A new Net Resource Factor Based Alternative Method to Calculate Revised Target in Interrupted One Day Cricket Matches
Abstract: This paper proposes an alternative method to calculate the revised target in interrupted 50 overs One Day international (ODI) cricket matches. Existing Duckworth Lewis (D/L) method and its modified versions only take available batting resources of the batting team into account and ignore the individual player’s excellence to calculate the revised target. Here, it is worth mentioning that individual player’s excellence varies in reality, and therefore quality of the available resources may affect the revised target significantly. Further in D/L method, revised target calculation depends only on the available batting resources of the batting team and does not consider the available bowling resources of the fielding team. Proposed method overcomes these two shortcomings by taking individual player’s excellence and available bowling resources of the fielding team into account. Individual player’s excellence has been determined by Data Envelopment Analysis (DEA), a well-known non parametric mathematical programming technique. A new idea of “Net Resource Factor” has been introduced to capture both batting and bowling resources to calculate the revised target. To the best of our knowledge, this is the first attempt to incorporate the ability of individual players and bowling resources of the fielding team for calculating the revised target. A comparative analysis between the proposed method and D/L method has been carried out using the data of real ODI matches held in the past. To facilitate ground application of the proposed method, a flow chart and a “Net Resource Factor Table” have been designed.
Cite this paper: Singh, S. and Adhikari, A. (2015) A new Net Resource Factor Based Alternative Method to Calculate Revised Target in Interrupted One Day Cricket Matches. American Journal of Operations Research, 5, 151-167. doi: 10.4236/ajor.2015.53012.
References

[1]   Jayadevan, V. (2002) A New Method for the Computation of Target Scores in Interrupted, Limited-Over Cricket Matches. Current Science, 83, 577-586.

[2]   Preston, I. and Thomas, J. (2002) Rain Rules for Limited Overs Cricket and Probabilities of Victory. Journal of the Royal Statistical Society Series D (The Statistician), 51, 189-202.
http://dx.doi.org/10.1111/1467-9884.00311

[3]   Bhattacharya, R., Gill, P.S. and Swartz, T.B. (2011) Duckworth-Lewis and Twenty20 Cricket. Journal of the Operational Research Society, 62, 1951-1957.
http://dx.doi.org/10.1057/jors.2010.175

[4]   Duckworth, F.C. and Lewis, A.J. (2004) A Successful Operational Research Intervention in One-Day Cricket. Journal of the Operational Research Society, 55, 749-759.
http://dx.doi.org/10.1057/palgrave.jors.2601717

[5]   McHale, I.G. and Asif, M. (2013) A Modified Duckworth-Lewis Method for Adjusting Targets in Interrupted Limited Overs Cricket. European Journal of Operational Research, 225, 353-362.
http://dx.doi.org/10.1016/j.ejor.2012.09.036

[6]   Stern, S.E. (2009) An Adjusted Duckworth-Lewis Target in Shortened Limited Overs Cricket Matches. Journal of the Operational Research Society, 60, 236-251.
http://dx.doi.org/10.1057/palgrave.jors.2602536

[7]   Farrell, M.J. (1957) The Measurement of Productive Efficiency. Journal of the Royal Statistical Society Series A (General), 120, 253-290.
http://dx.doi.org/10.2307/2343100

[8]   Charnes, A., Cooper, W. and Rhodes, E. (1978) Measuring the Efficiency of Decision Making Units. European Journal of Operational Research, 2, 429-444.
http://dx.doi.org/10.1016/0377-2217(78)90138-8

[9]   Einolf, K.W. (2004) Is Winning Everything? A Data Envelopment Analysis of Major League Baseball and the National Football League. Journal of Sports Economics, 5, 127-151.
http://dx.doi.org/10.1177/1527002503254047

[10]   Haas, D.J. (2003) Technical Efficiency in the Major League Soccer. Journal of Sports Economics, 4, 203-215.
http://dx.doi.org/10.1177/1527002503252144

[11]   Wu, J., Zhou, Z. and Liang, L. (2010) Measuring the Performance of Nations at Beijing Summer Olympics Using Integer-Valued DEA Model. Journal of Sports Economics, 11, 549-566.
http://dx.doi.org/10.1177/1527002509352619

[12]   Ruiz, J.L., Pastor, D. and Pastor, J.T. (2011) Assessing Professional Tennis Players Using Data Envelopment Analysis (DEA). Journal of Sports Economics, 14, 276-302.
http://dx.doi.org/10.1177/1527002511421952

[13]   Singh, S. (2011) Measuring the Performance of Teams in the Indian Premier League. American Journal of Operations Research, 1, 180-184.
http://dx.doi.org/10.4236/ajor.2011.13020

[14]   Amin, G. and Sharma, S. (2014) Cricket Team Selection Using Data Envelopment Analysis. European Journal of Sport Science, 14, S369-S376.
http://dx.doi.org/10.1080/17461391.2012.705333

[15]   Sharp, G.D., Brettenny, W.J., Gonsalves, J.W., Lourens, M. and Stretch, R.A. (2011) Integer Optimisation for the Selection of a Twenty20 Cricket Team. Journal of the Operational Research Society, 62, 1688-1694.
http://dx.doi.org/10.1057/jors.2010.122

[16]   Lemmer, H.H. (2013) Team Selection after a Short Cricket Series. European Journal of Sport Science, 13, 200-206.
http://dx.doi.org/10.1080/17461391.2011.587895

[17]   Liu, F.H.F. and Hsuan Peng, H. (2008) Ranking of Units on the DEA Frontier with Common Weights. Computers and Operations Research, 35, 1624-1637.
http://dx.doi.org/10.1016/j.cor.2006.09.006

[18]   Coelli, T. (1996) A Guide to DEAP Version 2.1: A Data Envelopment Analysis (Computer) Program. CEPA Working Papers, Centre for Efficiency and Productivity Analysis, University of New England, Australia.

Top