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

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)236-251
Number of pages16
JournalJournal of the Operational Research Society
Volume60
Issue number2
DOIs
Publication statusPublished - Feb 2009
Externally publishedYes

Fingerprint

Distribution functions
Cricket
Resources

Cite this

@article{10a4d03fc8574dff8944dd1f83317c92,
title = "An adjusted Duckworth-Lewis target in shortened limited overs cricket matches",
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.",
author = "Stern, {S. E.}",
year = "2009",
month = "2",
doi = "10.1057/palgrave.jors.2602536",
language = "English",
volume = "60",
pages = "236--251",
journal = "Operational Research Quarterly",
issn = "0160-5682",
publisher = "Taylor & Francis",
number = "2",

}

An adjusted Duckworth-Lewis target in shortened limited overs cricket matches. / Stern, S. E.

In: Journal of the Operational Research Society, Vol. 60, No. 2, 02.2009, p. 236-251.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - An adjusted Duckworth-Lewis target in shortened limited overs cricket matches

AU - Stern, S. E.

PY - 2009/2

Y1 - 2009/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=58449108533&partnerID=8YFLogxK

U2 - 10.1057/palgrave.jors.2602536

DO - 10.1057/palgrave.jors.2602536

M3 - Article

VL - 60

SP - 236

EP - 251

JO - Operational Research Quarterly

JF - Operational Research Quarterly

SN - 0160-5682

IS - 2

ER -