A sportsbook is a place where bettors can place wagers on a variety of sporting events. These establishments accept bets and offer a number of different betting options, including moneylines, point spreads, and Over/Under totals. Parlays, which combine multiple bet types and outcomes in a single stake, are also available at some sites. While winning a parlay is harder than placing individual bets, the payoff can be considerable.

In this article, we use empirical analysis to estimate the magnitude of a sportsbook’s error that must be tolerated in order for wagering to yield a positive expected profit. This error is measured as the mean of the conditional cumulative distribution functions (CDFs) of the median margin of victory for the propositions proposed by a sportsbook, and it is evaluated at offsets of 1, 2, and 3 points from the true median in both directions.

The result of this study suggests that, in the vast majority of matches, a sportsbook’s proposed point spread and total capture approximately 86% and 79% of the variability in the median outcome, respectively. Furthermore, it is found that the upper bound on the expected value of a unit bet when wagering on the team with the higher estimated probability of winning against the point spread or total is lower bounded by 47.6%, while the minimum error rate is lower bounded by 52.4%. Furthermore, the results of this work suggest that, if a sportsbook’s estimation is not within these bounds, wagering will always yield a negative expected profit.