A sportsbook is a place where people can make wagers on various sports. A person can bet on a team to win or lose, how many points or goals a team will score and even on individual players’ statistical performance. These wagers can be made in a number of ways, from straight bets to spread bets. In the United States, until recently, the only legal sportsbooks were located in Nevada and operated in limited forms in Montana, Oregon and Delaware. However, after a Supreme Court decision, more than 20 states now have sportsbooks.
A central issue in the theory of optimal wagering is how accurately a sportsbook captures the median outcome in a given match. To explore this question, an empirical analysis of 5000 matches from the National Football League is conducted. The results show that, under the assumptions of the model used, point spreads and totals proposed by sportsbooks generally reflect the median outcome distribution. They also show that, for the vast majority of matches, a sportsbook error of only a single point from the median is sufficient to permit a positive expected profit.
In the case of point spreads, this is true even when the deviation from the median is large. To estimate this, the CDF of the margin of victory was measured empirically for each match, and the values of the observations were used to compute the expected value of a unit bet placed on the team with the higher probability of winning. This value was then compared to the sportsbook’s point spread and the expected value of a bet on a team with the lower probability of winning.