23 During the 1972 football season, the games shown in Table 76 were played by the Miami Dolphins, the Buffalo Bills, and the New York Jets. Suppose that on the basis of these games, we want to rate these three teams. Let M=

Miami rating, J = Jets rating, and B = Bills rating. Given values of M, J, and B, you would predict that when, for example, the Bills play Miami, Miami is expected to win by M - B points. Thus, for the first Miami–Bills game, your prediction would have been in error by |M - B - 1| points.

Show how linear programming can be used to determine ratings for each team that minimize the sum of the prediction errors for all games.

At the conclusion of the season, this method has been used to determine ratings for college football and college basketball. What problems could be foreseen if this method were used to rate teams early in the season?

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FIGURE 31 3 1 2 TABLE 76 4 Miami Bills Jets 27 17 28 24 24 23 30 16 24 41 3 41