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

在數據包絡分析中檢驗環境變量對效率的影響和為交叉評價生成多組權重 : 在美國職業籃球聯賽中的應用

Student thesis: Master's Thesis

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Author(s)

  • Feng BAI

Related Research Unit(s)

Detail(s)

Awarding Institution
Supervisors/Advisors
Award date2 Oct 2009

Abstract

This thesis conducts an overall efficiency analysis of professional basketball players in the National Basketball Association (NBA). We rely on data envelopment analysis (DEA) in order to assess player efficiency. The technical efficiency, the aggregate efficiency and the scale efficiency of each player are obtained using the BCC multiplier model. According to an efficiency decomposition and cluster analysis, 339 basketball players are categorized into six homogenous groups: scorers, generals, 3p-experts, stealers, assisters and rebounders. Following the DEA and cluster analysis, this thesis is directed at two topics in the context of the efficiency analysis of basketball players in the NBA. The first topic focuses on testing the effects of environmental variables on the efficiency of basketball players. As player performance may be influenced by a variety of environmental variables, a conventional DEA study is not sufficient to measure their effects on performance measures. Therefore, we identify two groups of environmental variables, namely: personal attributes and team characteristics, to reflect the “advantages” and “disadvantages” in the environment under which a player is playing. We then apply the ordinary least square (OLS) model to regress the environmental variables on the efficiency scores of the players in each cluster. Instead of including all of the explanatory variables, we select the proper variables using a backwards method in order to avoid multicollinearity. After identifying the environmental variables that have a substantial impact on player performance, we illustrate how player efficiency can be re-evaluated by adjusting DEA scores in terms of the coefficients obtained from regression models. The second topic involves generating multiple weight sets for cross-evaluation. As a considerable portion of players are rated to be efficient, we use cross-evaluation to improve the discriminating capability of DEA. Because there are alternate optima and zero values in some of the alternate optima, selecting reasonable weight sets among alternate optima for calculating cross-efficiency ratios is crucial in a DEA study. Therefore, we propose a new method called GP-MWTS that aims to generate multiple weight sets to perform cross-evaluation. The proposed method generates multiple weight sets by choosing different values for a factor weight within its maximum and minimum values. For the sake of comparison, we apply both GP-MWTS and a two-stage MILP procedure developed by Cooper et al. (2009) to select weight sets for 11 efficient players in the scorers’ category. The weight sets generated from both approaches contain less zero weights when compared to those obtained from the classical DEA. Zero weights only exist when some of the inputs or outputs are zero values. Our findings suggest that GP-MWTS may be a good alternative to the Cooper et al. (2009) approach. Moreover, the weight sets obtained from GP-MWTS may represent the weight structure of an efficient DMU better than using just a single weight set.

    Research areas

  • United States, Basketball players, Cluster analysis, Rating of, Data envelopment analysis