A version of simple exponential smoothing can be used to predict the outcome of sporting events. To illustrate, consider pro football. Assume for simplicity that all games are played on a neutral field. Before each day of play, assume that each team has a rating. For example, if the rating for the Bears is +10 and the rating for the Bengals is +6, the Bears are predicted to beat the Bengals by 10 - 6 = 4 points. Suppose that the Bears play the Bengals and win by 20 points. For this game, the model under predicted the Bears’ performance by 20 - 4 = 16 points. Assuming that the best α for pro football is 0.10, the Bears’ rating will increase by 16(0.1) = 1.6 points and the Bengals’ rating will decrease by 1.6 points. In a rematch, the Bears will then be favored by (10 + 1.6) - (6 - 1.6) = 7.2 points.
a. How does this approach relate to the equation Lt = Lt - 1 + αEt?
b. Suppose that the home field advantage in pro football is three points; that is, home teams tend to outscore equally rated visiting teams by an average of three points a game. How could the home field advantage be incorporated into this system?
c. How might you determine the best α for pro football?
d. How could the ratings for each team at the beginning of the season be chosen?
e. Suppose this method is used to predict pro football (16-game schedule), college football (11-game schedule), college basketball (30-game schedule), and pro basketball (82-game schedule). Which sport do you think will have the smallest optimal α? Which will have the largest optimal α? Why?
f. Why might this approach yield poor forecasts for major league baseball?