## Wednesday, February 09, 2011

### Packers win, casinos barely profit

It turns out that Las Vegas casinos didn't make a whole lot of money on this year's Super Bowl. According to the State of Nevada Gaming Board (.pdf), the sports books' profit was a mere 0.83 percent of the \$87,491,098 wagered on the game. That's a total profit of only \$724,176.

For the last ten years, the average profit was about 8 percent, or about 10 times higher.

If you make the assumption that all bettors need to wager \$6 to win \$5, then, on average, the casino keeps \$1 of every \$12 bet, which is 8.3%. That's not too far off from the actual amounts for the last decade, so let's assume that's the case, and see where it leads us.

Making that assumption and doing a bit of algebra, I get that the relationship between the amount of profit and the percentage bet on the winning team is

Percent Winners = (6 - 11 * profit percentage) / 6

Plugging 0.83% into the equation gives that 54.09% of bettors won their bets on Sunday.

Here are the numbers for all 10 years:

2011: 54.90% winners, 0.83% profit
2010: 50.01% winners, 8.30% profit
2009: 50.07% winners, 8.20% profit
2008: 56.07% winners, 2.90% loss
2007: 46.96% winners, 13.9% profit
2006: 49.47% winners, 9.30% profit
2005: 45.27% winners, 17.0% profit
2004: 46.20% winners, 15.3% profit
2003: 50.56% winners, 7.30% profit
2002: 52.74% winners, 3.30% profit

The highest proportion of winners was 56.07 percent, in 2008 (when the Giants beat the undefeated Patriots). That's pretty high. Put into baseball team terms (which I think all percentages should do), it's almost 91-71.

However, we need to take those percentages with a grain of salt, for a couple of reasons.

First, we assumed all bettors are betting \$6 to win \$5. That's not necessarily true. Big bettors probably get better odds than that. And some proposition bets probably pay worse odds than \$5 to \$6. Without knowing the expected percentage the house takes, the percentages of winners in the table are only rough estimates.

If you change your assumption to assume that bettors get a better deal than 5:6, the percentage of winners will move closer to 50% in every case.

UPDATE: here are the numbers assuming 10:11 odds:

2011: 51.94% winners, 0.83% profit
2010: 48.03% winners, 8.30% profit
2009: 48.09% winners, 8.20% profit
2008: 53.84% winners, 2.90% loss
2007: 45.10% winners, 13.9% profit
2006: 47.51% winners, 9.30% profit
2005: 43.48% winners, 17.0% profit
2004: 44.37% winners, 15.3% profit
2003: 48.56% winners, 7.30% profit
2002: 50.66% winners, 3.30% profit

Second: the usual assumption is that the casinos want to eliminate risk by having the same amount of money on both sides of the bet. That way, the bookies are certain to win a fixed amount: no matter what happens, they pay the winners with \$5 of the losers' money, and keep the remaining \$1.

So, one naive assumption is that the sports books weren't that great in predicting how bettors would behave. They obviously had the spread too low if 55% of bettors successfully picked the Packers -- and they nearly lost money because of it.

That might be true: the original line favored the Packers by 2.5 points. In response to the Packers attracting too much action, the bookmakers could have moved the spread to -3. But, because so many games are won by a field goal, 3 points might have been too big a gap from 2.5, and the pendulum might have swung too far towards the Steelers.

However, it's also possible that the bookmakers have an excellent idea of the "true" odds, and are willing to take a certain amount of additional risk if it's in their favor. For instance, suppose the casinos realized that the chance the Packers would beat the spread was only 45 percent. In that case, they might have been happy to take a bit more action on the Patriots. They assumed a bit more risk for that game, and it cost them -- but, over time, they make more money on average by going with the odds.

So, we can't really draw any detailed conclusions, because of our assumptions. However, we CAN say that:

1. If all bets were taken at 5:6 odds, then almost 55% of "pick 'em" bets on the Super Bowl were winners last Sunday.

2. Regardless, there was much more winning than usual on Sunday, enough to almost wipe out the oddsmakers' profits.

I know there are lots of gambling experts out there who might have enough information to explain what really did happen on Sunday (and correct any bad assumptions I may have made). Anyone?

Hat Tip: The Sports Economist

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At Wednesday, February 09, 2011 6:55:00 PM,  Anonymous said...

For the Super Bowl, I think most bets are 11:10 thanks to the magic of volume.

At Wednesday, February 09, 2011 7:10:00 PM,  Phil Birnbaum said...

Thanks. 11:10 means a house percentage of 4.5%. That means that bettors in the last ten Super Bowls were unluckier than expected, unless worse odds on some of those weird proposition bets made up for it.

At Wednesday, February 09, 2011 9:06:00 PM,  Alex said...

I don't know what it was in Vegas, but at Bodog a bet on the Packers to cover was +105 (at least at one point). They were also -140 to win outright. And then there's the over/under, and all the prop bets. All of those would have had different amounts of money on any given side and different proportions of money from professional gamblers versus the general public. So it's hard to say where exactly things went wrong for casinos this year or what the 'overall odds' would mean exactly.

One of the ESPN Insider blogs (http://insider.espn.go.com/insider/blog?name=millman_chad&id=6098886) said that this year was kind of a perfect storm against the casinos. The Packers won and covered; they hit the over; there was a two-point conversion, touchdowns by popular guys, etc. But you note the casinos still came out ahead.

At Wednesday, February 09, 2011 9:59:00 PM,  Phil Birnbaum said...

Alex: That makes sense about the 2-point conversion and the touchdowns by popular guys ... any long shots that came through at long odds would have that effect.

Not sure why the over, though. Do more bettors choose over than under?

At Thursday, February 10, 2011 2:00:00 AM,  Vic Ferrari said...

Your best post yet, Phil. Do you have the natural holds for those lines? That would really drive the point home with a hammer.

The margins from baseball game lines shame even that. Especially a certain type of game line. You've established that bookies are trying to make money, not do God's work.

Who is making the casual baseball bettor so terrible? And how?

That's the million dollar question.

At Thursday, February 10, 2011 3:39:00 AM,  j holz said...

All sides on NFL games are 11:10, although sometimes they will adjust the odds so one team is 6:5 and the other is 1:1.

Chad Millman is an idiot. You will learn nothing useful from reading him.

Remember that not every sportsbook has the same odds and the people who are betting the heaviest are shopping around for the best odds. For example, different casinos offered the Packers at 14:10 to win outright and the Steelers at 10:14; the savvy bettor is giving Vegas an effective hold of 0% on either bet.

One problem is that the game landed close to the spread and the total, so teaser bets (where the bettor can move the spread 6-7 points by paying more vigorish) all won.

At Thursday, February 10, 2011 10:49:00 AM,  Alex said...

I'm not sure how typical it is, but one of the casino guys that Chad talked to in that article said that people like to bet 'for' things instead of 'against' things. So maybe they like to bet for lots of points and offense, and take the over? The odds on the over/under are -110 a lot of the time as far as I know, so the money must stay relatively even though. Maybe it's a Super Bowl thing.

At Thursday, February 10, 2011 6:40:00 PM,  Vic Ferrari said...

This comment has been removed by the author.

At Saturday, February 26, 2011 9:32:00 AM,  King Yao said...

Bettors in general like betting on events where they can root for something to happen rather than root for "nothing" to happen. This leads them to generally take more Overs than Unders and more Favorites than Underdogs (when Favorites cover, they are doing something...when Underdogs cover, they are often preventing the Favorites from doing something).

So in that sense, seeing the Packers (a small favorite) and the Over on the total both win were bad for the sportsbooks.

In addition, there are a lot of prop bets on the Super Bowl, stuff like "will Hines Ward score a TD?" and "Will there be a successful 2-point conversion?". A lot of different things happened in the game with many different prominent players scoring, a 2-point conversion was successful. This was not good news for the sharp bettors nor the sportsbooks. Additionally, from the prop lines on QBs, WRs and RBs, the public clearly favored a passing game, which is exactly what happened. They don't break down how much they won on props versus the game line or totals, and in the end that may not matter since one can be somewhat of a substitute for the other (they are related after all).

With all this said, it doesn't necessarily mean it should have been a bad game for sportsbooks in general or any particular sportsbook. I don't know how unbalanced they were, but it wouldn't have been difficult for them to balance their action (by moving the line only slightly towards GB) if they wanted to.