Efficiency analysis of professional basketball players Feng BAI *, Kim Fung Lam Department of Management Science, City University of Hong Kong 83 Tat Chee Avenue, Kowloon, Hong Kong *Corresponding author. Tel.:

I.We apply DEA to measure the relative efficiency of basketball players in the National Basketball Association (NBA); II.Basketball players are classified into groups of similar playing styles based on cluster analysis; III.We examine the effects of environmental variables on player performance.

1)Evaluating efficiency scores of basketball players

Efficiency measures of basketball players in the NBA a)NBA: Efficiency = ((Points + Rebounds + Assists + Steals + Blocks) - ((Field Goals Att. - Field Goals Made) + (Free Throws Att. - Free Throws Made) + Turnovers)); b)Stiroh (2007), Berri (1999): predefined factor weights derived from statistical or econometric models. Playing opportunity, measured by Minutes is included in their efficiency measures. c)Cooper et al. (2009) apply data envelopment analysis (DEA) to evaluate the “effectiveness” of basketball players in each position, respectively.

Other relevant studies d)DeOliveira and Callum (2004) suggest including salary as another input in DEA to provide additional insight into player efficiency, especially in the context of a sports league under salary cap system, such as the National Basketball Association (NBA); e)Staw and Hoang (1995) state that the amount teams spent for players have significant influences on personnel decisions in the NBA. Players with higher inputs may have advantages to gain a higher efficiency score than the others.

To extend previous studies in efficiency analysis of basketball players, we use data envelopment analysis (DEA) to assess the relative performance of basketball in the National Basketball Association (NBA); We include both playing opportunity and salary as inputs in DEA to provide additional insight into player evaluation; We use the BCC model, which assumes a variable return to scale (VRS) technology, to account for the effect of inputs scale.

Input-outputs Inputs: minutes per game (MPG), logarithm of the average contracted salary (LnSalary); Outputs: Number of 3-point goals made per game (3pGM), Weighted sum of 2-point and 1-point goals made per game (N3pGM), Total rebounds per game (RPG), Assists per game (APG), Steals per game (SPG) and Blocks per game (BPG).

We use the BCC model (Banker et al., 1984), which assumes a variable returns to scale (VRS) technology, to evaluate player performance.

Efficiency Efficiency decomposition N3pGM3pGMRPGAPGSPGBPG Mean Standard Deviation Minimum Maximum Sum No. of Efficient DMUs45 No. of DMUs339 Efficiency scores and decomposition

2)Are we comparing “apples” with “oranges”? vs

a)Ghosh and Steckel (1993) cluster NBA players into six distinct roles: scorers, bangers and dishers, inner court members and walls, based on their playing statistics. They propose that these roles correspond to distinct offensive and defensive playing styles and not necessarily tied to unique positions; b)Sexton et al. (1986) state that Decision Making Units (DMUs) selecting similar weighting patterns are likely to use similar production processes, and suggest the application of cluster analysis in terms of their weights to provide the analyst with additional insight; c)Kao and Hung (2008) conduct an efficiency decomposition and cluster analysis to categorize four groups of university departments of similar characteristics.

To classify basketball players, we apply a two-stage cluster analysis based on the virtual weights obtained from DEA (Kao and Hung, 2008). Each classified group of players is correspondent to a distinct playing style..

Classification of basketball players: Efficiency decomposition and cluster analysis (Kao and Hung, 2008).

Final cluster centers Cluster scorersgenerals3p-expertsstealersassistersreboundersTotal N3pGM pGM RPG APG SPG BPG Cluster Mean N

3)The effects of environmental variables (contextual variables) on player performance a)Sexton et al. (1986) suggest the usage of analysis of covariance to investigate the dependence of the computed efficiency score upon variables that are not explicitly contained in the input- outputs;. b)Ray (1991) regresses DEA scores on socio-economic factors to identify important performance drivers in public schools; c)Howard and Miller (1993) apply DEA to derive an objective estimate of pay equity in professional baseball. They suggest the usage of two-stage analyses to test the effects of contextual variables.

Methodology a)Simar and Wilson (2007) recommend truncated regression with double bootstrap; b)Banker and Natarajan (2008) argue that OLS is more robust and appropriate for productivity analysis than Simiar and Wilson’s result; c)OLS is also endorsed by Hoff (2007) in an empirical study; d) McDonald (2009) proposes that OLS is a consistent estimator and there is considerable merit in using OLS, which is familiar, easy to compute and understood by a broad community of people.

Regression analysis using the efficiency scores obtained from DEA as dependent variables is conducted to identify the effects of various environmental variables; Since we have classified players into more homogenous groups, we carry out the OLS regression analysis on each classified group, each position-defined group and the whole sample, respectively.

Environmental Variables (1)Personal attributes: Height, Weight, Age, AgeSquare and HighSchool, International, LotteryPick, Undrafted; (2)Team characteristics: Pace, defensive rating (DR), offensive rating (OR) (Wright et al., 1995), and total salary paid by a team (TotalSalary).

Conclusion 1)Data envelopment analysis is an advantageous alternative to previously used method in efficiency analysis of basketball players. The efficiency score obtained contains information of both on-field and financial efficiency of a player. 2)The scale inefficiency is the dominant source of the overall inefficiency. Most players are in the region of increasing returns to scale; therefore, improvements in efficiency may be achieved by increasing resources distributed. 3)Based on the results from DEA, we conduct a two-stage cluster analysis to classify 339 basketball players into six more homogenous groups: scorers, generals, 3p-experts, stealers, assisters and rebounders. 4)Our findings suggest the classification of basketball players by cluster analysis may be more appropriate than the classification by positions. 5)After identifying the environmental variables that have a substantial impact on player performance, player efficiency can be re-evaluated by adjusting DEA scores in terms of the coefficients obtained in regression models.

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