# Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football

By Wayne Winston | Go to book overview

40
RATING SPORTS TEAMS

Most gamblers believe that when bookies set point spreads their goal is to have half the money bet on each team. If I bet \$10, for example, on a 7.5- point favorite to cover the spread, I win \$10 if the team covers but I lose \$11 if the favorite does not cover. If the favorite covers the points spread half the time, on average each \$10 bet results in an expected profit of (1/2)(\$10) + (1/2)(—\$11) = \$—.50. Thus a bettor loses on average \$0.50/ \$10.50 or \$1/21 per dollar bet. Assuming we bet the same amount on each game, to break even we would have to win a fraction p of our bets where p(10) + (1 — p)(—11) = 0. The value p = 11/21 = .524 solves this equation. Thus to win money on average we must beat the point spread at least 52.4% of the time.

Most bookmakers have power ratings on NFL and NBA teams.1 These ratings can be used to set point spreads for which the favorite has approximately a 50% chance of covering the spread. For example, if the Colts have a power rating of + 10 and the Browns have a power rating of —4, we would expect on a neutral field the Colts to win by 10 — (—4) = 14 points. Of course, teams play better at home. Home edges for various sports (based on the last ten years) are 3 points for the NFL, NBA and college football and 4 points for NCAA men's basketball. We will see later in the chapter how to estimate the home edge for a given set of games. Using the NFL home edge of 3 points the bookies would favor the Colts by 14 + 3 = 17 points at home and favor the Colts by 14 — 3 = 11 points at Cleveland. Predictions created from power ratings usually create (in the absence of injuries) a “fair line” in the sense that the favorite and underdog have an equal chance of covering the prediction.

1 In baseball you bet on a team to win. The probability of a baseball team winning depends
heavily on the starting pitchers. We will ignore baseball in our discussions because of this

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