A sportsbook is a place where people can place wagers on the outcome of sports events. In the past, these establishments were only found in Nevada and a few other states, but now they are available online and in many other places. The purpose of a sportsbook is to accept bets from customers and pay winners. To do this, it collects a commission on losing bets, which is known as the vig or juice. The amount of this commission varies from book to book, but it is usually around 10%.
To make money, a sportsbook sets odds that almost guarantee a return for every unit bet. These odds are a function of the expected margin of victory for each team, which is determined by a combination of the probability of winning and the amount of money a bettor can win on a bet. The profit a bettor makes when correctly placing a bet on the home team is given by phh and phv, where b is the bet size.
To determine how large of a sportsbook bias is needed to permit a positive expected profit, an empirical analysis of more than 5000 National Football League matches is conducted. The results indicate that the point spreads and totals proposed by sportsbooks capture 86% of the variability in the true median margin of victory. These estimates also provide a statistical framework for evaluating the performance of betting algorithms.