How Does Expectation Value Impact Sports Betting?

If you have read the previous article on expectation value, you saw that the expectation value of betting on red (or black) in American Roulette is negative because there is a less than 50% chance of winning an even money bet.

But in sports betting the book sets the spread on the game.  If it is correctly set as the game's likely outcome then a bettor should have exactly a 50% chance of winning, yes?  Randomly throwing a dart at the board could select 50% winners.  How then does the book tip the odds in their favor?

It's called Juice or vigorish (vig for short).  Instead of creating a negative epectation value for their bettors by skewing the odds of winning in their favor, they skew the payout on the bet.  Standard vig on spread bets is known as "-110".  To win $100 on your spread bet, you need to bet $110.  How does this effect your expectation value?

• 50% chance of winning $100
• 50% chance of losing $110

 Mathematically

• (.50)($100) + (.50)(-$110) =
• $50 + (-$55) =
• -$5

For every $110 bet, you should expect to lose $5 if your ability to pick winning bets against the spread is no higher than random.  That's 5/110 = 4.55% advantage for the house over bettors who cannot pick better than 50% winners.

How then can you win long term against the spread?  You have to be able to pick > 50% winners.  As it turns out, 52.38% is the magic number for sports bettors betting against -110 juice.  You must pick > 52.38% winners in the long term in order to beat the bookie laying -110 juice on spread bets.

If you can get reduced juice on your bets, you can reduce the amount of winning picks required to beat the book accordingly.