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A Statistical Analysis of NFL Quarterback Rating Variables


  • Stimel Derek

    (Menlo College)


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.

Suggested Citation

  • Stimel Derek, 2009. "A Statistical Analysis of NFL Quarterback Rating Variables," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 5(2), pages 1-26, May.
  • Handle: RePEc:bpj:jqsprt:v:5:y:2009:i:2:n:1

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    References listed on IDEAS

    1. Hoover, Kevin D & Sheffrin, Steven M, 1992. "Causation, Spending, and Taxes: Sand in the Sandbox or Tax Collector for the Welfare State?," American Economic Review, American Economic Association, vol. 82(1), pages 225-248, March.
    2. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    3. Selva Demiralp & Kevin D. Hoover, 2003. "Searching for the Causal Structure of a Vector Autoregression," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(s1), pages 745-767, December.
    4. Hoover, Kevin D & Siegler, Mark V, 2000. "Taxing and Spending in the Long View: The Causal Structure of US Fiscal Policy, 1791-1913," Oxford Economic Papers, Oxford University Press, vol. 52(4), pages 745-773, October.
    5. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    6. Hoover, Kevin D., 2003. "Some causal lessons from macroeconomics," Journal of Econometrics, Elsevier, vol. 112(1), pages 121-125, January.
    7. Prodan, Ruxandra, 2008. "Potential Pitfalls in Determining Multiple Structural Changes With an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 50-65, January.
    8. Hoover, Kevin D., 2005. "Automatic Inference Of The Contemporaneous Causal Order Of A System Of Equations," Econometric Theory, Cambridge University Press, vol. 21(01), pages 69-77, February.
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    Cited by:

    1. Stimel Derek S, 2011. "Dependence Relationships between On Field Performance, Wins, and Payroll in Major League Baseball," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(2), pages 1-19, May.
    2. Brady Ryan R & Stimel Derek S, 2011. "How the Housing and Financial Wealth Effects Have Changed over Time," The B.E. Journal of Macroeconomics, De Gruyter, vol. 11(1), pages 1-45, August.
    3. von Dohlen Paul, 2011. "Tweaking the NFL's Quarterback Passer Rating for Better Results," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(3), pages 1-14, July.

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