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. 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? 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? c. How could you determine the best α for pro football? d. How might you determine ratings for each team at the beginning of the season? 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 ? f. Why would this approach probably yield poor forecasts for Major League Baseball?

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Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659
BuyFind

Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659

Solutions

Chapter
Section
Chapter 13.7, Problem 30P
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 Lt = Lt−1 + αEt. 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?

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Chapter 13 Solutions

Practical Management Science
Ch. 13.4 - Suppose you are an analyst for a company that...Ch. 13.4 - A trucking company wants to predict the yearly...Ch. 13.4 - An antique collector believes that the price...Ch. 13.4 - Stock market analysts are continually looking for...Ch. 13.4 - Suppose that a regional express delivery service...Ch. 13.4 - The owner of a restaurant in Bloomington, Indiana,...Ch. 13.6 - The file P13_19.xlsx contains the weekly sales of...Ch. 13.6 - The file P13_20.xlsx contains the monthly sales of...Ch. 13.6 - The file P13_21.xlsx contains the weekly sales of...Ch. 13.6 - The file P13_22.xlsx contains total monthly U.S....Ch. 13.7 - You have been assigned to forecast the number of...Ch. 13.7 - Simple exponential smoothing with = 0.3 is being...Ch. 13.7 - The file P13_25.xlsx contains the quarterly...Ch. 13.7 - The file P13_26.xlsx contains the monthly number...Ch. 13.7 - The file P13_27.xlsx contains yearly data on the...Ch. 13.7 - The file P13_28.xlsx contains monthly retail sales...Ch. 13.7 - The file P13_29.xlsx contains monthly time series...Ch. 13.7 - A version of simple exponential smoothing can be...Ch. 13 - Many companies manufacture products that are at...Ch. 13 - A power company located in southern Alabama wants...Ch. 13 - Management of a home appliance store would like to...Ch. 13 - A small computer chip manufacturer wants to...Ch. 13 - The file P13_35.xlsx contains the amount of money...Ch. 13 - When potential workers apply for a job that...Ch. 13 - Callaway Golf is trying to determine how the price...Ch. 13 - Let Yt be the sales during month t (in thousands...Ch. 13 - The Baker Company wants to develop a budget to...Ch. 13 - The auditor of Kiely Manufacturing is concerned...Ch. 13 - The file P13_42.xlsx contains monthly data on...Ch. 13 - The belief that larger majorities for an incumbent...Ch. 13 - The auditor of Kaefer Manufacturing uses...Ch. 13 - (Based on an actual court case in Philadelphia.)...Ch. 13 - Confederate Express is attempting to determine how...Ch. 13 - Pernavik Dairy produces and sells a wide range of...

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