by on February 7, 2006

in Sports

(This post has been updated now that I’ve heard from Levitt on the source of the numbers discussed below.)

In this past Sunday’s New York Times, Steve Levitt and Stephen Dubner make the claim that people systematically miss an opportunity to profit on the betting market.  If you always take the underdog at home in the NFL, you’ll make money:

As it happens, there is one betting strategy that will routinely beat a
bookie, and you don’t even have to be smart to use it. One of the most
undervalued N.F.L. bets is the home underdog — a team favored to lose
but playing in its home stadium. If you had bet \$5,000 on the home
underdog in every N.F.L. game over the past two decades, you would be
up about \$150,000 by now (a winning rate of roughly 53 percent).

That figure of \$150,000 seems like a pretty good deal.  Of course it requires betting \$5,000 per game to get up to \$150,000.  But is it true?  Is it true that a naive strategy of playing the home underdog wins 53% of the time and cumulates to winnings of \$150,000 over two decades?  Where did those number come from?

I emailed Steve Levitt.  He responded that the results are from his Economic Journal paper.

There he reports that between 1980 and 2001, home underdogs beat the spread 53.3% of the time.  There were 1483 games during that time when the home team was the underdog.  Playing the home underdog in those games leads to a profit over the 21 years of \$143,110 or roughly \$150,000 as the article in the Times suggested.

Can you count on those returns holding up?

Stephen and Philip Gray looked at NFL point spreads from 1976-1994 in their paper, "Testing Market Efficiency: Evidence from the NFL Sports Betting Market" in the Journal of Finance.  They found that a naive strategy of betting on the home underdog wins 52.51% of the time.

If the next 20 years are like the 1976-1994 period you will only make \$20,000 betting \$5,000 on every home underdog.

Do not try this at home.  Do not bet the home underdog for the next 20 years.  Not only do readers of the New York Times now know about this strategy,  but it ignores the opportunity cost of putting thousands of dollars every week on betting football games instead of investing it elsewhere.

The bottom line is that betting the home
underdog from here on out is not a "betting strategy that will
routinely beat a bookie."   Don’t bet on it.

Levitt and Dubner close their article with a worse suggestion:

A look at the past reveals this interesting anomaly: whereas only
one-tenth of regular-season N.F.L. games have a final point spread in
the double digits, fully one-third of the past Super Bowls (13 out of
the Super Bowl matches the best team from each conference, whereas
regular games often pit a good team against a poor one.

What does
this yawning gap mean? It suggests that faced with the risk of wiping
out a season’s profits, bookmakers play it safe on Super Bowl Sunday.
Unlike a typical N.F.L. game, the Super Bowl gives a bookie incentive
to balance his books and simply pocket the vig. To do so, he needs to
inflate the spread against the favorite even more than usual, bringing
in more underdog money and making the odds of the favorite’s covering
the bet even lower than usual.

A strategy of consistently betting
the underdog has not done so well in past Super Bowls, paying off only
17 times in 39 years (the favorite covered the spread 19 times, and
there were three pushes). But a small sample set should not get in the
way of a larger truth: the economics of bookmaking suggest that betting
the underdog today remains the single best bet of the year.

The claim (which is explored earlier in the article) is that bookies exploit biased bettors during the regular season.  Bettors systematically overvalue the favorite and undervalue the underdog.  Bookies know this and during the regular season tilt the point spread toward the underdog, essentially betting along with the underdog and punishing all that money that naively took the favorite.  Bookies take this risk because they realize that bettors are biased and underestimate the value of the underdog.

Could be.  I’m skeptical of the claim that bookies during the regular season systematically take on risk.  (Levitt makes this claim in his EJ paper.) Maybe it’s true but I’m skeptical.  But somehow, bookies get risk averse on Super Bowl Sunday and try to even out the money.  To do that, they’ve got to give the underdog more points to get enough biased bettors to take the underdog.

The implication is that the underdog bet on Super Bowl Sunday is an even better bet than the rest of the year.

But the Super Bowl is a neutral site.  Even the optimistic 53% number comes from home underdogs.  Neutral underdogs don’t overperform.  So betting on the underdog shouldn’t be a profitable strategy.

At Super Bowl XL, the underdog again failed to cover the spread.  The "single best bet of the year" has still only won 17 times and failed 20 times.  I don’t think the small sample has anything to do with it.

The lesson: beware the free lunch, even when it’s given away by an economist.

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chump February 7, 2006 at 4:21 pm
chump February 7, 2006 at 4:35 pm

actually, this is the same paper you cite in your blog-post. however, (I haven't read their paper nor do i know where they get their numbers) over the last five years, the home underdog could have won more that 53% of the time.

chump February 7, 2006 at 4:45 pm

disregard my last post…i understand what you are saying now (sorry i am slow)

Russ Roberts February 7, 2006 at 4:48 pm

Chump,

The data in the Levitt NFL paper is about an unusual betting tournament where bettors competed against each other. It only covers a single year of data. So it can't be the source for the 53% figure.

chump February 7, 2006 at 5:03 pm

russ,
i thought you did an excellent job in disputing their numbers; i am now curious, too, about what they will they say. i naively told the story to my family when we were watching the superbowl. i am appreciative of skeptics like you who don't accept things just because their published in a newspaper. you truly see the unseen …. keep us informed.

mobile February 7, 2006 at 5:08 pm

RTFP (Table II), Levitt says that home underdogs win 57.7% of the time, and that the home team was an underdog about 30% of the time.

Steve Sailer February 7, 2006 at 5:36 pm

Also, if you bet \$5,000 per game, even when the odds are slightly in your favor, there's a very high chance that, unless you are independently rich, you will suffer Gambler's Ruin somewhere along the way and be wiped out. You will lose all your money, have your house repossessed and your wife will leave you.

Sam February 7, 2006 at 6:14 pm

Do these net winning numbers take into account the vig? I believe you need to be a 52.5% winner to break even with games at -110.

Sam February 7, 2006 at 6:17 pm

I've only read their piece once, but I thought they made entirely separate arguments: 1) using home underdogs to say that NFL betting is not a perfect market and 2) use the idea of balanced books on a large game like the Superbowl to get favorable odds on the non-public-favorite team.

John Jenkins February 7, 2006 at 6:18 pm

I just ran these numbers in a spreadsheet and it looks to me like his claims are correct.

This is the quick table I generated from the data provided

1483 5000
53.3 790.439 3952195
46.7 692.561 3809085.5 (calculated as games lost *5500)

143109.5

So what's wrong exactly with his numbers?

Russ Roberts February 7, 2006 at 6:23 pm

I just updated the post to reflect the numbers Levitt sent me. They are from the Economic Journal article. While that paper focuses on one year, it also has some data for 1980-2001. The cumulative numbers do include the vigorish, the amount you pay the bookie when you lose, and as John Jenkins points out in his comment, the \$150,000 is right under that time period. But as I point out in the updated post, that was then. Over the earlier time period, the lower rate of winning pushes the gains to \$20,000.

Scotch Drinker February 7, 2006 at 6:29 pm

Two quick items:

1. A 53% win percentage is just barely break even so if they are saying that nets you a big profit, there's a problem right there though I expect that it's the 57.5% that mobile alludes to that they base the numbers on.

2. Losers do not pay the vig, winners do. This is a common misunderstanding amoung non-gamblers but it's fairly critical to understand. Think about it this way, if two people take opposite sides of a game and bet \$110 each, the winner wins \$110 and the loser loses \$110. However, with a bookie in the middle, the winner only wins \$100 and hence, pays the vig of \$10. This is why you have to have at least a 52.5% winning percentage to break even.

All hypothetically speaking, of course.

mark adams February 7, 2006 at 7:01 pm

As I understand it, bookies' spreads are influenced by the number of bets placed each way. I think the theory goes that the betters, collectively, have more knowledge than any formula the bookmaker might devise – hence it pays to listen to what the punters have to say.

Sam February 7, 2006 at 7:20 pm

Mark, Levitt talks about how books are comfortable on regular game days with an 80/20 book as long as they feel they are on the right side of the bet. His point is that books are less willing to do that for the Super Bowl because of the huge volume (and possibility of destroying a season's worth of profit).

mark adams February 7, 2006 at 10:20 pm

If I am reading this correctly, the spread is skewed so that the 80% get worse odds than the 20% – to the extent that the 20% might actually profit. Therefore, the bookmaker is, to some extent, always allowing the spread to be pulled by the majority of the punters. This effect is less pronounced on normal match days than on super-bowl, but still present.

I assume the bookmakers have some formula to calculate how much credence to give the views of bettors, based on the estimated level of neutrality and the risk involved in betting against the fans. Also, there must be a market at work in setting the odds that bookmakers offer so I would guess they watch each others spreads as well.

Barry P. February 8, 2006 at 12:32 am

Any chance of Leavitt (or Roberts) defining the return in terms of an annualized yield, so that we can compare it to other investment opportunities?

For \$5000 to grow to \$143,000 over 21 years you require an average annualized yield of 17.3%, but I imagine the calculation is a little bit more complicated, because if you don't win the first game, you need an extra \$5,000 to invest on the second game, and so on.

If there is a betting strategy that regularly yields 17% pa, I can't imagine it staying effective for too long once it comes to light.

Neal Phenes February 8, 2006 at 9:30 am

You have to assume a fairly wealthy bettor because if you should lose the first, or first few bets, where is the capital for more bets going to come from? If you borrow it, the there are interest payments to make until the debt is cleared. Then you must deduct lost opportunities while you wait for enough wins to pay down the debt and get onto the winning track. Also, the vig will increase the number of wins necessary to make a full payoff of the debt.

Neal Phenes February 8, 2006 at 9:31 am

You have to assume a fairly wealthy bettor because if you should lose the first, or first few bets, where is the capital for more bets going to come from? If you borrow it, the there are interest payments to make until the debt is cleared. Then you must deduct lost opportunities while you wait for enough wins to pay down the debt and get onto the winning track. Also, the vig will increase the number of wins necessary to make a full payoff of the debt.

Chrees February 8, 2006 at 2:29 pm

I would imagine you would be a lot more successful in such a strategy (betting the home underdog) if you avoid dreadful teams, like last year's San Francisco 49ers or Oakland Raiders. (Yeah, I'm from the area and suffered through their seasons)

By avoiding the home teams most likely to lose short of a deus ex machina (or two), would the odds go up significantly enough to justify such a strategy? A rhetorical question, I know, but still maybe worth looking into…

Stretch February 8, 2006 at 3:40 pm

"As I understand it, bookies' spreads are influenced by the number of bets placed each way. I think the theory goes that the betters, collectively, have more knowledge than any formula the bookmaker might devise – hence it pays to listen to what the punters have to say."

I don't think it has anything to do with using the punters knowledge, as much as it has to do with spreading out the money on both sides. Remember that the spread is not supposed to be an accurate prediction of the games outcome, it is only intended to get people to bet on both sides. I have a hard time accepting that 80/20, but it's certainly true that they don't always need (or want) to balance their books. I mean, they are bookies, they like to gamble a little too.

I thought this years SuperBowl was an interesting case, as nearly every pundit and man on the street was picking the Steelers, yet the spread remained resolutely between 3 and 4 points. Since the spread didn't grow, one can only assume that there were a ton of bets on Seattle. Either that or the bookmakers took a serious beating this year, which I doubt.

Jim February 8, 2006 at 3:43 pm

I am also skeptical of the claim that a bookmaker can systematically alter the line away from a 50/50 split such that the majority of money ends up on the losing side. It seems to me that such practices would create a market for professional gamblers (with big money) to take advantage of, something the books certainly do not want.

I was also disappointed that there was no mention of the fact that most bookmakers do not typically set their initial lines themselves (as the article implies), but rather get them from an independent service, most commonly Las Vegas Sports Consultants. I've linked to an interview with LVSC founder Roxy Roxborough published in the statistical journal Chance. Among other things, he corroborates that because the market is efficient, over time there is no real difference between the line and the likely outcome.

econgeek February 9, 2006 at 2:08 am

Rewarding a free lunch offered by an economist, what is yoru take on:
Save More Tomorrow: Using Behavioral Economics to Increase Employee Saving, RH Thaler, S Benartzi – Journal of Political Economy, 2004
http://www.journals.uchicago.edu/cgi-bin/resolve%3Fid%3Ddoi:10.1086/380085

Do you believe the free lunch argument they make?

AJ February 11, 2006 at 12:23 pm

Stretch, you indicated that you were going to link to an article from Chance re: LVSC. I didn't see the link. Would you mind reposting it – or anyone with that link, for that matter. Thx.

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