# zbMATH — the first resource for mathematics

An objective approach of balanced cricket team selection using binary integer programming method. (English) Zbl 1360.90158
Summary: Selecting a balanced playing XI in the game of cricket with the right mix of players of different specialization is a difficult decision making problem for the team management. To make the process more objective, optimization techniques can be applied to the process of selection of players from a given squad. Such an exercise has two dimensions. First, a suitable tool for performance measurement of cricketers needs to be defined. Secondly, for selecting a balanced team of XI players, an appropriate objective function and some constraints need to be formulated. Since the captain gets an obvious inclusion in the cricket team, the area specialization of the captain influences the selection of other ten positions in the playing XI. This study attempts to select the optimum balanced playing XI from a squad of players given the specialization of the captain using binary integer programming. To validate the exercise, data from the fifth season of the Indian Premier League has been used.
##### MSC:
 90B90 Case-oriented studies in operations research 90C10 Integer programming 90B70 Theory of organizations, manpower planning in operations research
Full Text:
##### References:
 [1] Saikia, H; Bhattacharjee, D, On classification of all-rounders of the indian premier league (IPL): a Bayesian approach, Vikalpa: J. Decis. Mak., 36, 51-66, (2011) [2] Lemmer, HH, Team selection after a short cricket series, Eur. J. Sport Sci., (2011) [3] Salas, E; Rosen, MA; Burke, CS; Goodwin, GF; Fiore, SM; Ericsson, KA (ed.); Charness, N (ed.); Feltovich, PJ (ed.); Hoffman, RR (ed.), The making of a dream team: when expert teams do best, 439-453, (2006), New York [4] Kamble, A; Rao, R; Kale, A; Samant, S, Selection of cricket players using analytical hierarchy process, Int. J. Sports Sci. Eng., 5, 207-212, (2011) [5] Ahmed, F; Jindal, A; Deb, K, Multi-objective optimization and decision making approaches to cricket team selection, Appl. Soft Comput., (2012) [6] Barr, GDI; Kantor, BS, A criterion for comparing and selecting batsmen in limited overs cricket, J. Oper. Res. Soc., 55, 1266-1274, (2004) · Zbl 1088.90545 [7] Gerber, H; Sharp, G, Selecting a limited overs cricket squad using an integer programming model, S. Afr. J. Res. Sport Phys. Educ. Recreat., 28, 81-90, (2006) [8] Lourens, M.: Integer optimization for the selection of a twenty20 cricket team$$.$$ Nelson Mandela Metropolitan University. http://statssa.gov.za/isi2009/ScientificProgramme/IPMS/0738.pdf (2010). Accessed 21 June 2010 [9] Brettenny, W.: Integer optimisation of the selection of a fantasy league cricket team$$.$$ Nelson Mandela Metropolitan University. http://dspace.nmmu.ac.za:8080/jspui/bitstream/10948/…/W20%B.pdf (2010). Accessed 21 December 2010 [10] Staden, PJ, Comparison of cricketers’ bowling and batting performances using graphical displays, Curr. Sci., 96, 764-766, (2009) [11] Beaudoin, D; Swartz, T, The best batsmen and bowlers in one-day cricket, S. Afr. Stat. J., 37, 203-222, (2003) · Zbl 1139.62344 [12] Singh, G; Bhatia, N; Singh, S, Fuzzy cognitive maps based cricket player performance evaluator, Int. J. Enterp. Comput. Bus. Syst., 1, 1-15, (2011) [13] Damodaran, U, Stochastic dominance and analysis of ODI batting performance: the Indian cricket team, 1989-2005, J. Sports Sci. Med., 5, 503-508, (2006) [14] Boon, BH; Sierksma, G, Team formation: matching quality supply and quality demand, Eur. J. Oper. Res., 148, 277-292, (2003) · Zbl 1036.90503 [15] Das, D.: Moneyballer: an integer optimization framework for fantasy cricket league selection and substitution. http://debarghyadas.com/files/IPLpaper.pdf (2014). Accessed 11 July 2015 [16] Lewis, A, Towards fairer measures of player performance in one-day cricket, J. Oper. Res. Soc., 56, 804-815, (2005) · Zbl 1084.90513 [17] Iyenger, NS; Sudarshan, P, A method of classifying regions from multivariate data, Econ. Pol. Wkly, 5, 2048-2052, (1982) · Zbl 0505.35075 [18] Lemmer, HH, An analysis of players’ performances in the first cricket twenty20 world cup series, S. Afr. J. Res. Sport Phys. Educ. Recreat., 30, 73-79, (2008) [19] Lemmer, HH, The combined bowling rate as a measure of bowling performance in cricket, S. Afr. J. Res. Sport Phys. Educ. Recreat., 24, 37-44, (2002) [20] Lemmer, HH, A method for the comparison of the bowling performances of bowlers in a match or a series of matches, S. Afr. J. Res. Sport Phys. Educ. Recreat., 27, 91-103, (2005) [21] Narayanan, A.: Test wicket keepers - an analysis. The ESPNcricinfo Blog. http://blogs.cricinfo.com/itfigures/archives/wicketkeepers/ (2008). Accessed 4 March 2010 · Zbl 1139.62344 [22] Lemmer, HH, A measure for the batting performance of cricket players, S. Afr. J. Res. Sport Phys. Educ. Recreat., 26, 55-64, (2004) [23] Chakrabarty, N; Bhattacharjee, D, Aggregation and weightage issues concerning composite index development: experience with digital divide in Asian countries, Asia Pac. J. Libr. Inf. Sci., 2, 24-37, (2012) [24] Bracewell, PJ; Ruggiero, K, A parametric control chart for monitoring individual batting performances in cricket, J. Quant. Anal. Sports, 5, 1-19, (2009)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.