A Statistical Analysis of NFL Quarterback Rating Variables

Using data from NFL seasons 1960-2007, we examine the quarterback rating and the four variables of which it consists: average yards per attempt, completion percentage, interception percentage, and touchdown percentage. We test for structural breaks in the means and standard deviations of each variable. The analysis finds evidence that there are structural breaks in the series likely associated with rule changes designed to promote the passing game and the implementation of the salary cap. The break test results as a whole suggest that comparisons of quarterbacks from different regimes are inappropriate unless the regime differences are taken into account. There appears to have been a simultaneous improvement in quarterback performance and reduction in volatility suggestive of the idea that the relative difference between above average and average quarterbacks has been reduced. Using graph theory and the information gleamed from structural break tests, we examine the causal relationships among the four quarterback rating variables over the most recent stable period, which is 2000-2007. The causal analysis shows that completion percentage is commonly caused by interception percentage and average yards per attempt over the course of a season. Also, touchdown percentage causes average yards per attempt. We suggest possible explanations of the findings and suggest avenues for future research.