IDEAS home Printed from https://ideas.repec.org/a/wsi/apjorx/v25y2008i04ns0217595908001833.html
   My bibliography  Save this article

Optimal Strategies In One-Day Cricket

Author

Listed:
  • PAM NORTON

    (School of Mathematical Sciences, Monash University, Victoria, Australia, 3800, Australia)

  • RAVI PHATARFOD

    (School of Mathematical Sciences, Monash University, Victoria, Australia, 3800, Australia)

Abstract

Using a dynamic programming formulation, an analysis is presented of both the first and second innings of a one-day cricket match assuming variation in type of ball bowled and subsequent selection of a strategy by the batsman. We assume that the team batting first uses the strategy to maximize the expected score, and the team batting second uses the strategy to maximize the probability of outscoring the first team and thus of maximizing the probability of a win. The dynamic programming formulation allows a calculation, at any stage of the innings, of the optimal scoring strategy depending on the type of ball bowled, along with an estimate of the maximum of the expected number of runs scored in the remainder of the first innings, and the maximum probability of a win in the second innings. Modifications are then introduced to examine the effect of tailender batsmen and a "fifth bowler". Finally a simulation is done to estimate the variance in total score by following the optimal strategy used in the first innings.

Suggested Citation

  • Pam Norton & Ravi Phatarfod, 2008. "Optimal Strategies In One-Day Cricket," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 25(04), pages 495-511.
    • Handle: RePEc:wsi:apjorx:v:25:y:2008:i:04:n:s0217595908001833
    DOI: 10.1142/S0217595908001833
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0217595908001833
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0217595908001833?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    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. Ajit Karnik, 2010. "Valuing Cricketers Using Hedonic Price Models," Journal of Sports Economics, , vol. 11(4), pages 456-469, August.
    2. Silva, Rajitha M. & Manage, Ananda B.W. & Swartz, Tim B., 2015. "A study of the powerplay in one-day cricket," European Journal of Operational Research, Elsevier, vol. 244(3), pages 931-938.

    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. Voelkel, Michael A. & Sachs, Anna-Lena & Thonemann, Ulrich W., 2020. "An aggregation-based approximate dynamic programming approach for the periodic review model with random yield," European Journal of Operational Research, Elsevier, vol. 281(2), pages 286-298.
    2. Tan, Madeleine Sui-Lay, 2016. "Policy coordination among the ASEAN-5: A global VAR analysis," Journal of Asian Economics, Elsevier, vol. 44(C), pages 20-40.
    3. D. W. K. Yeung, 2008. "Dynamically Consistent Solution For A Pollution Management Game In Collaborative Abatement With Uncertain Future Payoffs," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 517-538.
    4. Hanafi, Said & Freville, Arnaud, 1998. "An efficient tabu search approach for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 659-675, April.
    5. Renato Cordeiro Amorim, 2016. "A Survey on Feature Weighting Based K-Means Algorithms," Journal of Classification, Springer;The Classification Society, vol. 33(2), pages 210-242, July.
    6. Dmitri Blueschke & Ivan Savin, 2015. "No such thing like perfect hammer: comparing different objective function specifications for optimal control," Jena Economics Research Papers 2015-005, Friedrich-Schiller-University Jena.
    7. Changming Ji & Chuangang Li & Boquan Wang & Minghao Liu & Liping Wang, 2017. "Multi-Stage Dynamic Programming Method for Short-Term Cascade Reservoirs Optimal Operation with Flow Attenuation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(14), pages 4571-4586, November.
    8. Ghassan, Hassan B. & Al-Jefri, Essam H., 2015. "الحساب الجاري في المدى البعيد عبر نموذج داخلي الزمن [The Current Account in the Long Run through the Intertemporal Model]," MPRA Paper 66527, University Library of Munich, Germany.
    9. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    10. Mercedes Esteban-Bravo & Jose M. Vidal-Sanz & Gökhan Yildirim, 2014. "Valuing Customer Portfolios with Endogenous Mass and Direct Marketing Interventions Using a Stochastic Dynamic Programming Decomposition," Marketing Science, INFORMS, vol. 33(5), pages 621-640, September.
    11. Ohno, Katsuhisa & Boh, Toshitaka & Nakade, Koichi & Tamura, Takayoshi, 2016. "New approximate dynamic programming algorithms for large-scale undiscounted Markov decision processes and their application to optimize a production and distribution system," European Journal of Operational Research, Elsevier, vol. 249(1), pages 22-31.
    12. Oleg Malafeyev & Achal Awasthi, 2015. "A Dynamic Model of Functioning of a Bank," Papers 1511.01529, arXiv.org.
    13. Bellemare, Charles, 2007. "A life-cycle model of outmigration and economic assimilation of immigrants in Germany," European Economic Review, Elsevier, vol. 51(3), pages 553-576, April.
    14. Daniel Adelman & George L. Nemhauser & Mario Padron & Robert Stubbs & Ram Pandit, 1999. "Allocating Fibers in Cable Manufacturing," Manufacturing & Service Operations Management, INFORMS, vol. 1(1), pages 21-35.
    15. Fosgerau, Mogens & Frejinger, Emma & Karlstrom, Anders, 2013. "A link based network route choice model with unrestricted choice set," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 70-80.
    16. Alipanah, A. & Razzaghi, M. & Dehghan, M., 2007. "Nonclassical pseudospectral method for the solution of brachistochrone problem," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1622-1628.
    17. M Batty, 1971. "Exploratory Calibration of a Retail Location Model Using Search by Golden Section," Environment and Planning A, , vol. 3(4), pages 411-432, December.
    18. Li, Haitao & Womer, Norman K., 2015. "Solving stochastic resource-constrained project scheduling problems by closed-loop approximate dynamic programming," European Journal of Operational Research, Elsevier, vol. 246(1), pages 20-33.
    19. Jih-Jeng Huang, 2016. "Resource decision making for vertical and horizontal integration problems in an enterprise," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(11), pages 1363-1372, November.
    20. Mauro Boianovsky, 2002. "Simonsen and the early history of the cash\in-advance approach," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 9(1), pages 57-71.

    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:wsi:apjorx:v:25:y:2008:i:04:n:s0217595908001833. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/apjor/apjor.shtml .

    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.