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A Parametric Control Chart for Monitoring Individual Batting Performances in Cricket

Author

Listed:
  • Bracewell Paul J

    (Offlode)

  • Ruggiero Katya

    (University of Auckland)

Abstract

A control chart is developed specifically for monitoring batting performances in cricket. Issues associated with the need to retain extreme values and limited sampling opportunities are overcome by using a parametric approach to obtain theoretical quartiles from the distribution of individual batting scores. A mixed distribution, named the Ducks 'n' Runs distribution, is proposed. A beta distribution models zero scores (ducks) and a geometric distribution describes the distribution of non zero scores (runs). This suitability of this probability distribution model is demonstrated using data from New Zealand first class batsmen in domestic three day cricket over a four year period. Changes in the process (player performance) are detected using rules adapted from the supplementary rules for Shewhart control charts.

Suggested Citation

  • Bracewell Paul J & Ruggiero Katya, 2009. "A Parametric Control Chart for Monitoring Individual Batting Performances in Cricket," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 5(3), pages 1-21, July.
    • Handle: RePEc:bpj:jqsprt:v:5:y:2009:i:3:n:5
    DOI: 10.2202/1559-0410.1160
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    Citations

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    Cited by:

    1. Stevenson Oliver George & Brewer Brendon J., 2017. "Bayesian survival analysis of batsmen in Test cricket," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 13(1), pages 25-36, March.
    2. Mukherjee, Satyam, 2012. "Identifying the greatest team and captain—A complex network approach to cricket matches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6066-6076.
    3. Oliver G. Stevenson & Brendon J. Brewer, 2021. "Finding your feet: A Gaussian process model for estimating the abilities of batsmen in test cricket," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(2), pages 481-506, March.
    4. Bracewell Paul J & Farhadieh Farinaz & Jowett Clint A & Forbes Don G. R. & Meyer Denny H, 2009. "Was Bradman Denied His Prime?," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 5(4), pages 1-26, October.
    5. Chitresh Kumar & Girish Balasubramanian, 2023. "Comparative Analysis of Pitch Ratings in All Formats of Cricket," Management and Labour Studies, XLRI Jamshedpur, School of Business Management & Human Resources, vol. 48(3), pages 307-324, August.
    6. Dibyojyoti Bhattacharjee & Hemanta Saikia, 2016. "An objective approach of balanced cricket team selection using binary integer programming method," OPSEARCH, Springer;Operational Research Society of India, vol. 53(2), pages 225-247, June.
    7. Borooah Vani K & Mangan John E, 2010. "The "Bradman Class": An Exploration of Some Issues in the Evaluation of Batsmen for Test Matches, 1877-2006," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 6(3), pages 1-21, July.
    8. Sargent Jonathan RT & Bedford Anthony, 2012. "Using Conditional Estimates to Simulate In-Play Outcomes in Limited Overs Cricket," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 8(2), pages 1-20, June.
    9. G D Sharp & W J Brettenny & J W Gonsalves & M Lourens & R A Stretch, 2011. "Integer optimisation for the selection of a Twenty20 cricket team," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(9), pages 1688-1694, September.

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