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Using Local Correlation to Explain Success in Baseball

Listed author(s):
  • Hamrick Jeff

    (Rhodes College)

  • Rasp John

    (Stetson University)

Registered author(s):

    Statisticians have long employed linear regression models in a variety of circumstances, including the analysis of sports data, because of their flexibility, ease of interpretation, and computational tractability. However, advances in computing technology have made it possible to develop and employ more complicated, nonlinear, and nonparametric procedures. We propose a fully nonparametric nonlinear regression model that is associated to a local correlation function instead of the usual Pearson correlation coefficient. The proposed nonlinear regression model serves the same role as a traditional linear model, but generates deeper and more detailed information about the relationships between the variables being analyzed. We show how nonlinear regression and the local correlation function can be used to analyze sports data by presenting three examples from the game of baseball. In the first and second examples, we demonstrate use of nonlinear regression and the local correlation function as descriptive and inferential tools, respectively. In the third example, we show that nonlinear regression modeling can reveal that traditional linear models are, in fact, quite adequate. Finally, we provide a guide to software for implementing nonlinear regression. The purpose of this paper is to make nonlinear regression and local correlation analysis available as investigative tools for sports data enthusiasts.

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    Article provided by De Gruyter in its journal Journal of Quantitative Analysis in Sports.

    Volume (Year): 7 (2011)
    Issue (Month): 4 (October)
    Pages: 1-29

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    Handle: RePEc:bpj:jqsprt:v:7:y:2011:i:4:n:5
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    1. Lawrence Hadley & John Ruggiero, 2006. "Final-offer arbitration in major league baseball: A nonparametric analysis," Annals of Operations Research, Springer, vol. 145(1), pages 201-209, July.
    2. Smith Lloyd & Downey James, 2009. "Predicting Baseball Hall of Fame Membership using a Radial Basis Function Network," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 5(1), pages 1-21, January.
    3. Freiman Michael H., 2010. "Using Random Forests and Simulated Annealing to Predict Probabilities of Election to the Baseball Hall of Fame," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 6(2), pages 1-37, April.
    4. Jahn K. Hakes & Raymond D. Sauer, 2006. "An Economic Evaluation of the Moneyball Hypothesis," Journal of Economic Perspectives, American Economic Association, vol. 20(3), pages 173-186, Summer.
    5. Young William A & Holland William S & Weckman Gary R, 2008. "Determining Hall of Fame Status for Major League Baseball Using an Artificial Neural Network," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 4(4), pages 1-46, October.
    6. Timothy Anderson & Gunter Sharp, 1997. "A new measure of baseball batters using DEA," Annals of Operations Research, Springer, vol. 73(0), pages 141-155, October.
    7. Kaplan David, 2006. "A Variance Decomposition of Individual Offensive Baseball Performance," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 2(3), pages 1-18, July.
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