Efficiency analysis of professional basketball players

1
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. [phone]
• Email addressamuoman7_at_hotmail.com

2

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

3

• Evaluating efficiency scores of basketball
  players

4
Efficiency measures of basketball players in the
NBA

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

5
Other relevant studies

1. 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)
2. 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.

6

• 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.

7
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).

8

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

9
Efficiency scores and decomposition
Efficiency Efficiency decomposition Efficiency decomposition Efficiency decomposition Efficiency decomposition Efficiency decomposition Efficiency decomposition
Efficiency N3pGM 3pGM RPG APG SPG BPG
Mean 0.7996 0.1369 0.1350 0.2393 0.0781 0.1734 0.0368
Standard Deviation 0.1344 0.1514 0.1749 0.2079 0.1346 0.2032 0.0886
Minimum 0.4673 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Maximum 1.0000 0.9539 0.8805 0.9250 0.6404 0.9956 0.7200
Sum 271.05 46.42 45.76 81.11 26.47 58.79 12.49
No. of Efficient DMUs 45
No. of DMUs 339 339 339 339 339 339 339
10

1. Are we comparing apples with oranges?

vs
11

1. 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
2. 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
3. Kao and Hung (2008) conduct an efficiency
   decomposition and cluster analysis to categorize
   four groups of university departments of similar
   characteristics.

12

• 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.
• .

13

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

14
Final cluster centers
Cluster Cluster Cluster Cluster Cluster Cluster
scorers generals 3p-experts stealers assisters rebounders Total
N3pGM 0.3799 0.1197 0.0711 0.0420 0.0781 0.1001 0.7907
3pGM 0.0686 0.0255 0.3861 0.0943 0.0686 0.0282 0.6713
RPG 0.1653 0.3152 0.2128 0.0436 0.0738 0.6032 1.4140
APG 0.0447 0.0236 0.0503 0.0252 0.3630 0.0234 0.5303
SPG 0.0581 0.2882 0.0681 0.5899 0.1528 0.0062 1.1633
BPG 0.0913 0.0131 0.0278 0.0311 0.0126 0.0410 0.2169
Cluster Mean 0.8080 0.7854 0.8162 0.8260 0.7489 0.8022 4.7866
N 61 62 82 42 44 48 339
15

• The effects of environmental variables
  (contextual variables) on player performance
• 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.
• Ray (1991) regresses DEA scores on socio-economic
  factors to identify important performance drivers
  in public schools
• 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.

16
Methodology

• Simar and Wilson (2007) recommend truncated
  regression with double bootstrap
• Banker and Natarajan (2008) argue that OLS is
  more robust and appropriate for productivity
  analysis than Simiar and Wilsons result
• OLS is also endorsed by Hoff (2007) in an
  empirical study
• 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.

17

• 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.

18
Environmental Variables

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

19
(No Transcript)
20
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.

21
Thanks!