FROM POINT RATINGS TO PROBABILITIES
In chapter 40 we learned how to calculate “power ratings,” which allow us to estimate how many points one team is better than another.1 In this chapter we will show how to use power ratings to determine the probability that a team wins a game, covers a point spread bet, or covers a teaser bet. For NBA basketball, we will see how to use power ratings to determine the probability of each team winning a playoff series. At the end of the chapter we'll look at how power ratings can be used to compute the probability of each team winning the NCAA basketball tournament.
Using power ratings we would predict that the average amount by which a home team will win a game is given by home edge + home team rating — away team rating. The home edge is three points for the NFL, college football, and the NBA. For college basketball the home edge is four points. Stern showed that the probability that the final margin of victory for a home NLF team can be well approximated by a normal random variable margin with mean = home edge + home team rating — away team rating and a standard deviation of 13.86.2 For NBA basketball, NCAA basketball and college football, respectively, Jeff Sagarin has found that the historical standard deviation of game results about a prediction from a rating system is given by 12, 10, and 16 points, respectively.
Let's now focus on NFL football. A normal random variable can assume fractional values but the final margin of victory in a game must be an inte-
1 Even if you do not run the proposed rating systems, you can always look up power rat-
ings at Jeff Sagarin's site on usatoday.com.
2 Hal Stern, “On the Probability of Winning a Football Game,” American Statistician 45,
no. 3 (August 1991): 179–83