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The Effects of Salary Cap Spikes on Free Agent Spending in the NBA

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The Effects of Salary Cap Spikes on Free Agent Spending in the NBA
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Lann, Steven Alexander
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After the adoption of a new national television deal, the NBA's salary cap jumped by 34% during the 2016 offseason. This massive year-over-year increase resulted in a free agent spending spree, which has led many NBA analysts and fans to believe that players signed that summer were "overpaid" relative to comparable players in previous years. This paper seeks to test this observation by analyzing a sample of 308 new free agent contracts from 2014 to 2018. A multivariate regression was run using a dummy variable for the jump year while controlling for time effects, player position, team, and player performance. The results show a significant, positive relationship between the dummy and the relative size of contracts, implying that players signed during the cap spike were paid more than players in other years, controlling for the above factors. ( en )
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Awarded Bachelor of Arts, summa cum laude, on May 8, 2018. Major: Economics
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College or School: College of Liberal Arts and Sciences
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Advisor: Michelle Phillips. Advisor Department or School: Economics

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Copyright Steven Alexander Lann. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.

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The Effects of Salary Cap Spikes on Free Agent Spending in the NBA Steven Lann University of Florida Abstract 2016 offseason. This massive year over year increase resulted in a free agent spending spree, which has led many NBA analysts and fans to believe that playe rs signed that summer were overpaid relative to comparable players in previous years. This paper seeks to test this observation by analyzing a sample of 308 new free agent contracts from 2014 to 2017. A multivariate regression was run using a dummy varia ble for the jump year while controlling for time effects, player position, team, and player performance. The results show a significant, positive relationship between the dummy and the relative size of contracts, implying that players signed during the cap spike were paid more than players in other years, controlling for the above factors.

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Introduction Before the start of the 2016 2017 season the National Basketball Association entered the first year of a new national television deal worth $24 billion over nine years. Since the players are entitled to half of the related income this new deal resulted in salary cap, from $70 million in the 2015 16 season to $94.1 million. This 34% year over year jump led to a record spending spree during the summer of 2016, with teams and free agents agreeing to $2 billion in new contracts in the fir st two days of free agency alone In the following year many NBA analysts, media members and fans have been critical of the size of contracts given to mid level, non star players, with the pervasive attitude being that many of these players were overpaid given their skill level and past performance. T his paper seeks to investigate empirically whether free agents in the summer of the cap jump were overpaid relative to free agents in other years and what this suggests about the behavior of NBA teams. Historically, economic analysis of NBA salaries has most heavily invo lved testing for discrimination equal labor market (Dey, 1997; Jenkins, 1996) research on the earnings of NBA players slowed down. Recently, studies inv olving the determinants of NBA salaries have been focused on more varied factors such as being foreign born (Yang and Lin, 2010), consistency of performance (Deutscher, Grtler, Prinz and Weimar, 2016), and player reputation and status (Ertug and Castelucc i, 2013). The major interest of this paper, the currently unstudied 2016 salary cap spike, provides a unique opportunit y to contribute to the growing body of new research on NBA salaries. Sample The sample being used consists of 308 new contracts from 2014 to 2017. This sample only includes contracts above The sample includes 238 players, with many of them signing multiple contracts in this four year span. Undrafted free agents and newly signed players from oth er professional leagues are omitted, as there is little to no relevant data on their past performance Dependent Variable First Year Contract Value as a Percent of the Salary Cap (C ontract Percent ) : The dependent variable is the value of the first year of each newly signed contract as a percent of that The total value of each contract was not used because c omparable players often agree to contracts of different lengths due to player or team preferences or for strategic reasons. This anal ysis

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only focuses on the i mmediate effects of a free agency decision, i.e. the value of the new contract in the upcoming year. Independent Variables Cap Jump (JUMP) : This is a dummy variable denoting if a player signed a contract during the summer of the cap jump (2016). The key focus of this paper is to test the significance and effect of this variable on the value of new contracts. The hypothesis here is that this variable will have a significant and positive effect, meaning that players signed in the su mmer of 2016 were paid more than players signed in other years, controlling for factors explained below. Year (YEAR) : related income, and usually increases by seven to ten percent each year. As a result, NBA salaries naturally rise over time, and newly signed contracts will be expected to increase every year. It is necessary to include this variable in order to separate the se time effect s from the effects of the one year jump. This variable is exp ected to have a significant and positive coefficient for the above reasons. Player Age (AGE) and Age Squared (AGE 2 ) : While the age of a free agent will obviously be a factor in determining how much they are offered, it is unclear what the effect is. Whil e some young players are paid handsomely based o n their potential to improve, others are paid less because of their inexperience and uncertainty regarding their development. There are similar ambiguities for older players because of survivorship effects. Some older players are offered less because of declining athleticism or injury concerns but only the best NBA players are able to have long careers, so others are still paid highly as they near retirement. While this study predicts that a ge and age square d will be significant variable s in determining contract sizes, a prediction will not be made about the sign of th ese variable s Position (GUARD, FORWARD, CENTER) : Basketball players can be grouped into three relatively broad positions based on ascending o rder of size: guards, forwards, and centers. In basketball, u nlike in other sports such as football, each position is on the court for both o ffense and defense This means that while play styles and skillsets can vary greatly betw een the positions, each is of roughly the same

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in determining the value of each position. It is still necessary to c ontrol for the position of each free agent, as this variable would be expected to capture some of the variance in contract values. Team Signed With : Dummy variables representing each NBA team are included to control for differences in negotiation ability among teams. Some teams have reputations for being strong negotiators, while others are known for overpaying players. Like Position, this study does not make any prediction regarding the significance and sign of these variables. Games Played (G) : This variable measures the number of games played by each free agent in the previous season. Since rotation players are expected to play every game when healthy, a high number of games played (i.e. approaching 82 games) most likely would not result in a la rger contract. However, a low number of games played in the previous season could indicate injury and durability concerns, making a low games player less valuable. It is predicted that this variable will have a positive sign but may or may not be significant. Minutes p er Game (MP) : This variable represents the amount of playing time each free agent received in the previous season. Since every basketball player plays on both offense and defense, better players will generally be p layed more than worse players. Thus, it is easily assumed that players who play more minutes per game are better and more valuable than players earning fewer minutes. Based on this assumption, this variable is expected to be significant and positive. Perf ormance Measures (OBPM, DBPM) : Two measures of player performance, Offensive and Defensive Box Plus/Minus during the year before free agency are used here. These metrics represent how well a team performs on offense and defense when a given player is on the court. A player with a positive OBPM or DBPM value causes their team to perfo rm better on offense or defense, respectively, when they are on the court. Th ese measures take into ir opponents, and league wid e performance, making it a robust statistic The league average OBPM and DBPM is 0, meaning that an the floor. The best OBPM from the 2016 17 season in this sample, for example, is 7.8, while the worst is 4.1. The best and worst DBPMs from the 2016 17 season in the sample are 3. 7 and 3.4, respectively.

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Box Plus/Minus stats are not calculated based on minutes played, so they can be used along with Minutes per Game to measure player value and performance. Intuitively, players with high O/DBPMs sh ould be better than players with l ower O/DBPMs, so they should also be worth more. These variables are both expected to be significant and positive. Counting stats such as points, rebounds, and assists were not used to measure performance Yang and Lin (2010) used these stats along with minutes to measure performance, but this resulted in only points per game being significant The insignificance of the other stats is a result of multicollinearity between counting stats and minutes played. In addition, some stats are more important for so me positions/roles than others, which needlessly complicates the analysis. Minutes and Box Plus/Minus alone should be court value.

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Summary Statistics More detailed statistics can be found in the appendix MEAN STANDARD ERROR MEDIAN STANDARD DEVIATION MINIMUM MAXIMUM CONTRACT % 0.1096 0.0045 0.0841 0.0784 0.0164 0.3561 JUMP 0.3084 0.0264 0 0.4626 0 1 YEAR 2015.4805 0.0602 2016 1.0568 2014 2017 AGE 28.6721 0.2134 28 3.7460 22 40 GUARD 0.4156 0.0281 0 0.4936 0 1 FORWARD 0.4383 0.0283 0 0.4970 0 1 CENTER 0.1461 0.0202 0 0.3538 0 1 G 67.7143 0.7666 72 13.4531 19 83 MP 24.6052 0.3825 24.6 6.7134 7 38.7 OBPM 0.0036 0.1178 0.2 2.0673 5.9 8 DBPM 0.0117 0.0945 0 1.6584 3.9 4.8 Standard deviations of the team dummy variables: Variable Team Standard Deviation t16 MIA 0.24098 0 t17 MIL 0.138431 t18 MIN 0.149275 t19 NOP 0.185879 t20 NYK 0.20139 0 t21 OKC 0.138431 t22 ORL 0.185879 t23 PHI 0.126579 t24 PHX 0.177527 t25 POR 0.168699 t26 SAC 0.193817 t27 SAS 0.208638 t28 TOR 0.20139 0 t29 UTA 0.138431 t30 WAS 0.215593 Variable Team Standard Deviation t1 ATL 0.193817 t2 BKN 0.159317 t3 BOS 0.168699 t4 CHA 0.177527 t5 CHI 0.168699 t6 CLE 0.185879 t7 DAL 0.20139 0 t8 DEN 0.126579 t9 DET 0.215593 t10 GSW 0.185879 t11 HOU 0.177527 t12 IND 0.159317 t13 LAC 0.185879 t14 LAL 0.177527 t15 MEM 0.168699

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Change in selected variables over time: Graphs showing the change over time for each of these statistics can be found in the appendix Regressions Model 1: This regression will be the main model of interest, and the one that will be analyzed most in the results section of the paper Model 1 is a log linear model, which means that the coefficients of the independent variables will denote percent changes in the dependent variable rather than absolute changes. The model will include every variable listed above, including the thirty dum my variab les representing each NBA team. This model uses robust standard errors. Guards, Forwards, and Centers: For these three regressions, the players in the sample were grouped by position and Model 1 was run for each. GUARD, FORWARD and CENTER were ex cluded from these regressions. The number of observations for Guards, Forwards and Centers were 128, 135, 45, respectively. These three r egressions were run to see how each variable affects players by position. Like Model 1, these three regressions use robust standard errors. 2014 2015 2016 2017 GUARDS 29 32 40 27 FORWARDS 36 33 36 30 CENTERS 6 15 19 5 TOTAL 71 80 95 62 MEDIAN CONTRACT PERC ENT 0.067391 0.082579 0.097862 0.080409 MEAN AGE 28.91549 28.0625 28.65263 29.20968 MEAN GAMES PLAYED 66.49296 69.8625 67.06316 67.33871 MEAN MINUTES PLAYED 25.46197 24.83125 23.48632 25.04677

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Results Regression Outputs: Model 1 Guards Forwards Centers ln Contract Percent ln Contract Percent ln Contract Percent ln Contract Percent YEAR 0.0619* 0.0945* 0.053 0.261 (2.430) (2.420) (1.380) (1.580) JUMP 0.167** 0.166 0.200* 0.164 (2.600) (1.770) (2.000) (0.720) GUARD 0.387*** ( 3.56) FORWARD 0.234* ( 2.47) AGE 0.013 0.048 0.013 0.359 ( 0.13) (0.350) (0.070) (0.870) AGE 2 0.000 0.001 0.001 0.005 ( 0.07) ( 0.42) ( 0.29) ( 0.68) G 0.002 0.001 0.006 0.004 (0.930) ( 0.27) (1.490) ( 0.45) MP 0.0632*** 0.0638*** 0.0654*** 0.0724*** (12.550) (7.410) (7.110) (7.120) OBPM 0.0822*** 0.0808** 0.0769* 0.027 (4.480) (2.700) (2.320) (0.550) DBPM 0.0533** 0.0959* 0.035 (0.064) (2.760) (2.380) (1.300) ( 0.96) _cons 128.1* 196.0* 109.500 536.700 ( 2.49) ( 2.48) ( 1.42) ( 1.63) N 308 128 135 45 R 2 0.641 0.697 0.737 0.966 Adjusted R 2 0.588 0.577 0.637 0.866 t statistics in parentheses p < 0.05, ** p < 0.01, *** p < 0.001 Outputs for the team dummies can be found in the appendix

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Model 1 has an R squared of 0.641 and an adjusted R squared of 0.588, which indicates that the regression has too many variables. Year: The variable YEAR was found to be significant at the 95% confidence level. The coefficient of 0.06 2 means that an increase in this variable of one (or each year that passes) results in a 6. 2 percent increase in the size of contracts as a percent of the salary cap. This supports the hypothesis that YEAR would have a significant and positive relationship on Contract Percent. Jump: The variable JUMP was found to be significa nt at the 99% confidence level. The coefficient can be interpreted to mean tha t contracts signed during the jump year were 16.7% larger in terms of percentage of cap compared to contracts signed in other years. This is the most important result of this study, as it conclusively shows that players signed in 2016 received relatively l arger contracts than players in other years controlling for other factors. Age and Age Squared : AGE and AGE 2 were found to not be significant. This was not the predicted result, and it shows that there is neither a linear nor nonlinear relationship between player age and size of free agent contracts. As mentioned in section IV, there is a high level of variance in the size of contracts for players of all ages, so this may be the reason for this result. Guard and Forward: The variables GUARD and FORW ARD were found to be significant at the 99.9% and 95% levels, respectively. Both variables have negative signs, which means that centers would be expected to sign larger contracts than guards or forwards. This can be easily explained as a result of scarcit y; centers are generally the tallest players on the court, and since extremely tall players are rare, they will be more highly valued than shorter players. Games Played: As predicted, G was not significant and had a very small, positive coefficient. This result is consistent with the intuition described in section IV and can be seen in the summary statistics for this variable. The median games played was 72, and the mode (see appendix) was 81. Since most players in this sample

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played nearly every game, sim ply appearing in as many games as possible will not make a free agent more valuable. Minutes Played: With a t statistic of 12. 55 the variable MP was strongly significant at the 99.9% confidence level. The coefficient of 0.06 3 me ans that a n increase of one minute per game results in a 6.3 percent larger contract value when it comes to free agent contracts. Offensive and Defensive Box Plus/Minus The variables OBPM and DBPM were significant at the 99.9% and 99% levels, respectively. OBPM had a larger coefficient than DBPM, which implies that offense performance is more highly val ued than defensive performance. Similar to the intuition behind the re sult of the position variables, this result can be explained by scarcity. Great offensive players are rarer than great defenders, so are more highly valued. In addition, due to the nature of the sport, an elite offensive player generally has a greater impa ct on winning than an elite defender, so will be considered more valuable. Conclusions The results of this study support the hypothesis that players signed in the 2016 offseason were paid more as a percentage of the salary cap than players in other years. This is consistent with the observations made by fans, media members and team executives The cap sp i ke and consequent spending spree had a chilling effect on the free agent market in 2017 with mid level free agents receiving significantly smaller contracts than in the previous summer. This is shown by the median contract value dropping from 0.0979% of the salary cap in 2017 to 0.0804% in 2017. According to ESPN reporter Tim McMahon, 27 teams had cap space entering free agency in 2016, but o nly 14 had cap space in 2017 Only nine teams are projected to have cap space next offseason, showing the lasting impact of the contracts given out in 2016. On the players' side, the winners of the cap spike were players who were free agents in 2016, while the losers a re the mid level free agents in consequent years. On the other hand, the s curse is clearly present in this situation as teams who signed free agents for a large share of the ir cap space in 2016 are encounter ing problems signing players in future offseasons. If this outcome is deemed to not be in the best interest of the NBA or the players, a potential solution would be to implement cap smoothing. This plan, which involves a gradual increase in the salary cap over a period of three to four years, was originally

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proposed by the NBA before the new TV deal took effect. The NBA player's union declined smoothing in favor of the one time increase but perhaps in the futur e the union will reconsider this plan This paper provides evidence that when given a large increase in budget size, NBA front offices will respond by paying players more than would be expected given their age, position and performance. It is important to note that the NBA has a salary floor, meaning each team must spend at least 90% of the salary cap each year While this will explain some of the increase in contract sizes, many teams spent f ar more than this floor, some ending the 2016 offseason far above the years, this does not necessarily mean that the players were paid more than the 51% share of basketball related income that they are entitled to. Data on BRI and total expenditures on players, including benefits, is not publicly available, so it would be difficult to test this assertion. In any case, there are measures put in place b y the CBA to prevent the players from receiving more than 51% of BRI in any given year, so In seeking to explain why teams would spend more than they needed to, i t is important to consider the i ncentives front office personnel face when making roster building decisions. Many team owners mandate that their teams be competitive every year, which may lead executives to overspend on potential impact players in order to keep their jobs. On the other h and the NBA has a revenue sharing system that redistributes the revenue from profitable teams to struggling ones. This system may subsidize reckless spending by general managers as moves that worsen team performance (and thus revenues) are less impactful financially due to revenue sharing. More research on the incentive structure faced by NBA front offices is needed in order to help explain the results of this study. There are a few omitted factors that could have unaccounted for effects on the results of this study. There were significantly more free agents in the summer of 2016 than in previous years The sample contains 95 non minimum free agents from 2016, while the next highest year was 2015 with just 80 free agents. Teams, players and agent s knew of the cap spike two years before it would happen, allowing for strategic maneuvering by both sides leading up to the summer of 2016. Each party had a strong incentive for there to be as many free agents as possible that offseason, and the spike bei ng an expected occurrence is difficult to factor in to the analysis. There are also concerns with the accuracy of Defensive Box Plus/Minus. While DBPM generally matches with good defensive reputations have higher DBPMs

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than worse defenders), defense is notoriously difficult to quantify in basketball. In addition, an important omitted variable is the length of each new contract. Teams might be more willing to sign players for a greater per year amount if the contract is shorter, and vice versa. Excluding this variable means that the Going forward, this study could be improved upon by increasing the number o f observations. This could be accomplished by using f ree agency data from more years prior to 2014. Other variables such as contract length could be added extraneous variables could be identified and removed, and more work could be done on finding a bette r defensive metric. As it stands, this study provides new insights into the decision making of NBA front offices, and leaves room for future iterations and improvements.

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References 1. NBA Transactions. (n.d.). Retrieved Aug. & sept., 2017, from http://www.spotrac.com/nba/transactions/all/signed free agent/ 2. NBA & ABA Player Directory. (n.d.). Retrieved Aug. & sept., 2017, from https://www.basketball reference.com/players/ 3. MacMahon, T., & Marks, B. (2017, July 27). Next summer could be the wrong time to be an NBA free agent. Retrieved October 02, 2017, from http://www.espn.com/nba/story/_/id/20143724/nba nuclear winter forecasted free agents summer 2018 4. Golliver, B. (2016, July 2). NBA announces record salar y cap for 2016 17. Retrieved November 30, 2017, from https://www.si.com/nba/2016/07/02/nba salary cap record numbers 2016 adam silver 5. Yang, C., & Lin, H. (2010). Is There Salary Discrimination by Nationality in the NBA? Journal of Sports Economics, 13 (1), 53 75. doi:10.1177/1527002510391617 6. Deutscher, C., Grtler, O., Prinz, J., & Weimar, D. (2016). The Payoff To Consistency In Performance. Economic Inquir y, 55 (2), 1091 1103. doi:10.1111/ecin.12415 7. Ertug, G., & Castellucci, F. (2012). Getting What You Need: How Reputation and Status Affect Team Performance, Hiring, and Salaries in the NBA. Academy of Management Journal, 56 (2), 407 431. doi:10.5465/amj.2010 .1084 8. Dey, M. S. (1997). Racial Differences in National Basketball Association Players Salaries: A New Look. The American Economist, 41 (2), 84 90. doi:10.1177/056943459704100211 9. Jenkins, J. A. (1996). A Reexamination of Salary Discrimination in Professio nal Basketball. Social Science Quarterly, 77 (3), 594 608. Retrieved from http://www.jstor.org/stable/42863504

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Appendix Expanded summary statistics: ContractPercent JUMP YEAR AGE GUARD FORWARD Mean 0.109626 0.308442 2015.481 28.67208 0.415584 0.438312 Standard Error 0.00447 0.026359 0.060218 0.213446 0.028127 0.028318 Median 0.08412 0 2016 28 0 0 Mode 0.030783 0 2016 27 0 0 Standard Deviation 0.078443 0.462602 1.056827 3.745955 0.493624 0.496987 Sample Variance 0.006153 0.214 1.116883 14.03218 0.243665 0.246996 Kurtosis 0.325797 1.3137 1.21137 0.050761 1.89383 1.95027 Skewness 1.099403 0.833592 0.0235 0.666266 0.344259 0.249872 Range 0.339723 1 3 18 1 1 Minimum 0.016386 0 2014 22 0 0 Maximum 0.356109 1 2017 40 1 1 Sum 33.76476 95 620768 8831 128 135 Count 308 308 308 308 308 308 CENTER G MP OBPM DBPM Mean 0.146104 67.71429 24.60519 0.00357 0.011688 Standard Error 0.020159 0.766563 0.382533 0.117798 0.094495 Median 0 72 24.6 0.2 0 Mode 0 81 32.9 0.5 0.7 Standard Deviation 0.353785 13.45312 6.71343 2.06734 1.658379 Sample Variance 0.125164 180.9865 45.07014 4.273896 2.750221 Kurtosis 2.06839 1.344857 0.83126 1.869798 0.21448 Skewness 2.013703 1.29326 0.05841 0.756447 0.238078 Range 1 64 31.7 13.9 8.7 Minimum 0 19 7 5.9 3.9 Maximum 1 83 38.7 8 4.8 Sum 45 20856 7578.4 1.1 3.6 Count 308 308 308 308 308

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Outputs for team dummies: Model 1 Guard Forward Center t1 0.265 0.755** 1.052** 0.634 ( 1.89) (3.010) ( 2.82) (2.170) t2 0.151 0.679** 0.979** 1.544** ( 0.84) (2.720) ( 2.67) (4.110) t3 0.006 1.160*** 0.903* 1.081** 0.040 (5.050) ( 2.14) (3.260) t4 0.415* 0.574* 0.983* 0.000 ( 2.52) (2.390) ( 2.25) (.) t5 0.305 0.600* 0.905* 0.000 ( 1.66) (2.310) ( 2.27) (.) t6 0.365 0.509 1.116* 1.776*** ( 1.66) (1.640) ( 2.38) (5.820) t7 0.219 0.736** 0.785* 0.399 ( 1.16) (2.820) ( 2.06) (0.590) t8 0.000 1.051*** (0.798) 0.000 (.) (5.810) ( 1.89) (.) t9 0.247 0.740* 0.900* 1.044* ( 1.36) (2.280) ( 2.09) (2.820) t10 0.356 1.028*** 1.217** (0.704) ( 1.53) (4.770) ( 2.89) ( 1.24) t11 0.400* 0.812*** 1.258** 0.096 ( 2.39) (3.480) ( 3.31) (0.200) t12 0.218 0.822*** 0.945* 0.229 ( 1.44) (3.800) ( 2.58) (0.590) t13 0.285 0.870** 1.258** 1.423** ( 1.53) (2.750) ( 3.02) (4.140) t14 0.158 0.927** 1.427** 1.468*** ( 0.75) (3.270) ( 3.25) (6.300) t15 0.177 1.047*** 1.182** 1.286** ( 0.98) (5.400) ( 2.67) (3.570) t16 0.146 0.662* (0.813) 1.038* ( 0.87) (2.240) ( 1.93) (2.600) t17 0.005 0.877** 1.034* 1.485***

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( 0.02) (3.360) ( 2.24) (4.800) t18 0.102 0.735** 0.000 (0.177) ( 0.41) (3.380) (.) ( 1.45) t19 0.331 0.487 1.057* 1.079** ( 1.61) (1.470) ( 2.00) (3.410) t20 0.052 0.962*** 0.985** 1.195* ( 0.40) (4.550) ( 2.68) (2.790) t21 0.276 0.547 1.202* 1.749** ( 1.23) (1.480) ( 2.60) (3.730) t22 0.145 1.119*** 0.798* 1.802*** (0.880) (4.050) ( 2.11) (9.280) t23 0.169 1.156*** (0.581) 0.000 (0.850) (4.030) ( 1.52) (.) t24 0.160 0.913*** 0.978* 0.845 ( 1.07) (3.860) ( 2.43) (2.060) t25 0.042 0.000 0.763* 0.896* ( 0.23) (.) ( 1.98) (2.370) t26 0.094 0.843*** 0.985* 1.898*** ( 0.53) (4.430) ( 2.06) (13.270) t27 0.110 0.895** 0.759* 0.267 ( 0.65) (3.000) ( 2.00) (1.270) t28 0.189 1.036*** 1.098** 1.019* ( 1.14) (3.600) ( 2.76) (2.810) t29 0.339 0.000 1.153** 0.000 ( 1.60) (.) ( 2.93) (.) t30 0.174 0.701** 0.813* 0.973** ( 1.12) (2.650) ( 2.13) (4.270)

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Change in selected variables over time: 29 32 40 27 0 10 20 30 40 50 2014 2015 2016 2017 Guards by Year 36 33 36 30 0 10 20 30 40 2014 2015 2016 2017 Forwards by Year 6 15 19 5 0 5 10 15 20 2014 2015 2016 2017 Centers by Year 71 80 95 62 0 20 40 60 80 100 2014 2015 2016 2017 Total Players by Year 0.0674 0.0826 0.0979 0.0804 0 0.05 0.1 0.15 2014 2015 2016 2017 Median Contract Percent by Year 28.9155 28.0625 28.6526 29.2097 0 5 10 15 20 25 30 35 2014 2015 2016 2017 Mean Age by Year 66.4930 69.8625 67.0632 67.3387 0 20 40 60 80 2014 2015 2016 2017 Mean Games Played by Year 25.46197 24.83125 23.48632 25.0468 0 5 10 15 20 25 30 2014 2015 2016 2017 Mean Minutes Played by Year