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Efficiency, RTS, and marginal returns from salary on the performance of the NBA players: A parallel DEA network with shared inputs

  • * Corresponding author: Muhammad Salman Mansoor

    * Corresponding author: Muhammad Salman Mansoor 
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  • 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.

    Mathematics Subject Classification: Primary: 90B10, 90B30, 90C05, 90C90; Secondary: 90C08.

    Citation:

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  • Figure 1.  Classical parallel structure

    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
     | Show Table
    DownLoad: CSV

    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%
     | Show Table
    DownLoad: CSV

    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$ {}^{09-10} $ $ (\lambda =0.7412) $,
    Kobe Bryant$ {}^{05-06} $ $ (\lambda =0.2588) $
    Referent players for defensive process Andre Drummond$ {}^{15-16} $ $ (\lambda =0.6834) $,
    Chris Paul$ {}^{07-08} $ $ (\lambda =0.3166) $
     | Show Table
    DownLoad: CSV

    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%
     | Show Table
    DownLoad: CSV
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