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<p>In limited–overs cricket, rain interruptions require adjustment of the target score for the chasing team. The Duckworth–Lewis–Stern (DLS) method is widely used for this purpose but does not explicitly include factors such as pitch condition, dew accumulation, or player strength. To address this limitation, we propose a Fuzzy-DLS model that includes fuzzy logic into a generalized resource function. The method allows batting quality index (BQI), bowling threat index (BTI), pitch state, and weather effects to adjust the resource curve in a continuous and interpretable way. For the 30 illustrative cases in Appendix A, the proposed formulation differs from the DLS resources by a mean absolute amount of 0.0152, with a mean relative difference of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2.66\%\)</EquationSource> </InlineEquation> and a mean absolute par-score difference of 2.13 runs. In the 100-match ODI sample analysed here, chasing teams won <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(56.5\%\)</EquationSource> </InlineEquation> of winter matches compared with <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(37.0\%\)</EquationSource> </InlineEquation> in non-winter matches, giving an odds ratio of 2.21 and a chi-square <i>p</i>-value of 0.081. These results support the use of fuzzy match-condition inputs transparently.</p>

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Duckworth–Lewis–Stern modeling with fuzzy logic and contextual indices for target revision in cricket

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  • 发表日期：

    2026年3月30日

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  • Sovan Samanta,
  • Tofigh Allahviranloo,
  • Leo Mrsic,
  • Antonios Kalampakas

摘要

In limited–overs cricket, rain interruptions require adjustment of the target score for the chasing team. The Duckworth–Lewis–Stern (DLS) method is widely used for this purpose but does not explicitly include factors such as pitch condition, dew accumulation, or player strength. To address this limitation, we propose a Fuzzy-DLS model that includes fuzzy logic into a generalized resource function. The method allows batting quality index (BQI), bowling threat index (BTI), pitch state, and weather effects to adjust the resource curve in a continuous and interpretable way. For the 30 illustrative cases in Appendix A, the proposed formulation differs from the DLS resources by a mean absolute amount of 0.0152, with a mean relative difference of \(2.66\%\) and a mean absolute par-score difference of 2.13 runs. In the 100-match ODI sample analysed here, chasing teams won \(56.5\%\) of winter matches compared with \(37.0\%\) in non-winter matches, giving an odds ratio of 2.21 and a chi-square p-value of 0.081. These results support the use of fuzzy match-condition inputs transparently.