16 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 Bears’ rating is 10 and the Bengals’ rating is 6, we would predict the Bears to beat the Bengals by 10  6  4 points. Suppose the Bears play the Bengals and win by 20 points. For this observation, we “underpredicted” the Bears’ performance by 20  4  16 points. The best a for pro football is 0.10.

After the game, we 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.

a How does this approach relate to the equation At 

At1  a(et)?

b Suppose 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?

c How could we determine the best a for pro football?

d How might we determine ratings for each team at the beginning of the season?

e Suppose we tried to apply the above method 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 would have the smallest optimal a? Which sport would have the largest optimal a?

f Why would this approach probably yield poor forecasts for major league baseball?