Question: Max Gooding is tired of losing money
Max Gooding is tired of losing money in his office’s weekly football pool and has decided to try to do something about it. Figure 8.44 (and file Football.xlsx that accompanies this book) contains a listing of the teams in the Imaginary Football League (IFL) along with the outcomes of all the games played in the league last season.
For instance, cell F5 indicates the Minnesota Raiders beat the Atlanta Eagles by two points last year, whereas cell F6 indicates that Atlanta beat the Los Angeles Pirates by three points. Max believes it may be possible to use the evolutionary algorithm in Solver to estimate the margin of victory in a match-up between any two teams. Using last season’s data, Max wants to identify ratings or weights for each team such that the estimated margin of victory for any match-up would be:
With this information, Max could estimate the margin of victory in a match-up between any two teams. He wants to do this in a way that minimizes the sum of the squared differences between the actual and estimated margins of victory for each of the games last year. (Assume each team’s rating should be between 0 and 100 and the home field advantage should be between 0 and 20.)
a. Create a Solver model that achieves Max’s objective.
b. If Max used this model to predict the winner in each of last year’s games, how many times would he have correctly picked the winning team?
c. Suppose Max wants to maximize the chance of picking the winning teams. Re-solve the problem to achieve this objective.
d. If Max used your model from part (c) to predict the winner in each of last year’s games, how many times would he have correctly picked the winning team?
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