A sportsbook is a place where people can make wagers on sporting and other events at pre-set odds. It can also take in bets on individual players or teams. Some sportsbooks also offer layoffs, which allow bettors to bet with another bookmaker or a different sportsbook to reduce their liability.
A successful sports betting operation requires accurate estimation of the outcome variable’s quantiles. For both point spreads and totals, this involves estimating the median margin of victory (or expected profit on a unit bet) and then comparing it to the sportsbook’s proposed value.
The paper develops a theoretical treatment of this problem, which leverages the distribution of the associated random variable to derive propositions that convey key answers to important questions. The analytical framework is then complemented by empirical analysis of 5000 matches from the National Football League that instantiates the derived propositions and sheds light on how closely sportsbook prices deviate from theoretical optima (i.e., those that permit positive expected profit to the bettor).
The results demonstrate that point spreads overestimate the true median margin of victory by an average of 0.5 points. This is most pronounced for home favorites, whose edge exceeds the implied value of their point spread by an average of 0.65 points. The results also show that the required sportsbook error for a positive expected profit on a unit bet is less than one point, which implies that a small bias in the median is sufficient to permit a profitable wager.
