A sportsbook is a type of gambling establishment that accepts bets on various sporting events. Depending on the state, some are legal while others are not. These gambling establishments typically charge a commission, known as the vig, on losing bets to make a profit. In addition to sports bets, some offer other types of wagers such as prop bets and futures bets. These bets can be based on a variety of factors including player performance, matchups, and the number of goals scored during a game. While these bets do not guarantee a winner, they are popular with sports betting enthusiasts and can help them earn some extra cash while watching the games.
The paper provides a statistical framework by which the astute sports bettor may guide their decisions. Wagering is cast in probabilistic terms by modeling the relevant outcome (e.g., margin of victory) as a random variable. The distribution of this random variable is employed to derive a set of propositions that convey the answers to key questions regarding the optimality of sportsbook odds. Empirical results based on over 5000 matches from the National Football League instantiate the derived propositions and shed light onto how closely sportsbook odds deviate from their theoretical optima.
Despite the large number of potential outcomes, each bet at a sportsbook yields a positive expected profit, so long as the bettor correctly wagers on the team with the higher probability of winning. Moreover, each bet at a sportsbook results in a loss, on average, if the bettor places a bet on the team with the lower probability of winning. Thus, each bet at a sportsbook is effectively a bet against the house.
For the purposes of the analysis, a “sportsbook spread” sR is employed as a surrogate for the true median margin of victory, so that a bet of unit size on the home team results in a profit of b(1 + phh) if m > s and a loss of b(1 + phv) if m
A similar analysis is performed for point totals, using the probability of a team scoring a given number of points as a proxy for the median team’s score. For both analyses, the estimated probability distributions are evaluated with confidence intervals that include the null hypothesis values for the slope and intercept of the regression line. The results show that the sportsbooks accurately capture 86% of the variability in the median margin of victory and 79% of the variability in the median total, respectively. The required sportsbook error to permit positive expected profit is thus less than one point. This is a much smaller error than would be expected if the sportsbooks were randomly biased in their estimates of the median. The results also suggest that the odds of a team scoring more points than its opponents in a particular match are approximately equal to the odds of the sportsbook’s estimate. This suggests that the bettor is better off betting on the over/under than on either of the individual point spreads.