A version of simple exponential smoothing can beused to predict the outcome of sporting events. To illustrate,consider pro football. We first assume that all games areplayed on a neutral field. Before each day of play, we assumethat each team has a rating. For example, if the Bears’ ratingis 10 and the Bengals’ rating is 6, we would predict theBears to beat the Bengals by 10 6 4 points. Supposethe Bears play the Bengals and win by 20 points. For thisobservation, we “underpredicted” the Bears’ performanceby 20 4 16 points. The best a for pro football is 0.10.After the game, we therefore increase the Bears’ rating by16(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?
A version of simple exponential smoothing can beused to predict the outcome of sporting events. To illustrate,consider pro football. We first assume that all games areplayed on a neutral field. Before each day of play, we assumethat each team has a rating. For example, if the Bears’ ratingis 10 and the Bengals’ rating is 6, we would predict theBears to beat the Bengals by 10 6 4 points. Supposethe Bears play the Bengals and win by 20 points. For thisobservation, we “underpredicted” the Bears’ performanceby 20 4 16 points. The best a for pro football is 0.10.After the game, we therefore increase the Bears’ rating by16(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?
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