Measuring the NBA Teams’ Cross-Efficiency by DEA Game

Luiz Aizemberg, Marcos Costa Roboredo, Thiago Graça Ramos, João Carlos C. B. Soares de Mello, Lidia Angulo Meza, Alessandro Martins Alves

Institute of Mathematics and Statistics, State University of Rio de Janeiro, Rio de Janeiro, Brazil.
Production Engineering Department, Fluminense Federal University, Niterói, Brazil.

DOI: 10.4236/ajor.2014.43010                

Abstract

In this paper, we use DEA to measure the NBA basketball teams’ efficiency in seasons 2006-2007, 2007-2008, 2008-2009 and 2009-2010. In this context, each team is a DMU; we select the payroll and the average attendance to be the inputs while the wins and the average points per game to be the outputs. First, in order to obtain benchmarks, we measure the DMUs efficiency through classic DEA BCC model with an assurance region for each one of the four seasons individually and together. When we consider the four seasons together, we may analyse whether the performance of each team increases or decreases over time. Next, we evaluate the teams cross efficiency by DEA game to consider that there is no cooperation among DMUs. This approach also improves the efficiencies discrimination.

Keywords

Data Envelopment Analysis, DEA Game, Cross-Efficiency

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Lozano, S., Villa, G., Guerrero, F. and Cortes, P. (2002) Measuring the Performance of Nations at the Summer Olympics Using Data Envelopment Analysis. Journal of the Operational Research Society, 53, 501-511.
[2]	Haas, D.J. (2003) Productive Efficiency of English Football Teams—A Data Envelopment Analysis Approach. Managerial and Decision Economics, 24, 403-410. http://dx.doi.org/10.1002/mde.1105
[3]	Lins, M.P.E., Gomes, E.G., Soares de Mello, J.C.C.B. and Soares de Mello, A.J.R. (2003) Olympic Ranking Based on a Zero Sum Gains DEA Model. European Journal of Operational Research, 148, 312-322. http://dx.doi.org/10.1016/S0377-2217(02)00687-2
[4]	Barros, C.P. and Leach, S. (2006) Performance Evaluation of the English Premier Football League with Data Envelopment Analysis. Applied Economics, 38, 1449-1458. http://dx.doi.org/10.1080/00036840500396574
[5]	Cooper, W.W. and Ruiz, J.L. (2009) Selecting Non-Zero Weights to Evaluate Effectiveness of Basketball Players with DEA. European Journal of Operational Research, 195, 563-574. http://dx.doi.org/10.1016/j.ejor.2008.02.012
[6]	Bai, F. (2009) Testing the Effects of Environmental Variables on Efficiency and Generating Multiple Weight Sets for Cross-Evaluation with DEA: An Application to the National Basketball Association. City University of Hong Kong, Hong Kong.
[7]	Moreno, P. and Lozano, S. (2012) A Network DEA Assessment of Team Efficiency in the NBA. Annals of Operations Research, 214, 99-124.
[8]	Doyle, J. and Green, R. (1994) Efficiency and Cross-Efficiency in DEA: Derivations, Meanings and Uses. Journal of the Operational Research Society, 45, 567-578. http://dx.doi.org/10.1057/jors.1994.84
[9]	Soares de Mello, J.C.C.B., Soares de Mello, A.J.R., Lins, M.P.E. and Gomes, E.G. (2002) Construction of a Smoothed DEA Frontier. Pesquisa Operacional, 22, 183-201. http://dx.doi.org/10.1590/S0101-74382002000200006
[10]	Wu, J., Liang, L. and Chen, Y. (2009) DEA Game Cross-Efficiency Approach to Olympic Rankings. Omega, 37, 909918. http://dx.doi.org/10.1016/j.omega.2008.07.001
[11]	Liang, L., Wu, J., Cook, W.D. and Zhu, J. (2008) Alternative Secondary Goals in DEA Cross-Efficiency Evaluation. International Journal of Production Economics, 113, 1025-1030. http://dx.doi.org/10.1016/j.ijpe.2007.12.006
[12]	Liang, L., Wu, J., Cook, W.D. and Zhu, J. (2008) The DEA Game Cross-Efficiency Model and Its Nash Equilibrium. Operations Research, 56, 1278-1288. http://dx.doi.org/10.1287/opre.1070.0487