games). The bettors won points based on whether they beat or tied the spread, and lost points if they lost the spread bet. Barely one-third of the participants played every week

So this is a very flawed study - small sample size of one season, further limited by only using five games per week, and the betting isn't real betting like gamblers do but rather was part of a long term game. Not to mention that every "bet" placed was exactly the same value which isn't close to realistic. People bet dollars, they don't bet for points.

At Monday, September 05, 2016 2:50:00 AM,  Unknown said...

Hey look I'm sorry to burst the bubble here but most of the math here is off.

I noticed that one of the main correct things is that you have to win 52.356% of the time to break even. (Based on a "regular" payout of -110 or \$.91 for every dollar bet).

I don't know where you guys are getting your numbers from but its physically impossible for "Road Favs" to win 47.8% of the time and "Home Dogs" to win 57.7% of the time. Common sense tells you that these two percentages have to add up to 100%. Whoever posted this wasn't think or is just being silly. If you have a Road Fav you also have a Home Dog. That means if Road Favs are winning 50% of the time, Home Dogs are winning 50% of the time as well. This is also true for 45%AF-55%HD or vice versa. I hope that you all will pay attention to simple things like this in the future.

Also, I've broken down the numbers on the payouts and a 3-team straight parlay is far and away the best to bet on.

I haven't really stumbled upon something like what I've done but I'm a math major and have deemed the term "factor of payout." It basically just takes the odds to win such as on a coin toss (if vegas does their job correctly in theory it should be a 50/50 shot) (however betting on different specifics such as home dogs and what not would alter the percentages slightly but not significantly for what my point is illustrating)

1 game straight- FOP= .455
2 game parlay- FOP=.65
3 game parlay- FOP=.78
4 game parlay- FOP=.6
5 game parlay- FOP=.75

This may look like meaningless numbers however they tell a lot about what the bookie is offering for odds. This number is essentially the odds to win x the payout on a \$1 bet for each different number of games. It makes lots of sense when looking at the payout. First we need to know the basics of probability. The likelihood of choosing a game correctly (for our sake we're assuming its 50-50 however if you believe home dogs are higher than thats all the better) is 50%. The payout is \$.91. Stay with me....the payout for a 2 game parlay is \$2.6. The odds are then sliced in half. Basically 1/4 or 25% chance of selecting two spreads at random. The payout for a 3 game parlay is \$6 (this is the sweet spot) and the odds are then halved again to just 12.5% chance. All you need to do is pay attention to when the payout stops more than doubling (to make up for your odds splitting in half with every additional pick). You can see when the payout jumps from \$6 to \$10 going from a 3 game teaser to a 4 game teaser is where you start to decline somewhat. It then goes from \$10 to \$25 (which is a 2.5x increase for those of you who aren't so hot in math) and your odds halve again. Basically what it all boils down to is this:

3 Game Parlays are the best payout vs odds bet to make.
Followed by:
5 game parlay
2 game parlay
4 game parlay
and then a straight spread pick respectively.

I hope this helps any bettors out there I know it's proven me successful. Just make sure to take into account how many teams you're gut is telling you that you like on a given week. Don't force yourself to make 3 picks just because (however I would because it only helps and Vegas probably has the spread right where they want it anyway.)

Good luck!!!