IDEAS home Printed from https://ideas.repec.org/a/bpj/jqsprt/v8y2012i3n1.html

Models for Third Down Conversion in the National Football League

Author

Listed:
  • Cafarelli Ryan

    (Southern Illinois University Edwardsville)

  • Rigdon Christopher J.

    (Southern Illinois UniversityEdwardsville)

  • Rigdon Steven E.

    (Saint Louis University)

Abstract

Several models are proposed for the probability of converting a third down attempt in the National Football League. The probability, which can depend on the number of yards to go, the strength of the offense, and the strength of the defense, leads to a logistic regression. We approach the problem through a hierarchical Bayes model and estimate parameters by using Markov chain Monte Carlo (MCMC). This MCMC estimation in the context of a hierarchical Bayes model may be relevant in other sports situations where a probability depends on the difference of strengths of the two teams. We find that the statistic "third-down conversion rate" to be a nearly meaningless measure of the efficiency of an offense. Even when this is adjusted for yards to go for a first down, there is little evidence that teams differ in their ability to achieve a first down on a third down conversion.

Suggested Citation

  • Cafarelli Ryan & Rigdon Christopher J. & Rigdon Steven E., 2012. "Models for Third Down Conversion in the National Football League," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 8(3), pages 1-26, October.
    • Handle: RePEc:bpj:jqsprt:v:8:y:2012:i:3:n:1
    DOI: 10.1515/1559-0410.1383
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/1559-0410.1383
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/1559-0410.1383?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Steven Rigdon & Robert Tsutakawa, 1983. "Parameter estimation in latent trait models," Psychometrika, Springer;The Psychometric Society, vol. 48(4), pages 567-574, December.
    2. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yurko Ronald & Ventura Samuel & Horowitz Maksim, 2019. "nflWAR: a reproducible method for offensive player evaluation in football," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 15(3), pages 163-183, September.
    2. Santos-Fernandez Edgar & Wu Paul & Mengersen Kerrie L., 2019. "Bayesian statistics meets sports: a comprehensive review," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 15(4), pages 289-312, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Robert Mislevy, 1986. "Bayes modal estimation in item response models," Psychometrika, Springer;The Psychometric Society, vol. 51(2), pages 177-195, June.
    2. Cees Glas, 1988. "The derivation of some tests for the rasch model from the multinomial distribution," Psychometrika, Springer;The Psychometric Society, vol. 53(4), pages 525-546, December.
    3. Feddag, M.-L. & Bacci, S., 2009. "Pairwise likelihood for the longitudinal mixed Rasch model," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1027-1037, February.
    4. Aeilko Zwinderman, 1991. "A generalized rasch model for manifest predictors," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 589-600, December.
    5. Robert Tsutakawa & Hsin Lin, 1986. "Bayesian estimation of item response curves," Psychometrika, Springer;The Psychometric Society, vol. 51(2), pages 251-267, June.
    6. Mark Reiser, 1989. "An Application of the Item-Response Model to Psychiatric Epidemiology," Sociological Methods & Research, , vol. 18(1), pages 66-103, August.
    7. C. Glas & N. Verhelst, 1989. "Extensions of the partial credit model," Psychometrika, Springer;The Psychometric Society, vol. 54(4), pages 635-659, September.
    8. Robert Mislevy, 1991. "Randomization-based inference about latent variables from complex samples," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 177-196, June.
    9. Sik-Yum Lee & Xin-Yuan Song, 2007. "A Unified Maximum Likelihood Approach for Analyzing Structural Equation Models With Missing Nonstandard Data," Sociological Methods & Research, , vol. 35(3), pages 352-381, February.
    10. Ying Cheng & Ke-Hai Yuan, 2010. "The Impact of Fallible Item Parameter Estimates on Latent Trait Recovery," Psychometrika, Springer;The Psychometric Society, vol. 75(2), pages 280-291, June.
    11. Wallin, Gabriel & Chen, Yunxiao & Lee, Yi-Hsuan & Li, Xiaoou, 2025. "A latent variable model with change-points and its application to time pressure effects in educational assessment," LSE Research Online Documents on Economics 128070, London School of Economics and Political Science, LSE Library.
    12. Alberto Maydeu-Olivares & Rosa Montaño, 2013. "How Should We Assess the Fit of Rasch-Type Models? Approximating the Power of Goodness-of-Fit Statistics in Categorical Data Analysis," Psychometrika, Springer;The Psychometric Society, vol. 78(1), pages 116-133, January.
    13. Carolina Navarro & Luis Ayala & José Labeaga, 2010. "Housing deprivation and health status: evidence from Spain," Empirical Economics, Springer, vol. 38(3), pages 555-582, June.
    14. Ji Seung Yang & Xiaying Zheng, 2018. "Item Response Data Analysis Using Stata Item Response Theory Package," Journal of Educational and Behavioral Statistics, , vol. 43(1), pages 116-129, February.
    15. M.-L. Feddag, 2016. "Pairwise likelihood estimation for the normal ogive model with binary data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(2), pages 223-237, April.
    16. Chen, Yunxiao & Li, Xiaoou, 2022. "Determining the number of factors in high-dimensional generalized latent factor models," LSE Research Online Documents on Economics 111574, London School of Economics and Political Science, LSE Library.
    17. Alexander Robitzsch, 2024. "Bias-Reduced Haebara and Stocking–Lord Linking," J, MDPI, vol. 7(3), pages 1-12, September.
    18. Elisabeth R. Gerber & Jeffrey B. Lewis, 2004. "Beyond the Median: Voter Preferences, District Heterogeneity, and Political Representation," Journal of Political Economy, University of Chicago Press, vol. 112(6), pages 1364-1383, December.
    19. Shiyu Wang & Georgios Fellouris & Hua-Hua Chang, 2019. "Statistical Foundations for Computerized Adaptive Testing with Response Revision," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 375-394, June.
    20. Ting Lin, 2007. "Identifying Optimal Items in Quality of Life Assessment," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(5), pages 661-672, October.

    More about this item

    Keywords

    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:jqsprt:v:8:y:2012:i:3:n:1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyterbrill.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.