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Professional sports leagues are motivated to promote competitive balance in order to maintain fan interest. The National Football League (NFL) has taken several steps to promote competitive balance, most notably free agency and the salary cap, which were instituted prior to the 1994 season. Previous research into competitive balance in sports focused on the variability of team strengths but ignored the year-to-year autocorrelation in team strengths. We present a Bayesian state-space model for paired comparisons that allows regression on the variance parameters. By modeling the variance parameters in a regression framework, we are able to simultaneously compare the variance and autocorrelation in team strengths over time. The autocorrelation of NFL team strengths has decreased over time while there has been little change in the variance in teams strengths since the 1970s.

A Comparison of the Autocorrelation and Variance of NFL Team Strengths Over Time using a Bayesian State-Space Model