The method for rating teams in Example 7.8 is based on actual and predicted point spreads. This method can be biased if some teams run up the score in a few games. An alternative possibility is to base the ratings only on wins and losses. For each game, you observe whether the home team wins. Then from the proposed ratings, you predict whether the home team will win. (You predict the home team will win if the home team advantage plus the home team’s rating is greater than the visitor team’s rating.) You want the ratings such that the number of predictions that match the actual outcomes is maximized. Try modeling this. Do you run into difficulties? (Remember that Solver doesn’t like IF functions.)
EXAMPLE 7.8 RATING NFL TEAMS9
We obtained the results of the 256 regular-season NFL games from the 2009 season and entered the data into a spreadsheet, shown at the bottom of Figure 7.33 (see the file NFL Ratings.xlsx). (Some of these results are hidden in Figure 7.33 to conserve space.) The teams are indexed 1 to 32, as shown at the top of the sheet. For example, team 1 is Arizona, team 2 is Atlanta, and so on. The first game entered (row 6) is team 25 Pittsburgh versus team 31 Tennessee, played at Pittsburgh. Pittsburgh won the game by a score of 13 to 10, and the point spread (home team score minus visitor team score) is calculated in column J. A positive point spread in column J means that the home team won; a negative point spread indicates that the visiting team won. The goal is to determine a set of ratings for the 32 NFL teams that most accurately predicts the actual outcomes of the games played.
Objective To use NLP to find the ratings that best predict the actual point spreads observed.
WHERE DO THE NUMBERS COME FROM? Sports fans thank heaven for the Web. The results of NFL games, as well as NBA, MLB, and other sporting games, can be found on a number of Web sites. We got this data from http://www.pro-football-reference.com/years/2009/games.htm. To see much more about sports ratings, go to Jeff Sagarin’s page at http://www.usatoday.com/sports/sagarin.htm. Of course, if you are an avid sports fan, you probably already know the good Web sites.