# Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football

By Wayne Winston | Go to book overview

46

We all know money can't buy love or happiness. In professional sports, can spending more money on players buy a team more success? Let's analyze this question for the NFL, NBA, and MLB.

Does a Larger Payroll Buy Success in the NFL?

In chapter 40 we learned how to calculate offensive and defensive power ratings for NFL teams. For example, an offensive team rating of + 3 means a team (after adjusting for the strength of opposition) scores 3 points more than average and a defensive rating of —5 means that (after adjusting for the strength of opposition) that a team gives up 5 fewer points than average. For the 2001–4 seasons we tabulated the amount of money each NFL team paid their offensive and defensive personnel. A sample of our data is shown in figure 46.1.

In 2004 NFL players were paid 28.6% more than in 2001, 22.9% more than in 2002, and 7.3% more than in 2003. We would like to predict team offensive performance as a function of total offensive salary and team defensive performance as a function of defensive salary. To ensure all expenditures are measured in 2004 dollars, we must multiply each team's 2001 expenditures by 1.286, each team's 2002 expenditures by 1.229 and each team's 2003 expenditures by 1.073. Using Excel's Trend Curve feature, we can find the straight line that best predicts a team's offensive rating from their offensive players' salaries (in millions of 2004 dollars). The results are shown in figure 46.2.

Offensive salary explains only 6% of offensive team rating and the correlation between offensive salary and team offensive rating is 0.24. Our best straight line equation for predicting offensive team rating is team rating = 5.4957 + .1556(offensive team salary in millions). This equation

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