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