Exploring Questions Surrounding Player Contracts in the NBA

Transcription

1 Exploring Questions Surrounding Player Contracts in the NBA Alec Strauss December

2 Introduction An article written by Cork Gaines discusses why Kevin Garnett is the highest paid player in NBA history. Throughout Garnett s career he happened to sign contracts a the perfect times. The summer after he won an MVP he signed a contract. The summer after he won a NBA championship he signed a contract. These and other various factors allowed for Kevin Garnett to make the most money by a player in NBA history. Reading about these circumstances brought up the question of what are the factors that affect how athletes get paid. It is difficult to compare athletes because there are so many various factors. In order to account for all of these factors a single statistic to compare all players would be created. A productivity equation was the answer, and linear regression models will be the tools used to create this statistic. With the idea of how to compare players, obtaining the data was the next step. Finally the most rewarding part of this process came from analyzing the data and seeing the results. But first, I will discuss all of these in further detail beginning with the productivity equation. 1 2 Productivity P roductivity = (X 1 X 1 ) cor(sal., X 1 ) + ( X 2 X 2 ) cor(sal., X 2 ) + (X n X n ) cor(sal., X n ) Above is the formalization of the productivity equation. It combines a few different methods. First there is an if then statement that is not explicitly stated. A player is productive if they are better than average, and they are not productive if they are worse than average. X 1 is used when it is productive to be better than average. Examples of these statistical categories are points per game, rebounds per game, steals per game, and so on. X 2 comes into play when it is productive to be worse than average. Examples of this are turnovers, field goals attempted per game, fouls, and so on. Once the players stats are compared to average they are weighted using linear weights. In order to make sure that everything does not have the same importance, they are weighted by their correlation with salary. Points per game is much more important than blocks per game, and the equation accounts for this. Variables that cannot be controlled by the player do not go into the equation, however they are entered into the model to see how well productivity explains the variation in salary. Variables that fall into this category are age, the number of years a player has played in the NBA, these were the only two of these. 1 An index of abreviations is at the end of the paper 2 All regression results presented are significant at the five percent level 2

3 Data The ideal situation was that all of the data was all ready accessible and no edits would be necessary. However this was not the case. Sean Lahman did have a lot of data. In fact he had data on all players from the 1940s to Data from basketball-reference.com was used in order to fill in the gap form 2010 to The players contract data was obtained from spotrac.com. This website has all of the yearly salaries and the structure of each players contracts. In order to correctly analyze why a NBA player gets paid what they do, their previous data has to be analyzed against their current salary. This data was not easily available, so the process of creating the data set began. Below is a table that exemplifies what each observation is. Player ID YoPoC LoNC Team SPY MPG PPG efgpct KDurant GSW 27,137, LJames CLE 15,095, MConley MEM 30,521, SO Neal LAL 29,500, This table is a simplified version of the 550 plus observations and 30 plus variable in the dataset. To begin there is the player ID this is just used in the graphs to easily figure out specifically what each point is representing. It is the players first letter of their first name, their whole last name, and the year they signed their new contract. Next is YoPoC, or years of play on contract. This is representative of the time between their contract signings, and for example Shaquille O Neal s statistics are seven year averages, and Mike Conley s are five year averages and so on. LoNC is length of new contract, which represents how long their new contract is. Then there is the team they signed their new contract with, salary per year, minutes per game, points per game, and effective field goal percentage. The rest of the variable for an observation are just the in game statistics like the last three in the table. Along with this dataset, analysis of player contracts also came from a yearly player dataset. This dataset has all of the same variables, except each observation is for one season of a player. This data set is not used to analyze why players get paid, but instead to analyze if the are playing up to the standards of what is expected of them. The data had been collected and the analysis could begin, however before the results are presented here are the questions peeked this interest, and guided the whole process. 3

4 Questions to Explore The original and most important question explored is, what element go into a players contract? Why do players get paid what they get paid? This question yielded some interesting results, which will be presented in detail further on in this paper. Another question that will be discussed later on is who is underpaid, and who is overpaid. This question came about from the analysis of the results. It was not initially a question of interest, however the answers to it became very interesting, and therefore it will be discussed. This process began with the assumption that player contracts increased each season at a fixed rate of 5%. This assumption created the question of, do players deserve a 5% increase each year? Is their play reflective of that pay increase? Or should players receive a different rate of increase, or even a decrease? However a realization quickly came to be, the assumption of a fixed increase was wrong. Players actually are paid based on a total salary. During contract negotiations teams and players discuss how long the player will be under contract, and how much, in total, the player will receive. Teams will set the rate of increase, decrease, or no-change based on their need to stay under the salary cap. Even though the specific question was not answered. An interesting result pertaining to how players get paid came to fruition, which was exciting, and heightened the excitement and interest for further answers even more. The final two topics are quite related, do players play well during the season that their contract is ending, and do players slump the year after they sign a contract? These two question are explored later in the paper as well. Here are the results. Process All of the variables were entered into a best subset analysis model. From there the best regression model was used to calculate each players productivity. Once the productivity was obtained it was regressed back upon the yearly salary to see how effective it is in predicting the variation. It was quickly obvious that the model could be improved, and to begin doing this an analysis of each individual position began. To analyze whether or not players slump or play better a players productivity is used to compare them to league averages and their personal averages. Also just looked at specific statistics to give a more complete answer. Here are the results. 4

5 Results All Players To begin the analysis, the productivity statistic for all players in the data set was developed. SP Y = 7, 477, ( 1, 431, 834)(P F P G) + 868, 252(P P G) + 1, 153, 293(DRBP G) + 2, 225, 703(2P P G) + ( 1, 546, 620)(2P AP G) + ( )(Age) + 47, 636(GP Y ) Variable std error t-stat Intercept 1,608, PFPG 414, PPG 85, DRBPG 168, PPG 641, PAPG 326, Age GPY 15, n 550 R Adjusted R The results from above seem to indicate that the dataset has outliers. Down in the lower left hand side of the graph there are a lot of data points that do not appear to fit the line. Running a test for outliers proved that there were indeed 31 outliers, after removing the outliers from the data set the results were as follows. The figure on the next page shows a much better fit around the line. The R 2 does fall from 0.56 to 0.51, but all the data points fit the line now, so it seems like a better predictor. The R 2 probably fell from having fewer data points. There are also fewer variables in the model, so less things to explain the variation in salary. With these two factors considered it is the case that the model without the outliers is a better predictor of all players salary. 5

6 SP Y = 7, 739, , 546(P P G) + 1, 025, 198(DRBP G) + 2, 199, 340(2P P G) + ( 1, 603, 432)(2P AP G) + ( 372, 449)(Age) Variable Std error t-stat Intercept 1,430, PPG 89, DRBPG 165, PPG 685, PAPG 349, Age 47, n 519 R Adjusted R The graph from above was obtained from the productivity model on the right. The R 2 drops which is to be expected because there are fewer variables in this model. However it is a very low R 2. This model is a representation of all players. There are five positions in basketball, and they are not asked to do the same thing. A center is asked to SP Y = 18, 077, , 816(P rod) +( 326, 512)(Age) Variable Std. error t-stat Intercept Prod 40, Age 51, n 519 R Adjusted R protect the rim, block shots, while a point guard is asked to distribute the ball, get assists. Knowing this it may help to analyze each position individually, since they do not play the same way, they are probably not paid for the same reasons. Point guards will be the first position analyzed. 6

7 Point Guards SP Y = 7, 735, , 018(P P G) + 1, 924, 377(DRBP G) + ( 413, 552)(Age) The model to the right is the best model of the point guard data, this is known from the regression analysis. Below is the plot of salary versus productivity for point guards, and the model for productivity and age regressed against salary. The point guard results do not improve much from the all player results. In fact this is the second worst of Varibale Std. error t-stat Intercept 3,016, PPG 111, DRBPG 599, Age 96, n 104 R Adjusted R the five position models. This reason for this could be the extreme variation in play styles of point guards. Some point guards are strictly offensive, they will score a lot and get a lot of assists. Other point guards are solely pass first and are fairly good at defense. Then there are combinations of these that some players play with. With all of these variations in play styles it is reasonable to believe that this model is not the best predictor. Changes will be discussed later on in the future aspirations section of the paper. But for the scope of this paper it was not possible to attempt to better the model any further. SPY = 17,870, ,086,288(Prod) + (-376,894)(Age) Variable Std. error t-stat Intercept 2,728, Prod 125, Age n 104 R Adjusted R This graph still gives answers as to who is overpaid and underpaid. Mike Conley is the most overpaid player of all time after he signed the largest contract of all time. Down towards the bottom right Allen Iverson is quite underpaid because this was towards the end of his career when he was signing a contract for veterans minimum just so he could play basketball. The other interesting thing to take away from this graph is that all of the score first point guards are towards the right or high end of productivity, and the 7

8 pass first point guards are lost in the middle. More evidence to show that the model may need to take into account the play style of players. Shooting Guards lnspy = (PPG) + ( )(Exp.) (GPY) Shooting guards had the worst model. There were some problems with multicollinearity has well as a lot of variation in the data. This position was to only position where taking the log of salary was necessary to yield reasonable results. Again on the right is the model from the best subset regression Variable Std. Error T-Value PPG Experience GPY n 117 R Adjusted R analysis, and below is the plot of productivity versus salary and the model of productivity and age versus salary. It is likely that the shooting guard is week because of the variation in play styles once again. However shooting guards very much more than point guards. There are some shooting guards who are straight shooting guards and their purpose is to shoot the ball at a high percentage. The rest however either play like small forwards or like point guards. Later on a graph will show how different point guards and small forwards are. Thus if shooting guards are combinations of small forwards and point guards the variation in them is immense and understandable for why the model is so weak. Once again it was not possible given the scope of this paper to analyze this assumption, and hopefully it will be explored in the future. lnspy = (Prod) Variable Std. Error T-Value Productivity n 107 R Adjusted R Experience is not put into the equation for finding a players productivity because the player cannot directly change it. It would be put into the final model as an extra variable, however it was not significant so it has 8

9 been left out. The graph above and on the left does not depict to much variation from the best fit line, but there are a few players who stand out which is to be expected. In the middle of the graph there is Allen Crabbe, towards the top, and then there is Kevin Martin, towards the bottom. Crabbe is overpaid because he plays the minutes of a starter but comes off the bench, so he is Portlands sixth man which is a very important role in basketball, so it makes sense why he appears to be overpaid. Kevin Martin signed this contract towards the end of his career, he was still playing well but he was old and teams did not want to pay him a lot so wanting to play basketball he was forced to take a pay cut which makes him underpaid. Small Forwards SPY = 8,294, ,576,481(TPG) + 1,226,759(3PAPG) + (-441,253)(Age) The small forward model had a small problem with multicollinearity the equation above has all ready been fixed to correct for the multicollinearity problem. The table to the right shows how even with just three predictor variables this model is the second strongest. An interesting result from this Variable Std. Error T-Value TPG 577, PAPG 329, Age 103, n 112 R Adjusted R model is the fact that turnovers are positive. Now this is not how it should be, but when you look at all of the highest paid small forwards they all have the most turnovers as well. This model in a sense is changing turnover to possessions. A lot of teams want the ball in the hands of their small forward, and that is shown by forgiving them for having a lot of turnovers. Changes for this are discussed in the future section of this paper. SPY = 21,331, ,181,832(Prod) + (-471,789)(Age) Variable Std. Error T-Value Productivity 473, Age 109, n 112 R Adjusted R

10 The small forward model raises a lot of interesting findings, so there are five data points to pay close attention to in the graph above. Starting with Harrison Barnes who can be found at about 23 million salary and -0.5 productivity. Harrison Barnes was a free agent, so salaries increase in free agency it becomes an auction and the prices go up. Looking to the right the is Chandler Parsons who is another example of the free agency price jump. However Barnes has championship experience. He won one title and lost in the final the year after that. For this paper championship data was not examined, but it may be a safe assumption to say Barnes was paid that much because of his experience in the Finals. Just below Barnes at around 18 million is Kawhi Leonard. Most teams do not pay their small forwards based on their defense. This is evident through the fact that no defensive statistic made it into the model. What this means for Leonard is he will appear to be overpaid, but he may not be overpaid since the Spurs are probably paying him that much for his stout defense. The next data point is down in the lower right Danny Granger. Seeing Granger here may be evidence to shortening the length of data that is looked at. Granger had a bad year or two right before this contract was signed, and that was reflected in the low pay. However he has a higher productivity because of the years before that when he had really good stats. The last data point is Lebron James in the upper right he is overpaid partly due to his superstar status and partly due to free agency. Lebron knows that almost all teams will pay a pretty penny for him, so he uses this leverage in negotiations to obtain higher salaries. Power Forward SPY = 6,678, ,091,491(SPG) + (-2,415,672)(TPG) + 1,296,657(PPG) + 1,343,016(DRPG) + (-1,054,784)FGAPG + 6,612,456(3PPct) + (-377,706)(Age) The analysis of power forwards yielded the best results. This is partly due to the power forwards model having the most variables that were significant. Also there is not much change at the power forward position regarding play style. Yes there are power forwards who play in the post, close to the basket, and there are stretch power forwards, ability to make three pointers. But it seems more so that a player that cannot shoot the three becomes Variable Std. Error T-Value SPG 1,484, TPG 1,056, PPG 370, DRPG 355, FGAPG 479, PPct 2,678, Age 88, n 117 R Adjusted R a center and power forwards are usually just players that can make threes. 10

11 SPY = 16,838, ,063,295(Prod) + ( )(Age) Variable Std. Error T-Value Productivity 158, Age 85, n 117 R Adjusted R This model does account for steals which is a defensive statistic however it does not account for blocks, and Anthony Davis who is in the upper right appears to be overpaid, but he may not be because of his rim protecting ability. Another interesting finding from the results is Dirk Nowitzki. One observation of Dirk can be found at the top of the graph, and the rest are all around the best fit line. This is due to the fact that throughout the 2000s Dirk would take pay cuts so the Mavericks could build a better team, and have a better shot at winning an NBA championship. Then the one where he is overpaid he just took a max out deal. Lastly there is a Kevin Garnett observation at about 20 million and 1 productivity. This is the one time he was vastly overpaid, and could help to explain why he is the highest paid NBA athlete in history. Centers SPY = 12,165,401 + (-3,511,961)(TPG) + 583,507(PPG) + 2,233,648(DRPG) + (-543,097)(Age) The model for centers was the third best model. Being in the middle or seemingly average means that not much interesting stuff came to be from the model. Something that was surprising was the fact that BLKPG was not significant. Most good centers are good at blocking shots, so it was reasonable to believe that BLKPG may make it in the Variable Std. Error T-Value TPG 1,378, PPG 154, DRPG 346, Age 100, n 109 R Adjusted R model. 11

12 SPY = 21,772, ,139,134(Productivity) + (-443,426)(Age) Variable Std. Error T-Value Productivity 112, Age 105, n 109 R Adjusted R There are a couple of observations that stand out as telling interesting stories in the graph above. At about 18 million in salary and negative 3 in productivity is Bismack Biyombo. He had an outstanding postseason, and that is why he received such a large contract. Hopefully more data in the future will be able to directly show this. Then there is Al Horford who is at about 28 million and 5 productivity. He was a free agent, and when a player is on the free agent it basically becomes an auction to see who can sign that player. Due to the free agency he became overpaid. But players do not just freely get millions of dollars, the free agent price jump only works for good players, which Al Horford is, and this model does reflect that he is a good player. Line Plot 12

13 The plot on the previous page is a graph containing all of the regression lines from the above models. From this plot it can be seen that each model is indeed different, and it further strengthens the need to analyze the NBA players by position. Missing from this plot is the line for the shooting guards model, because it was on a different scale. However if it is true that shooting guards are either a small forward or a point guard. The graph shows how vastly different those two positions are, which would give reason to why the shooting guard model had so many problems and was so weak. The next finding seen is the graph is that small forwards are the highest paid and point guards are the lowest. Something the begs an interesting question, and may be explored in the future, is the fact the the line for centers and point guards are nearly parallel. This may be a phenomenon are there could be a reason, however the answer to why this is is unknown at this time. Contract Years In sports when a contract year is referred to it means that at the end of the season the players contract is up and they will have to sign a new one with a team in order to keep playing. It is generally assumed that players play better in contract years. This makes sense because if you are playing better you will be paid better. Below is an analysis of this data, and the results are very interesting. Min First Quartile Median Mean Third Quartile Max All Players Contract Years All Players Non-Contract Years Point Guards Contract Years Point Guards Non-Contract Years Shooting Guards Contract Years Shooting Guards Non-Contract Years Small Forwards Contract Years Small Forwards Non-Contract Years Power Forwards Contract Years Power Forwards Non-Contract Years Centers Contract Years Centers Non-Contract Years

14 The results seem to show the opposite of what the main thought consensus of people is. For all models except for small forwards players get worse in contract years. This is a very surprising result. For the future attempts will be model to explore this topic in a different way. These are the results for now, but not completely confident to assume them to be correct. Year After Contract Signing There are two schools of thought for how players perform in the year after they sign a contract. The first is that players slump. Players will get paid a big salary and see that it is guaranteed for the future and then will not try as hard. The other theory is that players get better. They do not want to let the fans down, and they want to prove that they are worth the money they are receiving. Below here is a table, and in the table are summaries of productivity. This is to help answer whether or not players slump or get better. Min First Quartile Median Mean Third Quartile Max All Players YACS All Player NYACS Point Guards YACS Point Guards NYACS Shooting Guards YACS Shooting Guards NYACS Small Forwards YACS Small Forwards NYACS Power Forwards YACS Power Forwards NYACS Centers YACS Centers NYACS Except for the max of point guards it appears to be that players slump a little bit the year after they sign a contract. A combination of the contract year results and year after contract signing results appears to show that players do not play well around contract signings. This could be an anomaly so this will be explored in a different way in the future, and hopefully with more data. 14

15 Future Aspirations To begin changes for the future, data changes/additions will be the first topic of interest. A statistic for points responsible for will be added. Statistics accounting for players awards, championships, and playoff stats will be added in the future. Another statistic that will be added is a salary statistic that says how much a player is paid based on the salary cap. So instead of a yearly number they have a percentage of the salary cap. The most important step for the future is to simply obtain more data. The process of hand entering each persons data is takes way too much time. Hopefully there will be success in writing code that will read in files and sort data into excel sheets, but this will all be explored later. Then if obtaining data this way is possible. Possession based statistics for players will be added. With all of the extra data, accounting for play styles will be possible. More inclusive defensive statistics like defensive field goals made will be added as well. Conclusion The factors that affect the amount a player is played change for all positions, and have yet to be fully revealed. However, it seems that the most NBA owners pay their players based on how many points they score per game, and what their age is. This study has definitely raised questions, and solved some as well. However it has really fueled interest in player contracts, because results are out there, and with more data they should be uncovered. The models built were able to show which players were overpaid and which were underpaid. There were some player for whom a reasonable assumption could be made as to why they were either overpaid and underpaid. This assumptions always included data that was not in the analysis. Hopefully in the future more data will be added, so that a more accurate predictor of salaries will be obtained. Then with more data when someone is overpaid and a reason for it is not evident, a conclusion that they were simply overpaid would be reasonable. Regarding contract years, and the seasons after signing a contract. The analysis showed that players slump in both years. This goes against what most people believe, so future analysis of this topic will be vital. As of now a reason for the slumping could be the pressure of a contract. It is possible the superstars of the NBA fold a little but under the pressure of a new contract, or the pressure of fulfilling a previous one. 15

16 References Basketball Statistics and History Basketball-Reference.com. Basketball-Reference.com. N.p., n.d. Web. 18 Nov Gaines, Cork. How Kevin Garnett Made $315 Million To Become The Highest-Paid Player In NBA History. Blog post. Business Insider. N.p., 29 Apr Web. 18 Nov Gerard, David P. Baseball GPA: A New Statistical Approach to Performance and Strategy. Jefferson, NC: McFarland &, Print. Hakes, J. and Turner, C. (2007). Pay, productivity and aging in Major League Baseball. Retrieved June, 2016 from: Krautmann, Anthony C. Shirking or Stochastic Productivity in Major League Baseball? Southern Economic Journal, vol. 56, no. 4, 1990, pp Krohn, Gregory A. Measuring the Experience-Productivity Relationship: The Case of Major League Baseball. Journal of Business & Amp; Economic Statistics, vol. 1, no. 4, 1983, pp Lahman, Sean. Sean Lahman. Sean Lahman. N.p., n.d. Web. 03 June Scully, Gerald W. Pay and Performance in Major League Baseball. The American Economic Review, vol. 64, no. 6, 1974, pp Spotrac.com. Sports Contracts, Salaries, Caps, Bonuses, & Transactions. N.p., n.d. Web. 03 June Wiseman, Frederick and Chatterjee, Sangit (2010) Negotiating Salaries through Quantile Regression, Journal of Quantitative Analysis in Sports: Vol. 6: Iss. 1, Article 7. 16

17 Index 2PAPG - Two Point Field Goals Attempted Per Game 2PPG - Two Point Field Goals Made Per Game 3PAPG - Three Point Field Goals Attempted Per Game 3PPG - Three Point Field Goals Made Per Game ASTPG - Assists Per Game BLKPG - Blocks Per Game DRBPG - Defensive Rebounds Per Game efgpct - Effective Field Goal Percentage FGPct - Field Goal Percentage FTAPG - Free Throws Attempted Per Game FTPct - Free Throw Percentage FTPG - Free Throws Made Per Game GPY - Games Per Year LoNC - Length of New Contract MPG - Minutes Per Game NYACS - Not Year After Contract Signing ORBPG - Offensive Rebounds Per Game PFPG - Personal Fouls Per Game PPG - Points Per Game Prod - Productivity SPY - Salary Per Year STLPG - Steals Per Game TOVPG - Turnovers Per Game TRBPG - Total Rebounds Per Game YACS - Year After Contract Signing YoPoC - Years of Play on Contract 17