A sportsbook is a betting establishment that accepts bets on various events and then pays out winning bettors. It also takes a commission on losing bets, which is called the vigorish. Sportsbook owners set the odds and offer various promotions to attract bettors. The vigorish is the most significant source of profits for the sportsbook.
A major concern in sports betting is the adequacy of the sportsbook’s estimate of the median margin of victory for a match, which can be estimated using the average square root (th) of the variance of the bettor’s distribution over a sample of matches. Recent studies have reported that sportsbooks’ estimates deviate considerably from their theoretical optima, resulting in negative expected returns for bettors even when wagering consistently on the side with the higher probability of winning the bet.
However, many factors contribute to the variability of sportsbook estimates. For example, the asymmetrical nature of bets, which favor large bets on the underdog and limit the number of wagers placed on the favorite, may lead to inaccurate estimates. In addition, the public’s propensity for placing bets on home favorites is another important factor that may affect a sportsbook’s ability to capture the true margin of victory.
To assess the accuracy of sportsbook point spreads, we analyzed a series of match data from the National Football League, including a random subset of a total of 21 games matched against each other by both team and game-level variables. We computed the mean and standard deviation of th and found that, in a typical match, the asymmetrical nature of the bets results in a variation of
Using a linear regression, we found that the slope of the ordinary least squares (OLS) line of best fit (solid blue line in Figure 1) and intercept of the OLS line of best fit (dashed blue line in Figure 1) explained 86% of the variation in the true median margin of victory for each match, with both the slope and intercept exhibiting high confidence interval values within stratified samples. In other words, for most matches in a given season, the average point spread deviated from the true median margin of victory by one, two, or three points in either direction.
To better understand how sportsbooks generate their edge, we developed a theoretical framework that models the marginal cost of placing bets on any team. This framework enables us to derive a set of propositions that convey the key insights needed for the astute sports bettor to recognize mispriced lines. Specifically, the derived propositions show that the optimal bet is one that minimizes the sum of the expected costs of betting on the home and away teams. This is also known as the “home field advantage.” The results are corroborated by empirical analyses based on NFL match data. In short, our analysis sheds light on how to maximize the profitability of bets on NFL games.