Textbook Problem

A version of simple exponential smoothing can be used to predict the outcome of sporting events. To illustrate, consider pro football. We first assume that all games are played on a neutral field. Before each day of play, we assume that each team has a rating. For example, if the rating for the Bears is 110 and the rating for the Bengals is 16, you would predict the Bears to beat the Bengals by 10 − 6 = 4 points. Suppose that the Bears play the Bengals and win by 20 points. For this game, you under predicted the Bears’ performance by 20 − 4 = 16 points. The best α for pro football is α = 0.10. After the game, you therefore increase the Bears’ rating by 16(0.1) = 1.6 and decrease the Bengals’ rating by 1.6 points. In a rematch, the Bears would be favored by (10 + 1.6) − (6 − 1.6) = 7.2 points.

1. a. It can be shown that the basic equation for simple exponential smoothing is equivalent to the equation L_t = L_t−1 + αE_t. How does the approach in this problem relate to this latter equation?
2. b. Suppose that the home field advantage in pro football is 3 points; that is, home teams tend to outscore visiting teams by an average of 3 points a game. How could the home field advantage be incorporated into this system?
3. c. How could you determine the best α for pro football?
4. d. How might you determine ratings for each team at the beginning of the season?
5. e. Suppose you try to apply the previous method to predict pro football (16-game schedule), college football (12-game schedule), college basketball (over 30-game schedule), and pro basketball (82-game schedule). Which sport would probably have the smallest optimal α? Which sport would probably have the largest optimal α?
6. f. Why would this approach probably yield poor forecasts for Major League Baseball?