Sports Betting – A Probabilistic Framework

A sportsbook is a gambling establishment that accepts wagers on various sporting events. These bets are placed on teams or individual players and the winnings are determined by the odds that are offered. It is important for bettors to shop around and get the best odds before placing a bet. This will help them maximize their chances of winning.

The legalization of sports betting in the United States is a relatively recent development. Until recently, the Professional and Amateur Sports Protection Act of 1992 only allowed Nevada to offer sports betting. But the Supreme Court struck down that law in May 2018, opening the door for sports betting in any state that chooses to legalize it.

Sportsbooks make money by charging bettors for the right to place a wager on an outcome. They set their odds using a combination of internal and external data sources, including computer algorithms, power rankings, and outside consultants. Then they market those odds to attract customers. They present them in a variety of ways, with the most common being American odds, which are based on $100 bets and differ depending on whether the team is expected to win or lose.

This article explores the expected profit of a unit bet on a sportsbook spread or total using a probabilistic framework, and it shows that in matches where the sportsbook underestimates the true median result (i.e., its proposition odds deviate below their theoretical optima), wagering will yield a negative expected profit. In contrast, when the sportsbook correctly estimates the true median result, betting will generate a positive expected profit.