NBA Statistical Analysis
Econ 240AGroup Project II
12/3/08
Jeff LeeZhen Tian
Tsung-Ching HuangOystein TennumChristian Treubig
Eddie Bedach
Analysis Method
Statistics CollectedSalary – Dependent VariableHeightWeightPPG,RPG,APG,SPG,BPGAll-Star StatusNumber of teams played for
Analysis Method
300 player database created50 players from each division
- Starters and Second string from each team
Exploratory Data Analysis Investigation of various factors on salary
Ordinary Least Square - T-statistic, F-statisticAnalysis of Variance
Physical Attributes
Height and weight found to be insignificant.
Tall/Weak is undesirable
Short/Strong is undesirable
Dependent Variable: SALARY
Method: Least Squares
Sample: 1 300
Included observations: 300
Variable Coefficient Std. Error t-Statistic Prob.
HEIGHT 151029.1 103165.2 1.463954 0.1443
WEIGHT 16999.88 14633.30 1.161726 0.2463
C -9864304. 6208414. -1.588861 0.1132
R-squared 0.041654 Mean dependent var 5911743.
Adjusted R-squared 0.035223 S.D. dependent var 5018847.
S.E. of regression 4929667. Akaike info criterion 33.66936
Sum squared resid 7.24E+15 Schwarz criterion 33.70631
Log likelihood -5064.238 F-statistic 6.476267
Durbin-Watson stat 1.925366 Prob(F-statistic) 0.001765
Why I was picked after you?
U’re shorter yet fatter…
Physical Attributes
Created dummy variable:
- Body = height * weight
Body was found to be significant
Dependent Variable: SALARY
Method: Least Squares
Sample: 1 300
Included observations: 300
Variable Coefficient Std. Error t-Statistic Prob.
BODY 338.0742 94.68063 3.570680 0.0004
C -101890.1 1707911. -0.059658 0.9525
R-squared 0.040897 Mean dependent var 5911743.
Adjusted R-squared 0.037690 S.D. dependent var 5018847.
S.E. of regression 4923359. Akaike info criterion 33.66350
Sum squared resid 7.25E+15 Schwarz criterion 33.68813
Log likelihood -5064.357 F-statistic 12.74976
Durbin-Watson stat 1.933402 Prob(F-statistic) 0.000415
Statistical Performance
Most Important Factors
1. Blocks
2. Assists
3. Points
4. Rebounds
5. Steals
Dependent Variable: SALARY
Method: Least Squares
Sample: 1 300
Included observations: 300
Variable Coefficient Std. Error t-Statistic Prob.
APG 541720.3 159737.9 3.391307 0.0008
BPG 1727532. 488891.3 3.533571 0.0005
PPG 502778.7 52958.75 9.493781 0.0000
RPG 424591.4 130701.2 3.248565 0.0013
SPG -549798.2 664644.0 -0.827207 0.4088
C -2748804. 465895.7 -5.900042 0.0000
R-squared 0.641952 Mean dependent var 5911743.
Adjusted R-squared 0.635883 S.D. dependent var 5018847.
S.E. of regression 3028477. Akaike info criterion 32.70475
Sum squared resid 2.71E+15 Schwarz criterion 32.77865
Log likelihood -4916.065 F-statistic 105.7824
Durbin-Watson stat 1.682747 Prob(F-statistic) 0.000000
“Defense Wins Championships”
Dependent Variable: SALARYMethod: Least SquaresSample: 1 300Included observations: 300
Variable Coefficient Std. Error t-Statistic Prob.
DEFENSE 511695.3 43166.52 11.85399 0.0000OFFENSE 78918.61 6159.982 12.81150 0.0000
C 2453181. 266479.8 9.205881 0.0000
R-squared 0.553566 Mean dependent var 5911743.Adjusted R-squared 0.550570 S.D. dependent var 5018847.S.E. of regression 3364611. Akaike info criterion 32.90544Sum squared resid 3.37E+15 Schwarz criterion 32.94239Log likelihood -4949.269 Hannan-Quinn criter. 32.92022F-statistic 184.7563 Durbin-Watson stat 1.953691Prob(F-statistic) 0.000000
To investigate this, two dummy variables
were created
OFFENSE = PPG*APG
DEFENSE = RPG*BPG*SPG
Defense was found to be much more
significant.
Teams are willing to pay more for defensive stars
All-Star Status
Highly Significant
All Stars make over an average of $3,426,702 more than non all star players
Dependent Variable: SALARY
Method: Least Squares
Sample: 1 300
Included observations: 300
Variable Coefficient Std. Error t-Statistic Prob.
ALLSTAR 3426702. 624127.2 5.490390 0.0000
APG 462621.4 153067.2 3.022343 0.0027
BPG 1223729. 475336.2 2.574450 0.0105
PPG 363983.5 56493.55 6.442921 0.0000
RPG 425565.1 124687.2 3.413062 0.0007
SPG -569773.6 634071.1 -0.898596 0.3696
C -1448944. 503581.2 -2.877281 0.0043
R-squared 0.675249 Mean dependent var 5911743.
Adjusted R-squared 0.668622 S.D. dependent var 5018847.
S.E. of regression 2889123. Akaike info criterion 32.61378
Sum squared resid 2.45E+15 Schwarz criterion 32.70000
Log likelihood -4901.375 F-statistic 101.8850
Durbin-Watson stat 1.727203 Prob(F-statistic) 0.000000
All Star/Non All Star Difference
5 Yrs for $50,000,000 6 Yrs for $118,000,000
16.1 points/game 16.8 points/game
5.1 rebounds/game 5.8 rebounds/game
2.2 assists/game 1.8 assists/game
9 Years for 3 Teams 10 Years for 2 Team
78 inches + 225 lbs 82 inches + 230 lbs
All-Star? No All-Star? Yes, only 2005
Why I earn much less than u?
Franchise Player
A player who plays for one team for the majority of his career is considered a “Franchise Player.”
Create a dummy variable ‘FRANCHISEVET.’
Product of Variables Franchise and Veteran
Franchise = 1 if player has played for one team only
Veteran = 1 if Years Played >5
Franchise Players make nearly 3 million more per year, on average
Dependent Variable: SALARY
Method: Least Squares
Sample: 1 300
Included observations: 300
Variable Coefficient Std. Error t-Statistic Prob.
FRANCHISEVET 2997136. 774263.4 3.870952 0.0001
APG 554151.9 156114.3 3.549654 0.0004
BPG 1463554. 482542.9 3.033003 0.0026
PPG 471283.8 52382.18 8.997027 0.0000
RPG 432064.7 127723.9 3.382803 0.0008
SPG -411064.2 650417.5 -0.632001 0.5279
C -2616565. 456510.7 -5.731662 0.0000
R-squared 0.659316 Mean dependent var 5911743.
Adjusted R-squared 0.652363 S.D. dependent var 5018847.
S.E. of regression 2959150. Akaike info criterion 32.66168
Sum squared resid 2.57E+15 Schwarz criterion 32.74790
Log likelihood -4908.583 F-statistic 94.82814
Durbin-Watson stat 1.604668 Prob(F-statistic) 0.000000
Larry Bird Rule
Exceed the salary cap to re-sign their free agents
Up to maximum salary
Up to 6 Years in Length
Play 3 seasons without waived or traded as a free agent
Money, Money, Go My Home!
Linear Regression
Dependent Variable: SALARYMethod: Least SquaresSample: 1 301Included observations: 301
Variable Coefficient Std. Error t-Statistic Prob.
TEAM -1641837. 157925.7 -10.39626 0.0000YEARS 1243723. 71014.20 17.51373 0.0000
C 3018149. 376357.8 8.019361 0.0000
R-squared 0.507669 Mean dependent var 5911743.Adjusted R-squared 0.504365 S.D. dependent var 5018847.S.E. of regression 3533337. Akaike info criterion 33.00330Sum squared resid 3.72E+15 Schwarz criterion 33.04025Log likelihood -4963.997 Hannan-Quinn criter. 33.01809F-statistic 153.6418 Durbin-Watson stat 2.059176Prob(F-statistic) 0.000000
Two-Factor Anova
Yr3 Yr4 Yr5 Yr6 Yr7 Yr8 Yr9 Yr10 Yr11 Yr12
# Team1 2329805 8760335 14410581 15070550 15106000 15780000 5500000 18077903 20598704 21262500
# Team2 3448050 7800000 8353000 8500000 12222221 14431816 17810000 16447871 797581 20840625
# Team3 2272860 3850000 5050000 9249980 14232567 8640000 11250000 12528000 20370437 18388430
# Team4 797,581 3500000 4250000 10602667 4350000 8513916 10333334 9226250 10000000 13930000
Correlation Test for Team/Years
CorrelationTeam Years
Team 1 0.626692
Years 0.626692 1
Without Replication
ANOVA: Two-Factor Without Replication
Source of Variation SS df MS F P-value F crit
Rows 1.9E+14 3 6.33E+13 3.644741 0.025061 2.960351
Columns 7.31E+14 9 8.12E+13 4.670364 0.000857 2.250131
Error 4.69E+14 27 1.74E+13
Total 1.39E+15 39
Difference by Larry Bird Rule
$11,050,000 for 2008 $20,598,704 for 2008
NBA Finals MVP
NBA All Star Players
1997 NBA Draft (TD:1st Vs CP:3rd)
Mr. Big Shot The Big Fundamental
Played for 6 teams! Spurs is my home!
Why I earn much less than u?
Understand?
Final Regression
Selected most important factors to run a final regression
- Offense
- Defense
- Body
- Allstar
- Team
- Years
All found to be significant
.71 R-squared value
Dependent Variable: SALARYMethod: Least SquaresSample: 1 301Included observations: 301
Variable Coefficient Std. Error t-Statistic Prob.
OFFENSE 50790.70 6940.318 7.318209 0.0000DEFENSE 253314.5 41726.40 6.070846 0.0000
BODY 195.7037 63.62858 3.075720 0.0023ALLSTAR 2248836. 613261.7 3.667008 0.0003
TEAM -720187.6 136924.6 -5.259740 0.0000YEARS 631556.1 69170.72 9.130396 0.0000
C -1699360. 1205788. -1.409336 0.1598
R-squared 0.715824 Mean dependent var 5911743.Adjusted R-squared 0.710024 S.D. dependent var 5018847.S.E. of regression 2702620. Akaike info criterion 32.48032Sum squared resid 2.15E+15 Schwarz criterion 32.56653Log likelihood -4881.289 Hannan-Quinn criter. 32.51482F-statistic 123.4281 Durbin-Watson stat 2.014189Prob(F-statistic) 0.000000
Conclusions
Body=Money
Defense Wins Champions
Be an All-Star
Try to Stay in One Team for a Couple of Years
Thank You