409 Final Draft paper

A Time Series Analysis of the Highest Paid NBA Player from 1984 to 2022, by Season Jackie O’Neill Professor Halcoussis December 4, 2023

Table of Contents Introduction ............................................................................................................................. 3 Literature Review .................................................................................................................... 3 Methodology and Data ............................................................................................................ 5 Initial Results ........................................................................................................................... 6 Final Results ............................................................................................................................ 8 Conclusion ............................................................................................................................... 9 Discussion and Limitations ..................................................................................................... 10 Works Cited ........................................................................................................................... 11 Appendix ............................................................................................................................... 12

compensation. However, it is worth noting that other qualitative variables could affect these results. For example, how these players interact with their teammates on and off the court is vital to a team’s success. A player could have fantastic statistics but still be traded if they have an overall negative social impact on the team which would make him not worth the money. Franchises are for-profit organizations and when they sign players, they expect that they will be making an overall profit now or in the future. The Sale & Hunter (2009) study looks at the relationship between player salary cost and operating income. Total player salary costs and operating income for each NBA franchise were taken over 10 years, 1998-2007. It was found that there was a negative relationship between the two variables, meaning that the higher salaries paid to keep the star players don’t generate enough revenue to cover those higher costs. There isn’t enough of a return on investment for owners thus incentivizing lower salary costs. Koster & Aven (2018) attempted to describe the relationship between group and individual performance. To do this they examined the social media pages of NBA teammates in the 2014-2015 season, specifically looking at if high-paid or high-profile players were “following” their teammates. High-status players on underperforming teams were less likely to follow their teammates when compared to high-status players on successful teams. This implies that it is possible to predict group performance on individuals’ willingness to associate with the group and its members. There have been other studies in the past that have found that black players are paid less than white players with similar performances. Jenkins (1996) examined this through a slightly different lens. Those studies that found that relationship used a single season and incorporated career stats along with an annual salary that year and assumed that players sign a new contract every season. This assumption isn’t the case as the norm for NBA contracts is multi-year

oriented. Jenkins specifically looked at free-agent salaries over 12 years. By using players signing a new contract every year, a better fit is seen between salary and past performance. It was found that there is no significant difference in salary for black players, meaning that NBA free agency seems to be a level playing field for players. Methodology and Data In my research, I ran 1 base model to try and explain what factors affected the salaries of the NBA’s highest-paid players from 1984-2022. The salary of the highest-paid player per year was my dependent variable adjusting for inflation each year. The data used was a time-series regression from 1984-2022. The model and independent variables are listed below: Salary = B 0 + B 1 TeamWin + B 2 Points + B 3 Assists + B 4 Viewership Independent Variables: • Overall Team Win Percentage per year (TeamWin) –  This independent variable was used because having the highest-paid player in the league should indicate that you have one of the best players. Although it is a team sport, I assume having one of the best players in the league should translate to more team success.  • Average Points per Season (Points) –  Sigler & Sackley (2000) indicated that there is a positive relationship between higher salaries and performance on the court specifically mentioning points per game. With a higher salary, it was shown to have more points on average. Points serve as a big factor in a player’s success, the more points each player on a team puts the team in a better position to win. • Average Assists per Season (Assists) –  In a similar way to points, Sigler & Sackley also applies here as assists contribute to a player’s performance on the court. The difference here is how many points the player is generating for his teammates. This could also be an

For model 1 none of the independent variables were statistically significant. The overall results of the model don’t make much sense. TeamWin for example shouldn’t decrease the data and it has an extremely high coefficient when compared to the other independent variables. Assists was another independent variable that showed up being negative which doesn’t make sense that an increase in it would decrease salary. Adjusted R-squared was also extremely low at 0.026 indicating that the regression didn’t do a great job of fitting the data. OLS Violations            Since my analysis uses a time series data set the most prevalent concern when looking for OLS violations is autocorrelation. In Model 1 there were signs of autocorrelation and multicollinearity. When looking at the statistics provided with that model the Durbin Watson is extremely low at 0.5, no variables were significant, and some were negative which doesn’t make sense in the context of this model. 1st order autocorrelation is what the model had as Durbin Watson = 0.5 indicating that it was positive autocorrelation as well. I used the Breusch-Godfrey test to test for 1st order auto correlation, which confirmed the fact that autocorrelation is present in my model which you can see in Appendix 3. To fix this I used the AR-1 model as seen in Appendix 4 to mathematically achieve a Durbin Watson of 1.5 for the rest of my model which is the best case in this scenario. In addition to this, I added a linear time trend variable to help try to eliminate the autocorrelation present in the model.            After correcting the autocorrelation in the model, multicollinearity was the next issue to solve. The first aspect that was a tip-off was the fact that adjusted R-squared was 0.8 which is high while none of the independent variables were significant at 10 percent excluding the time trend variable, as seen in Appendix 4. Based on this, the two variables most likely to be related to each other were the variables Points and Assists. The correlation ended up being 0.8 as seen in

Appendix 6 which pointed me towards where the multicollinearity was coming from. The next step to eliminate the multicollinearity was to play around with the independent variables, TeamWin, Points, Assists, and Points. In Appendix 5 it is shown that I removed TeamWin from that model. Points and Assists have a higher p-value, so it doesn’t seem that TeamWin was significantly impacting the other variables. Viewership was the only statistically significant variable, none of the coefficients were negative, and the fixed Durbin Watson is at 1.4. The adjusted R-squared was at 0.79 meaning that it’s doing a pretty good job of explaining the data. The next model, as shown in Appendix 7, had TeamWin and points without Assists. Now the coefficient for Points is negative which doesn’t make sense in this model, but Viewership and Time are now statistically significant with the rest being like the previous model. Appendix 8 shows how it has the variable TeamWin without points or assists, which is comparable to Appendix 7 except for the fact that none of the independent variables’ coefficients are negative. The next model, Appendix 9, includes TeamWin and Assists without points. The only difference between this and the last model is that only viewership is significant now. Appendix 10 with Points but no TeamWin or Assist is again like the last model but instead time is the only significant variable. Appendix 11 with Assists and no TeamWin or Points has similar statistics as the previous models except for the fact that viewership and assists are both statistically significant which is the first time this happened across all models. Final Results Salary = 2.13 + 0.15 Viewership + 0.25 Time + 0.29 Assists Final Model results (See Appendix 7): Assists – For every additional assist by the highest paid player it increased salary by 0.29 keeping all other variables constant.

points per game. This experiment was not very conclusive. The data is clearly showing that the data simply doesn’t do a great job of representing the dependent variable. As time has gone on the NBA has gotten bigger as an entity and it seems that the simple fact here is that athletes just get paid more than they used to with almost no correlation to performance.            Explaining the increase in salary across 30-plus years is a complex issue that deserves to be explained. The methods of this paper were most likely not able to perform at that level, so I expected the conclusions drawn from this paper to be narrow. More advanced research techniques will be needed to narrow down the correct factors that are affecting player salaries. Discussion and Limitations            There were only 4 independent variables examined, there are many other variables that have the potential to explain the dependent, but some of the information needed for those more powerful variables, for example, NBA total revenue each year, was not available to me. Another aspect is more money doesn’t guarantee more success or more wins there are qualitative variables that go into that as well that weren’t looked at.

Works Cited Gough, C. (n.d.). Topic: Sports on TV . Statista. https://www.statista.com/topics/2113/sports-on- tv/#topicOverview Jenkins, J. A. (1996). A Reexamination of Salary Discrimination in Professional Basketball. Social Science Quarterly , 77 (3), 594–608. http://www.jstor.org/stable/42863504 Koster, J., & Aven, B. (2018). The effects of individual status and group performance on network ties among teammates in the National Basketball Association.   PloS one ,   13 (4), e0196013. https://doi.org/10.1371/journal.pone.0196013 NBA & ABA League index . Basketball. (n.d.). https://www.basketball-reference.com/leagues/ Published by                                    Statista Research Department, & 7, S. (2023, September 7). Highest paid NBA players each season 2023 . Statista. https://www.statista.com/statistics/1371735/nba-player-highest-salary-season/ Quinn, K. (2021). Sunk costs in the NBA: The salary cap and free agents.   Empirical Economics,   61 (6), 3445-3478. doi:https://doi.org/10.1007/s00181-020-01996-z Sale, M. L., & Hunter, D. R. (2009). NBA PLAYER: MONEY TREE OR MONEY PIT.   Academy of Strategic Management Journal,   8 , 81-86. Retrieved from

Appendix 1: Summary Statistics, using the observations 1984 - 2022 Variable Mean Median S.D. Min Max Salary 10.6 11.4 5.07 2.27 20.6 TeamWin 0.579 0.590 0.116 0.296 0.792 Points 23.0 22.9 5.16 8.20 32.0 Assists 5.14 5.00 2.74 1.10 12.6 Viewership 16.4 15.8 4.69 7.50 29.0 Appendix 2: Model 1: OLS, using observations 1984-2022 (T = 39) Dependent variable: Salary Coefficient Std. Error t-ratio p-value const 9.92239 5.56918 1.782 0.0837 * TeamWin −10.7319 7.79779 −1.376 0.1777 Points 0.249589 0.161634 1.544 0.1318 Assists −0.135518 0.322524 −0.4202 0.6770 Viewership 0.113714 0.177543 0.6405 0.5262 Mean dependent var 10.60821 S.D. dependent var 5.066949 Sum squared resid 849.7721 S.E. of regression 4.999330 R-squared 0.128984 Adjusted R-squared 0.026512 F(4, 34) 1.258724 P-value(F) 0.305213 Log-likelihood −115.4260 Akaike criterion 240.8521 Schwarz criterion 249.1699 Hannan-Quinn 243.8364 rho 0.749514 Durbin-Watson 0.493090 Appendix 3: Breusch-Godfrey test for first-order autocorrelation OLS, using observations 1984-2022 (T = 39) Dependent variable: uhat coefficient std. error t-ratio p-value -------------------------------------------------------------- const −2.62345 3.69227 −0.7105 0.4824 TeamWin 5.53416 5.20631 1.063 0.2955 Points −0.0567192 0.106894 −0.5306 0.5992 Assists 0.0938571 0.213089 0.4405 0.6625 Viewership~ 0.0193157 0.117084 0.1650 0.8700 uhat_1 0.785763 0.116842 6.725 1.16e-07 *** Unadjusted R-squared = 0.578144 Test statistic: LMF = 45.225690, with p-value = P(F(1,33) > 45.2257) = 1.16e-07 Alternative statistic: TR^2 = 22.547604, with p-value = P(Chi-square(1) > 22.5476) = 2.05e-06 Ljung-Box Q' = 22.78, with p-value = P(Chi-square(1) > 22.78) = 1.82e-06 Appendix 4: Model 2: Cochrane-Orcutt, using observations 1985-2022 (T = 38)

Dependent variable: Salary rho = 0.875748 Coefficient Std. Error t-ratio p-value const 9.20701 3.66595 2.511 0.0171 ** TeamWin 1.91774 3.27126 0.5862 0.5617 Points −0.00924228 0.0635222 −0.1455 0.8852 Assists 0.279444 0.181781 1.537 0.1338 Viewership 0.147982 0.0857751 1.725 0.0938 * Statistics based on the rho-differenced data: Sum squared resid 173.7589 S.E. of regression 2.294651 R-squared 0.808484 Adjusted R-squared 0.785269 F(4, 33) 1.707740 P-value(F) 0.171793 rho 0.254396 Durbin-Watson 1.471283 Statistics based on the original data: Mean dependent var 10.82421 S.D. dependent var 4.949647 Appendix 5: Model 3: Cochrane-Orcutt, using observations 1985-2022 (T = 38) Dependent variable: Salary rho = 0.791583 coefficient std. error t-ratio p-value ----------------------------------------------------------------- const 2.00455 4.81258 0.4165 0.6797 Viewership 0.155289 0.0879398 1.766 0.0867 * time 0.257682 0.164380 1.568 0.1265 Assists 0.292735 0.173131 1.691 0.1003 Points 0.00677020 0.0591254 0.1145 0.9095 Statistics based on the rho-differenced data: Sum squared resid 169.3331 S.E. of regression 2.265238 R-squared 0.813356 Adjusted R-squared 0.790733 F(4, 33) 2.176902 P-value(F) 0.093279 rho 0.268405 Durbin-Watson 1.446960 Statistics based on the original data: Mean dependent var 10.82421 S.D. dependent var 4.949647 Excluding the constant, p-value was highest for variable 3 (Points) Appendix 6: Correlation coefficients, using the observations 1984 - 2022

R-squared 0.807059 Adjusted R-squared 0.790035 F(3, 34) 2.889173 P-value(F) 0.049644 rho 0.216252 Durbin-Watson 1.559875 Statistics based on the original data: Mean dependent var 10.82421 S.D. dependent var 4.949647 Excluding the constant, p-value was highest for variable 2 (TeamWin) Appendix 9: Model 6: Cochrane-Orcutt, using observations 1985-2022 (T = 38) Dependent variable: Salary rho = 0.788042 coefficient std. error t-ratio p-value ----------------------------------------------------------------- const 0.869934 4.91548 0.1770 0.8606 Viewership 0.155190 0.0865737 1.793 0.0822 * time 0.272818 0.161608 1.688 0.1008 TeamWin 2.08134 3.04100 0.6844 0.4985 Assists 0.241668 0.187672 1.288 0.2068 Statistics based on the rho-differenced data: Sum squared resid 167.0367 S.E. of regression 2.249826 R-squared 0.815900 Adjusted R-squared 0.793584 F(4, 33) 2.343590 P-value(F) 0.075120 rho 0.268947 Durbin-Watson 1.446544 Statistics based on the original data: Mean dependent var 10.82421 S.D. dependent var 4.949647 Excluding the constant, p-value was highest for variable 2 (TeamWin) Appendix 10 Model 7: Cochrane-Orcutt, using observations 1985-2022 (T = 38) Dependent variable: Salary rho = 0.750986 coefficient std. error t-ratio p-value ----------------------------------------------------------------- const 1.91293 4.21379 0.4540 0.6527 Viewership 0.150781 0.0913016 1.651 0.1079 time 0.307313 0.139372 2.205 0.0343 ** Points 0.0138791 0.0616350 0.2252 0.8232

Statistics based on the rho-differenced data: Sum squared resid 183.3091 S.E. of regression 2.321948 R-squared 0.797903 Adjusted R-squared 0.780071 F(3, 34) 2.320848 P-value(F) 0.092680 rho 0.190218 Durbin-Watson 1.613354 Statistics based on the original data: Mean dependent var 10.82421 S.D. dependent var 4.949647 Excluding the constant, p-value was highest for variable 3 (Points) Appendix 11: Model 8: Cochrane-Orcutt, using observations 1985-2022 (T = 38) Dependent variable: Salary rho = 0.791997 coefficient std. error t-ratio p-value ----------------------------------------------------------------- const 2.13052 4.63696 0.4595 0.6488 Viewership 0.156724 0.0857308 1.828 0.0763 * time 0.258113 0.162215 1.591 0.1208 Assists 0.294017 0.170256 1.727 0.0933 * Statistics based on the rho-differenced data: Sum squared resid 169.4003 S.E. of regression 2.232120 R-squared 0.813272 Adjusted R-squared 0.796796 F(3, 34) 2.981213 P-value(F) 0.044928 rho 0.271127 Durbin-Watson 1.441517 Statistics based on the original data: Mean dependent var 10.82421 S.D. dependent var 4.949647 Excluding the constant, p-value was highest for variable 6 (time) Web Links to Data: https://www.basketball-reference.com/leagues/ https://www.nba.com/stats/teams/clutch-traditional https://www.statista.com/statistics/1371735/nba-player-highest-salary-season/ https://www.statista.com/topics/2113/sports-on-tv/#topicOverview https://www.statmuse.com/