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An adjusted Duckworth–Lewis target in shortened limited overs cricket matches

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  • S E Stern

    (The Australian National University)

Abstract

This paper presents an investigation of the Duckworth–Lewis (D/L) method for setting fair targets in limited overs cricket matches which have been shortened in duration due to interruptions. Specifically, the D/L method's fundamental structural assumption that the resource utilization table used to calculate adjusted targets is the same for interruptions of either the first or second innings is examined. The analysis is based on the results from over 1100 international matches, 989 of which were completely uninterrupted (excluding those matches where penalties in the form of shortened second innings were imposed) and 61 of which were decided by using the D/L method. Overall, the investigation shows that the D/L method is admirable in its fair modelling of appropriate targets. However, detailed analysis of the uninterrupted matches, employing tobit regression and random walk boundary crossing techniques, indicates that the assumption that resource utilization follows the same pattern in both innings is not sustainable. It appears that actual resource usage during the second innings is more heavily weighted towards the very early and very late overs. To account for this, an adjustment to the D/L method is proposed, whereby separate resource usage tables are employed for each innings. For the first innings, the current D/L method is retained, as it has been constructed based solely on first innings information; however, for the second innings, the resources available with any given number of overs remaining and wickets lost is determined by a simple transformation of the associated resources remaining from the current D/L method. The specific form of the transformation function is based on the cumulative distribution function of a beta distribution. This choice of transformation was based on a combination of structural appropriateness, flexibility and ease of implementation considerations. The adjusted method is evaluated on the 61 matches determined by the D/L method and is seen to predict a reversal of the result in five matches.

Suggested Citation

  • S E Stern, 2009. "An adjusted Duckworth–Lewis target in shortened limited overs cricket matches," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(2), pages 236-251, February.
    • Handle: RePEc:pal:jorsoc:v:60:y:2009:i:2:d:10.1057_palgrave.jors.2602536
    DOI: 10.1057/palgrave.jors.2602536
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    References listed on IDEAS

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    1. Amemiya, Takeshi, 1984. "Tobit models: A survey," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 3-61.
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    Cited by:

    1. Stephen Easton & Sean Pinder & Steven Stern, 2018. "Documenting the functional form of dynamic risk‐taking behaviour in a real options context using sporting contests," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 58(S1), pages 159-178, November.
    2. Muhammad Asif & Ali Ahmadian & Muhammad Azeem & Bruno Antonio Pansera, 2021. "A short comparative study on modified Duckworth-Lewis methods," PLOS ONE, Public Library of Science, vol. 16(11), pages 1-12, November.
    3. Lenten, Liam J.A. & Smith, Aaron C.T. & Boys, Noel, 2018. "Evaluating an alternative draft pick allocation policy to reduce ‘tanking’ in the Australian Football League," European Journal of Operational Research, Elsevier, vol. 267(1), pages 315-320.

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