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May
2022, 18(3): 2001-2016.
doi: 10.3934/jimo.2021053
Efficiency, RTS, and marginal returns from salary on the performance of the NBA players: A parallel DEA network with shared inputs
| 1. | Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China |
| 2. | School of Management, University of Science and Technology of China, Hefei 230026, China |
| 3. | Government College University Faisalabad, Punjab, Pakistan |
National Basketball Association (NBA) is one of the popular sports leagues worldwide and is also a business source that generates enormous financial resources. Generally, the salary of sports players is associated with their performance in the field. However, the NBA players' performance in the game is related to specific technical features in the offensive and defensive activities. This paper aims to measure the impact of NBA players' salary on their efficiency levels using a big data set of eleven seasons (2604 players from 2005 to 2016) by considering the players' performance in offensive and defensive activities. First, we propose models to measure players' overall, offensive, and defensive efficiencies based on a non-homogeneous parallel data envelopment analysis (DEA) network. Then, we introduce input-output oriented network models to estimate the marginal returns from salary on the outcomes of both offensive and defensive activities. Results indicated that all players' average overall efficiency is low (63.5%), with 17 efficient players. The offensive efficiency is 12.8% higher than the defensive efficiency. When the impact of salary on offensive (defensive) activity is considered, about 73% (47%) of the players' observations indicate increasing marginal returns, respectively.
Keywords:
Data envelopment analysis (DEA),
parallel processes,
returns to scale (RTS),
marginal returns,
NBA games,
salary.
Mathematics Subject Classification:
Primary: 90B10, 90B30, 90C05, 90C90; Secondary: 90C08.
Citation:
Saeed Assani, Muhammad Salman Mansoor, Faisal Asghar, Yongjun Li, Feng Yang. Efficiency, RTS, and marginal returns from salary on the performance of the NBA players: A parallel DEA network with shared inputs. Journal of Industrial and Management Optimization,
2022, 18
(3)
: 2001-2016.
doi: 10.3934/jimo.2021053
![]()
References:
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S. Assani, J. Jiang, A. Assani and F. Yang,
Scale efficiency of China's regional R & D value chain: A double frontier network DEA approach, Journal of Industrial & Management Optimization, 17 (2021), 1357-1382.
doi: 10.3934/jimo.2020025. |
| [2] |
S. Assani, J. Jiang, A. Assani and F. Yang, Most productive scale size of China's regional R & D value chain: A mixed structure network, preprint, arXiv: 1910.03805. |
| [3] |
S. Assani, J. Jiang, R. Cao and F. Yang,
Most productive scale size decomposition for multi-stage systems in data envelopment analysis, Computers and Industrial Engineering, 120 (2018), 279-287.
doi: 10.1016/j.cie.2018.04.043. |
| [4] |
S. Assani and M. S. Mansoor, Salary, offensive, and defensive stats of 2604 NBA players over 11 seasons (2005-2016), Mendeley Data, V1 (2020).
doi: 10.17632/fm86gnkw6x. 1. |
| [5] |
J. E. Boscá, V. Liern, A. Martínez and R. Sala,
Increasing offensive or defensive efficiency? An analysis of Italian and Spanish football, Omega, 37 (2009), 63-78.
doi: 10.1016/j.omega.2006.08.002. |
| [6] |
A. Charnes, W. W. Cooper and E. Rhodes,
Measuring the efficiency of decision making units, European Journal of Operational Research, 2 (1978), 429-444.
doi: 10.1016/0377-2217(78)90138-8. |
| [7] |
Y. Chen, Y. Gong and X. Li,
Evaluating NBA player performance using bounded integer data envelopment analysis, INFOR: Information Systems and Operational Research, 55 (2017), 38-51.
doi: 10.1080/03155986.2016.1262581. |
| [8] |
W. W. Cooper, J. L. Ruiz and I. Sirvent,
Selecting non-zero weights to evaluate effectiveness of basketball players with DEA, European Journal of Operational Research, 195 (2009), 563-574.
doi: 10.1016/j.ejor.2008.02.012. |
| [9] |
Ó. Gutiérrez and J. L. Ruiz,
Data envelopment analysis and cross-efficiency evaluation in the management of sports teams: The assessment of game performance of players in the Spanish handball league, Journal of Sport Management, 27 (2013), 217-229.
doi: 10.1123/jsm.27.3.217. |
| [10] |
C. -K. Hu, F. -B. Liu, H. -M. Chen and C. -F. Hu, Network data envelopment analysis with fuzzy non-discretionary factors, Journal of Industrial & Management Optimization.
doi: 10.3934/jimo. 2020046. |
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C. Kao,
Efficiency decomposition for general multi-stage systems in data envelopment analysis, European Journal of Operational Research, 232 (2014), 117-124.
doi: 10.1016/j.ejor.2013.07.012. |
| [12] |
C. Kao,
Network data envelopment analysis: A review, European Journal of Operational Research, 239 (2014), 1-16.
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C. Kao and S.-T. Liu,
Cross efficiency measurement and decomposition in two basic network systems, Omega, 83 (2019), 70-79.
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C. Kao and S.-N. Hwang,
Decomposition of technical and scale efficiencies in two-stage production systems, European Journal of Operational Research, 211 (2011), 515-519.
doi: 10.1016/j.ejor.2011.01.010. |
| [15] |
H. Katayama and H. Nuch,
A game-level analysis of salary dispersion and team performance in the national basketball association, Applied Economics, 43 (2011), 1193-1207.
doi: 10.1080/00036840802600335. |
| [16] |
B. L. Lee and A. C. Worthington,
A note on the 'Linsanity' of measuring the relative efficiency of National Basketball association guards, Applied Economics, 45 (2013), 4193-4202.
doi: 10.1080/00036846.2013.770125. |
| [17] |
Y. Li, L. Wang and F. Li,
A data-driven prediction approach for sports team performance and its application to National Basketball Association, Omega, 98 (2021), 102-123.
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Performance evaluation of nonhomogeneous hospitals: the case of Hong Kong hospitals, Health Care Management Science, 22 (2019), 215-228.
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Y. Li, X. Shi, A. Emrouznejad and L. Liang,
Environmental performance evaluation of Chinese industrial systems: A network SBM approach, Journal of the Operational Research Society, 69 (2018), 825-839.
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| [20] |
R. Lyons, E. N. Jackson and A. Livingston, Determinants of NBA player salaries, The Sport Journal, 18 (2015).
doi: 10.17682/sportjournal/2015.019. |
| [21] |
K. Mikolajec, A. Maszczyk and T. Zajac,
Game indicators determining sports performance in the NBA, Journal of Human Kinetics, 37 (2013), 145-151.
doi: 10.2478/hukin-2013-0035. |
| [22] |
P. Moreno and S. Lozano,
A network DEA assessment of team efficiency in the NBA, Annals of Operations Research, 214 (2014), 99-124.
doi: 10.1007/s10479-012-1074-9. |
| [23] |
A. Stefaniec, K. Hosseini, J. Xie and Y. Li, Sustainability assessment of inland transportation in China: A triple bottom line-based network DEA approach, Transportation Research Part D: Transport and Environment, 80 (2020), 102258.
doi: 10.1016/j. trd. 2020.102258. |
| [24] |
G. Villa and S. Lozano,
Dynamic network DEA approach to basketball games efficiency, Journal of the Operational Research Society, 69 (2018), 1738-1750.
doi: 10.1080/01605682.2017.1409158. |
| [25] |
M. Yang, Y. Wei, L. Liang, J. Ding and X. Wang, Performance evaluation of NBA teams: A non-homogeneous DEA approach, Journal of the Operational Research Society, (2020), 1–12.
doi: 10.1080/01605682.2020.1718560. |
| [26] |
L. Zhang and K. Chen,
Hierarchical network systems: An application to high-technology industry in China, Omega, 82 (2019), 118-131.
doi: 10.1016/j.omega.2017.12.007. |
show all references
References:
| [1] |
S. Assani, J. Jiang, A. Assani and F. Yang,
Scale efficiency of China's regional R & D value chain: A double frontier network DEA approach, Journal of Industrial & Management Optimization, 17 (2021), 1357-1382.
doi: 10.3934/jimo.2020025. |
| [2] |
S. Assani, J. Jiang, A. Assani and F. Yang, Most productive scale size of China's regional R & D value chain: A mixed structure network, preprint, arXiv: 1910.03805. |
| [3] |
S. Assani, J. Jiang, R. Cao and F. Yang,
Most productive scale size decomposition for multi-stage systems in data envelopment analysis, Computers and Industrial Engineering, 120 (2018), 279-287.
doi: 10.1016/j.cie.2018.04.043. |
| [4] |
S. Assani and M. S. Mansoor, Salary, offensive, and defensive stats of 2604 NBA players over 11 seasons (2005-2016), Mendeley Data, V1 (2020).
doi: 10.17632/fm86gnkw6x. 1. |
| [5] |
J. E. Boscá, V. Liern, A. Martínez and R. Sala,
Increasing offensive or defensive efficiency? An analysis of Italian and Spanish football, Omega, 37 (2009), 63-78.
doi: 10.1016/j.omega.2006.08.002. |
| [6] |
A. Charnes, W. W. Cooper and E. Rhodes,
Measuring the efficiency of decision making units, European Journal of Operational Research, 2 (1978), 429-444.
doi: 10.1016/0377-2217(78)90138-8. |
| [7] |
Y. Chen, Y. Gong and X. Li,
Evaluating NBA player performance using bounded integer data envelopment analysis, INFOR: Information Systems and Operational Research, 55 (2017), 38-51.
doi: 10.1080/03155986.2016.1262581. |
| [8] |
W. W. Cooper, J. L. Ruiz and I. Sirvent,
Selecting non-zero weights to evaluate effectiveness of basketball players with DEA, European Journal of Operational Research, 195 (2009), 563-574.
doi: 10.1016/j.ejor.2008.02.012. |
| [9] |
Ó. Gutiérrez and J. L. Ruiz,
Data envelopment analysis and cross-efficiency evaluation in the management of sports teams: The assessment of game performance of players in the Spanish handball league, Journal of Sport Management, 27 (2013), 217-229.
doi: 10.1123/jsm.27.3.217. |
| [10] |
C. -K. Hu, F. -B. Liu, H. -M. Chen and C. -F. Hu, Network data envelopment analysis with fuzzy non-discretionary factors, Journal of Industrial & Management Optimization.
doi: 10.3934/jimo. 2020046. |
| [11] |
C. Kao,
Efficiency decomposition for general multi-stage systems in data envelopment analysis, European Journal of Operational Research, 232 (2014), 117-124.
doi: 10.1016/j.ejor.2013.07.012. |
| [12] |
C. Kao,
Network data envelopment analysis: A review, European Journal of Operational Research, 239 (2014), 1-16.
doi: 10.1016/j.ejor.2014.02.039. |
| [13] |
C. Kao and S.-T. Liu,
Cross efficiency measurement and decomposition in two basic network systems, Omega, 83 (2019), 70-79.
doi: 10.1016/j.omega.2018.02.004. |
| [14] |
C. Kao and S.-N. Hwang,
Decomposition of technical and scale efficiencies in two-stage production systems, European Journal of Operational Research, 211 (2011), 515-519.
doi: 10.1016/j.ejor.2011.01.010. |
| [15] |
H. Katayama and H. Nuch,
A game-level analysis of salary dispersion and team performance in the national basketball association, Applied Economics, 43 (2011), 1193-1207.
doi: 10.1080/00036840802600335. |
| [16] |
B. L. Lee and A. C. Worthington,
A note on the 'Linsanity' of measuring the relative efficiency of National Basketball association guards, Applied Economics, 45 (2013), 4193-4202.
doi: 10.1080/00036846.2013.770125. |
| [17] |
Y. Li, L. Wang and F. Li,
A data-driven prediction approach for sports team performance and its application to National Basketball Association, Omega, 98 (2021), 102-123.
doi: 10.1016/j.omega.2019.102123. |
| [18] |
Y. Li, X. Lei and A. Morton,
Performance evaluation of nonhomogeneous hospitals: the case of Hong Kong hospitals, Health Care Management Science, 22 (2019), 215-228.
doi: 10.1007/s10729-018-9433-y. |
| [19] |
Y. Li, X. Shi, A. Emrouznejad and L. Liang,
Environmental performance evaluation of Chinese industrial systems: A network SBM approach, Journal of the Operational Research Society, 69 (2018), 825-839.
doi: 10.1057/s41274-017-0257-9. |
| [20] |
R. Lyons, E. N. Jackson and A. Livingston, Determinants of NBA player salaries, The Sport Journal, 18 (2015).
doi: 10.17682/sportjournal/2015.019. |
| [21] |
K. Mikolajec, A. Maszczyk and T. Zajac,
Game indicators determining sports performance in the NBA, Journal of Human Kinetics, 37 (2013), 145-151.
doi: 10.2478/hukin-2013-0035. |
| [22] |
P. Moreno and S. Lozano,
A network DEA assessment of team efficiency in the NBA, Annals of Operations Research, 214 (2014), 99-124.
doi: 10.1007/s10479-012-1074-9. |
| [23] |
A. Stefaniec, K. Hosseini, J. Xie and Y. Li, Sustainability assessment of inland transportation in China: A triple bottom line-based network DEA approach, Transportation Research Part D: Transport and Environment, 80 (2020), 102258.
doi: 10.1016/j. trd. 2020.102258. |
| [24] |
G. Villa and S. Lozano,
Dynamic network DEA approach to basketball games efficiency, Journal of the Operational Research Society, 69 (2018), 1738-1750.
doi: 10.1080/01605682.2017.1409158. |
| [25] |
M. Yang, Y. Wei, L. Liang, J. Ding and X. Wang, Performance evaluation of NBA teams: A non-homogeneous DEA approach, Journal of the Operational Research Society, (2020), 1–12.
doi: 10.1080/01605682.2020.1718560. |
| [26] |
L. Zhang and K. Chen,
Hierarchical network systems: An application to high-technology industry in China, Omega, 82 (2019), 118-131.
doi: 10.1016/j.omega.2017.12.007. |
Figure 2.
The non-homogeneous parallel network of NBA player activities
Figure 3.
The tendency of efficiency values for LeBron James in three different seasons
Figure 4.
Salary averages of players' activities based on efficiency's scores
Table 1.
Summary of inputs and outputs descriptive statistics of NBA players
| Variables | Mean | S.D. | Min | Max |
| Inputs | ||||
| Minutes played | 1923 | 573 | 1000 | 3424 |
| Salary | 6224124 | 5107788 | 160244 | 30453805 |
| Outputs | ||||
| Offensive activity | ||||
| Assists | 180 | 145 | 6 | 925 |
| Offensive rebounds | 85 | 65 | 5 | 440 |
| Field goals | 308 | 146 | 53 | 978 |
| Free throws | 153 | 110 | 9 | 756 |
| Defensive activity | ||||
| Defensive rebounds | 248 | 131 | 39 | 882 |
| Steals | 60 | 31 | 7 | 217 |
| Blocks | 38 | 37 | 1 | 285 |
| Variables | Mean | S.D. | Min | Max |
| Inputs | ||||
| Minutes played | 1923 | 573 | 1000 | 3424 |
| Salary | 6224124 | 5107788 | 160244 | 30453805 |
| Outputs | ||||
| Offensive activity | ||||
| Assists | 180 | 145 | 6 | 925 |
| Offensive rebounds | 85 | 65 | 5 | 440 |
| Field goals | 308 | 146 | 53 | 978 |
| Free throws | 153 | 110 | 9 | 756 |
| Defensive activity | ||||
| Defensive rebounds | 248 | 131 | 39 | 882 |
| Steals | 60 | 31 | 7 | 217 |
| Blocks | 38 | 37 | 1 | 285 |
Table 2.
Efficiency evaluation and RTS of NBA players from 2005-2016
| Season | Network BCC Models (2) and (3) | RTS | |||
| Overall | Offensive | Defensive | IRTS | DRTS | |
| 05-06 | 0.6440 | 0.6610 | 0.6281 | 54.8% | 45.2% |
| 06-07 | 0.6387 | 0.6584 | 0.6168 | 52.3% | 47.7% |
| 07-08 | 0.6415 | 0.6620 | 0.6020 | 52.8% | 47.2% |
| 08-09 | 0.6413 | 0.6738 | 0.5957 | 53.1% | 46.9% |
| 09-10 | 0.6402 | 0.6850 | 0.5916 | 53.4% | 46.6% |
| 10-11 | 0.6277 | 0.6724 | 0.5768 | 55.9% | 44.1% |
| 11-12 | 0.6134 | 0.6690 | 0.5741 | 54.6% | 45.4% |
| 12-13 | 0.6148 | 0.6570 | 0.5764 | 55.6% | 44.4% |
| 13-14 | 0.6254 | 0.6846 | 0.5864 | 53.5% | 46.5% |
| 14-15 | 0.6430 | 0.6969 | 0.6068 | 66.7% | 33.3% |
| 15-16 | 0.6537 | 0.7033 | 0.6265 | 64.3% | 35.7% |
| Average | 0.6349 | 0.6749 | 0.5983 | 58.6% | 41.4% |
| Season | Network BCC Models (2) and (3) | RTS | |||
| Overall | Offensive | Defensive | IRTS | DRTS | |
| 05-06 | 0.6440 | 0.6610 | 0.6281 | 54.8% | 45.2% |
| 06-07 | 0.6387 | 0.6584 | 0.6168 | 52.3% | 47.7% |
| 07-08 | 0.6415 | 0.6620 | 0.6020 | 52.8% | 47.2% |
| 08-09 | 0.6413 | 0.6738 | 0.5957 | 53.1% | 46.9% |
| 09-10 | 0.6402 | 0.6850 | 0.5916 | 53.4% | 46.6% |
| 10-11 | 0.6277 | 0.6724 | 0.5768 | 55.9% | 44.1% |
| 11-12 | 0.6134 | 0.6690 | 0.5741 | 54.6% | 45.4% |
| 12-13 | 0.6148 | 0.6570 | 0.5764 | 55.6% | 44.4% |
| 13-14 | 0.6254 | 0.6846 | 0.5864 | 53.5% | 46.5% |
| 14-15 | 0.6430 | 0.6969 | 0.6068 | 66.7% | 33.3% |
| 15-16 | 0.6537 | 0.7033 | 0.6265 | 64.3% | 35.7% |
| Average | 0.6349 | 0.6749 | 0.5983 | 58.6% | 41.4% |
Table 3.
Original and efficient inputs and outputs for LeBron James$ {}^{15-16} $
| MP | SLR | AST | ORB | FG | FT | DRB | STL | BLK | |
| Original | 2709 | 22970500 | 514 | 111 | 737 | 359 | 454 | 104 | 49 |
| Efficient | 2581 | 21883995 | 545 | 118 | 781 | 381 | 481 | 110 | 52 |
| Referent players for offensive process | Kevin Durant Kobe Bryant |
||||||||
| Referent players for defensive process | Andre Drummond Chris Paul |
||||||||
| MP | SLR | AST | ORB | FG | FT | DRB | STL | BLK | |
| Original | 2709 | 22970500 | 514 | 111 | 737 | 359 | 454 | 104 | 49 |
| Efficient | 2581 | 21883995 | 545 | 118 | 781 | 381 | 481 | 110 | 52 |
| Referent players for offensive process | Kevin Durant Kobe Bryant |
||||||||
| Referent players for defensive process | Andre Drummond Chris Paul |
||||||||
Table 4.
Marginal returns from salary on offensive and defensive activities of NBA players
| Season | Impact of salary on offensive | Impact of salary on defensive | ||||
| Increase | Constant | Decrease | Increase | Constant | Decrease | |
| 05-06 | 64.00% | 5.00% | 31.00% | 46.00% | 6.00% | 48.00% |
| 06-07 | 70.00% | 8.00% | 22.00% | 51.00% | 4.00% | 45.00% |
| 07-08 | 72.00% | 3.00% | 25.00% | 48.00% | 7.00% | 45.00% |
| 08-09 | 71.00% | 1.00% | 28.00% | 44.57% | 1.00% | 54.43% |
| 09-10 | 73.00% | 0.00% | 27.00% | 51.00% | 0.00% | 49.00% |
| 10-11 | 77.78% | 0.00% | 22.22% | 52.00% | 0.00% | 48.00% |
| 11-12 | 75.00% | 0.00% | 25.00% | 49.00% | 0.00% | 51.00% |
| 12-13 | 72.00% | 0.00% | 28.00% | 43.00% | 0.00% | 57.00% |
| 13-14 | 73.00% | 0.00% | 27.00% | 42.00% | 0.00% | 58.00% |
| 14-15 | 76.00% | 0.00% | 24.00% | 45.00% | 0.00% | 55.00% |
| 15-16 | 77.00% | 0.00% | 23.00% | 47.00% | 0.00% | 53.00% |
| Mean | 72.80% | 1.55% | 25.66% | 47.14% | 1.64% | 51.22% |
| Season | Impact of salary on offensive | Impact of salary on defensive | ||||
| Increase | Constant | Decrease | Increase | Constant | Decrease | |
| 05-06 | 64.00% | 5.00% | 31.00% | 46.00% | 6.00% | 48.00% |
| 06-07 | 70.00% | 8.00% | 22.00% | 51.00% | 4.00% | 45.00% |
| 07-08 | 72.00% | 3.00% | 25.00% | 48.00% | 7.00% | 45.00% |
| 08-09 | 71.00% | 1.00% | 28.00% | 44.57% | 1.00% | 54.43% |
| 09-10 | 73.00% | 0.00% | 27.00% | 51.00% | 0.00% | 49.00% |
| 10-11 | 77.78% | 0.00% | 22.22% | 52.00% | 0.00% | 48.00% |
| 11-12 | 75.00% | 0.00% | 25.00% | 49.00% | 0.00% | 51.00% |
| 12-13 | 72.00% | 0.00% | 28.00% | 43.00% | 0.00% | 57.00% |
| 13-14 | 73.00% | 0.00% | 27.00% | 42.00% | 0.00% | 58.00% |
| 14-15 | 76.00% | 0.00% | 24.00% | 45.00% | 0.00% | 55.00% |
| 15-16 | 77.00% | 0.00% | 23.00% | 47.00% | 0.00% | 53.00% |
| Mean | 72.80% | 1.55% | 25.66% | 47.14% | 1.64% | 51.22% |
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