DOES AN ALL-STAR PREMIUM EXIST IN THE NBA? AN ECONOMETRIC ANALYSIS OF NBA PLAYER SALARIES FROM 1999-2006 Except where reference is made to the work of others, the work described in this thesis is my own or was done in collaboration with my advisory committee. This thesis does not include proprietary or classified information. James Russell Hayles Certificate of Approval: ________________________________ _________________________________ James Edgar Long John D. Jackson, Chair Professor Professor Economics Economics ________________________________ _________________________________ Steven B. Caudill Stephen L. McFarland Professor Acting Dean Economics Graduate School DOES AN ALL-STAR PREMIUM EXIST IN THE NBA? AN ECONOMETRIC ANALYSIS OF NBA PLAYER SALARIES FROM 1999-2006 James Russell Hayles A Thesis Submitted to the Graduate School of Auburn University in Partial Fulfillment of the Requirement for the Degree of Master of Science Auburn, Alabama December 15, 2006 iii DOES AN ALL-STAR PREMIUM EXIST IN THE NBA? AN ECONOMETRIC ANALYSIS OF NBA PLAYER SALARIES FROM 1999-2006 James Russell Hayles Permission is granted to Auburn University to make copies of this thesis at its discretion, upon the request of individuals or institutions and at their expense. The author reserves all publication rights. _________________________________ Signature of Author _________________________________ Date of Graduation iv VITA James Russell Hayles, son of James Otis Hayles Jr. and Myna Corman Hayles, was born on January 15, 1982, in Auburn, Alabama. He attended elementary and high school at Escambia Academy in Atmore, Alabama and graduated in 2000. He attended Presbyterian College and Auburn University and received his degree of Bachelor of Science (Economics) from Auburn University in May 2005. He entered graduate school at Auburn University in August 2005. He is engaged to be married to Sara Michelle Webster in June of 2007. v THESIS ABSTRACT DOES AN ALL-STAR PREMIUM EXIST IN THE NBA? AN ECONOMETRIC ANALYSIS OF NBA PLAYER SALARIES FROM 1999-2006 James Russell Hayles Master of Science, December 15, 2006 (Bachelor Science, Auburn University, 2005) 61 Typed Pages Directed by John D. Jackson This thesis is a salary determination model for NBA players. It presents a review of previously published literature as well as discusses background information on the structure of the NBA s labor market. It uses the human capital approach to wage determination to create an estimating equation. It finds that for the period tested an all- star premium does exist. Lastly the findings are evaluated in terms of the NBA as it exists today in an effort to offer some insight into the implications of the results on the future performance of that industry. vi ACKNOWLEDGMENTS The author would like to thank his parents, Myna Corman Hayles and James Otis Hayles Jr., his sister Temple Hayles Marks, and his fianc?e Sara Webster. Their financial and emotional support has been greatly appreciated. The author would also like to thank committee chairman, Dr. John Jackson, and committee members Dr. James Long and Dr. Steven Caudill for their guidance and assistance throughout his Graduate School career. vii Style Manual of journal used Journal of Econometrics Computer Software used Word 6.0 and Limdep viii TABLE OF CONTENTS LIST OF TABLES ix CHAPTER 1: INTRODUCTION 1 CHAPTER 2: STRUCTURE OF THE NBA FREE AGENT MARKET 4 CHAPTER 3: THE HUMAN CAPITAL APPROACH 8 CHAPTER 4: LITERATURE REVIEW 15 CHAPTER 5: DATA AND METHODOLOGY 21 CHAPTER 6: RESULTS 29 CHAPTER 7: FAILED VARIABLES 36 CHAPTER 8: CONCLUSION 39 BIBLIOGRAPHY 42 APPENDIX 1 44 APPENDIX 2 52 ix LIST OF TABLES TABLE 1: VARIABLE DESCRIPTIONS AND SUMMARY STATISTICS 28 TABLE 2(A): OLS RESULTS 34 TABLE 2(B): OLS RESULTS 35 1 CHAPTER 1: INTRODUCTION In the world of professional sports perhaps no market is more critical to a franchise s success both on the field and in the books than the market for experienced free agents. As the popularity of professional sports has risen dramatically in the last few decades so too have the players salaries. As a result teams are often faced with the dilemma of attempting to sign available free agents without overpaying for them. Because of the possibility of overpaying, the team that is able to sign the desired free agent is often stuck with a winners curse. Winners curse is a scenario in which a franchise or firm, attempting to acquire rights to some agent, unknowingly overpays for that agent and is then stuck with it for the length of the contract1. In correlation to this, the winner s curse is a major problem in professional sports because of the size of player contracts and the amount of money a team could potentially lose if they overpay for a player. In spite of this, NBA franchises are more than willing to take chances on available free agents because of the profitability of acquiring the right players. Because of the extremely limited supply of qualified players for the NBA, the price players are able to demand is potentially extraordinarily high. In addition, extremely popular or talented players could potentially demand even higher compensation. It is not uncommon for the best players in the NBA to be paid as much as 25 million dollars a year for their services2. Thus NBA franchises must be very careful in evaluating 1 Eschker et al. (2004) 2 Player salary information taken from www.nba.com and Bender, Particia. (2006). 2 potentially elite athletes because overestimating a contract of that size could cripple the franchise for years into the future. The main goal of this paper is to developing a working model for predicting NBA player salaries using the human capital approach to wage determination, and to use this model to test if there existed at the time of this research a statistically significant salary premium for the elite or extremely popular players. Chapter 2 provides the information regarding the structure of the NBA free agent market, and also discusses any idiosyncrasies that exist because of its unique structure. In order to develop a model to predict salaries of NBA free agents, we must first understand the structure of the NBA s labor market. The structure of the NBA is governed by a Collective Bargaining Agreement (CBA) that is agreed upon by both the Players Association and the owners of all the teams. The CBA does everything from setting the salary cap each year to developing a scale of salaries for drafted rookies. The CBA also sets the minimum and maximum salaries for players, depending on their years of experience in the NBA, and it defines to specific exemptions to the salary cap that allow teams to exceed the cap. For these reasons, understanding the CBA and in particular the salary cap, is a vital step in developing a model such as this. When developing a salary determination model for professional sports it has generally been found that the human capital approach is the most popular and most effective method. The human capital approach to wage determination was first popularized by Gary Becker in his book Human Capital (1975). Chapter 3 of this paper uses the foundations laid by Becker, and others, to develop a model that is adapted specifically to fit the free agent market of the NBA. The human capital approach uses 3 individuals specific abilities or traits, known as human capital characteristics, to predict what that person might demand as compensation for employment. These abilities or traits are called human capital because like physical capital, individuals can generally invest time and or money into them in order to demand potentially higher wages. Perhaps the most popular and most researched of these traits is education. Individuals can invest time and money into their education in order to better understand the field of employment they hope to enter and in return receive higher wages. In the case of professional basketball, these attributes generally deal with a player s accumulation of certain basketball related statistics measuring that player s abilities to compete at the extremely high level of competition that is experienced in the NBA. The remaining sections of this thesis provide the information and methods used to arrive at my final conclusion. Chapter 4 gives a review of relevant literature, discusses their findings, and explains the relevance to the topic discussed in this paper. Chapter 5 gives a description of the data and methodology used. Chapter 6 gives the results of the tests performed, and lastly Chapter 7 presents my conclusions and discusses how they relate to NBA as it exists today. 4 CHAPTER 2: STUCTURE OF THE NBA FREE AGENT MARKET The market for free agents in the NBA is very different from most other labor markets. Because of the special nature of this labor market it is essential to understand how the NBA works in regards to the movement of players from team to team in the League. The NBA s Collective Bargaining Agreement (CBA) is essentially the constitution of the NBA. It sets everything from the salary cap for all the teams to the structure of the pay scale for rookies. Therefore, to fully understand the market in which the NBA is operating we must first understand how that labor market is structured. The CBA is a contract that is agreed upon by both the Players Association (PA) and the owners (League). The PA is the players union of the NBA. Like almost all other labor unions, its purpose is to give the players more negotiating power with the league than they would have if they worked separately. The CBA defines the salary cap, the procedures for determining how it is set, the minimum and maximum salaries, the rules for trades, the procedures for the NBA draft, and hundreds of other things that need to be defined in order for a league like the NBA to function3. In other words the CBA lays the boundaries for what both the players and owners are allowed to do. It should also be noted that the CBA is what keeps the NBA from being in violation of the Sherman Act. The Sherman Act prohibits the existence of things such as a draft or salary 3 Coon, Larry et al. (2005). 5 cap; however, because these things are agreed upon through a collective bargaining procedure they do not violate the Sherman Act4. For this paper, the most important aspect of the CBA is the salary cap. First it must be understood exactly what a salary cap is, and how that might affect wages. A salary cap is essentially a limit to a team s total payroll. In most professional sports leagues it is set as a percentage of projected total revenues (or some measure of projected earnings) for the league divided by the number of teams. Once the salary cap has been defined, teams are not allowed to have their yearly payroll exceed that number without facing some sort of harsh monetary penalty. In general, the league has to set the penalties in such a way as to make them costly enough to prevent every team from exceeding the cap, and thus rendering it irrelevant, but not so harsh as to cripple a franchise that is facing the penalty. Usually, this type of strict salary cap structure is called a hard cap . The basic goal of a salary cap is to level the playing field for small and large market franchises. Without a salary cap, the teams that have the most money to spend could simply buy up the best players in the league, and therefore ruin the competitive balance of the league. The evidence bears this out: For the 2001-02 NBA season, the correlation between team payroll and regular season wins was about 0.13. In other words, there is nearly no correlation between salary and wins. By comparison, MLB (with no salary cap) had a much stronger correlation of 0.43 for its 2002 season5. Clearly, the salary cap employed by the NBA allows for a much more level playing field for all franchises in the league. Also, the existence of a cap will almost certainly have some effect on the salary that players receive. Generally speaking, only those teams whose salary cap 4 Coon, Larry et al. (2005). 5 Coon, Larry et al. (2005). 6 position allows them the freedom to pay higher level free agents the money they demand, will be able to win those free agents. Therefore in a league that employs this type of hard cap , a player s salary will almost certainly be affected by the team s salary cap position. It thus follows that to estimate an earnings equation in a professional sports league with a salary cap would require knowledge of the salary cap position of every team at the time they signed every player. Interestingly, the NBA has a soft cap and not a hard cap like the one mentioned above. A soft cap is one in which there are exceptions and teams are allowed to go over the cap for certain reasons. There are several different types of exceptions for NBA franchises to employ when they are signing free agents. In general most of these exceptions deal with teams being able to resign their own free agents without having that salary count against their cap limit. In order to limit the potential for rampant abuse there are some restrictions on how a team can use these exceptions, what players they are allowed to use them on, and how many times each season they are allowed to use them. The main reason that the NBA employs a soft cap is for the fans. No one likes to see a player who has played with a team his entire career be forced into playing for another team simply because his present team doesn t have the salary cap room to sign him. Undoubtedly, the effect a soft cap will have on individual players salaries is different from the effect that a hard cap will have. Certainly a salary cap of any kind affects the total payroll of teams in the league. Studies done on the NFL and the NBA have shown that the overall effect of salary caps for teams is significant, but a cap s effect on individual players salaries, especially the top echelon players, has not been as pronounced. It is generally believed by those who study and follow the business of the 7 NBA, that it s salary cap does not affect players as much as the salary cap in other leagues. The main reason for this is because it is a soft cap with several loop holes. Generally speaking, if a team wants to sign a free agent, but does not currently have the cap room, they still go after that free agent. To sign available free agents that would generally put the over the cap, a team has two easily accessible options. The first is that they can readjust an existing player s contract and structure it in such a way as to allow the total team payroll to be under the cap. The second is to employ one of the several free agent exemptions to the salary cap set forth in the CBA. Because a team can go over the cap using the exceptions to the salary cap set forth in the CBA to sign their own free agents, if a team really wants another free agent, they can get them and pay them whatever is necessary. The best evidence of this is the fact that nearly 2/3 s of the teams in the NBA are over the cap every year. Therefore, while the salary cap probably does have some effect on salaries of some players, because this paper deals with all-star players that make more than $5 million per year, its effect on the types of players analyzed in this paper may be generally considered to be negligible. Clearly understanding the framework of the free agent market in the NBA is vital in establishing a salary determination model. Generally speaking a salary cap would certainly have some effect on player salaries, but because the NBA employs a soft cap , which allows teams to exceed or maneuver around the cap with relatively little effort, its effect is most likely insignificant. Now that an understanding of the structure of the free agent market has been established, the next step in the process of setting up a salary determination model is to discuss the implementation of an established theory in the field of salary determination. 8 CHAPTER 3: THE HUMAN CAPITAL APPROACH Wage determination has been a topic of much interest and analysis for many years, and its application to the field of professional athletics has grown more popular in the last decade. One of the most popular and respected methods of wage determination has been the human capital approach. The human capital approach uses an individual s attributes, skills, and talents in addition to other market based measures as a method of determining that individual s appropriate wage for a certain occupation. In the field of professional sports these characteristics can generally be easily measured and applied. For this reason, the human capital method is the preferred method of salary determination in professional sports models. It follows that to understand fully a model such as the one employed in this paper, we must outline the human capital approach, and analyze how it applies to the field of professional sports in general, and how it applies to professional basketball in particular. The field of labor economics, and the subfield of salary determination, is of great interest to not only economists, but also the general public. Generally speaking this is because its tenets are to almost everyone in the world. One of the most popular approaches to salary determination is the human capital approach. While physical capital consists of things such as land, property, bonds, etc; human capital consists of personal attributes that an individual has that makes him more appealing for employment. These attributes could be age, education, physical abilities, job specific training, 9 experience, and other attributes, job specific and general, that make him more appealing in the eyes of his potential employers. Applying the concept to the everyday business world is quite simple. Firms want to hire the most able individuals they can while not overpaying for the job they want done. Simply put, profit maximizers are unwilling to pay someone more than their value to the firm. It follows that a good way for firms to decide who to hire is to analyze each individuals stock of human capital, and chose the one whose qualifications best fits the job they want filled. A profit maximizing employer would be in equilibrium by hiring labor up the point the point where the marginal revenue product of the last laborer hired equal the wage paid to all laborers of that type. W = MRP Thus it follows that the higher an individual s human capital, the higher his MRP, and hence the higher potential wage he can demand. Lastly, it must be understood that to invest in one s human capital is to spend current earnings or wealth in such a way as to increase your human capital and therefore your expectation of future earnings. The best example of this is college education. Individuals in college are spending current wealth or earnings to increase their education level, which will hopefully result in higher future earnings and thus increased future wealth. In other words, they are investing in their stock of human capital now, in order to receive higher returns in the future. Expanding upon this concept, it can be seen how such a method is appealing to salary determination in the world of professional sports. Much like firms in real world, franchises do not want to overpay for players and be stuck with a winners curse, but even more so because of the length and value of the contracts. Likewise, they do not want to 10 offer free agent acquisitions too little and lose them to other competitors in the market. One of the best ways for teams to analyze potential free agent acquisitions is to refer to their stock of athletic human capital. By evaluating each player s stock of athletic human capital a franchise can determine what they believe that player s worth to be by comparing him to other players in the league that have a similar stock, and observing what they are paid. By doing so, they can limit the possibility of overpaying for players, and being stuck with a winners curse. For simplification reasons, models of a perfectly competitive world generally have a firm setting wage equal to some amount and then hiring workers up to the point where the marginal revenue product of the last person hired is exactly equal to the marginal revenue product the company receives for hiring that worker. However, the world of professional sports does not work this way at all. First, the markets of most professional sports are not generally perfectly competitive markets. There are only a few teams that demand the players services, and there are only few athletes that meet the ability levels required to compete on such a level. This results in a market for labor that is very different from the one seen in other instances. Unlike in most other labor markets, teams negotiate with each player separately to determine what that player in particular will be paid. High profile, upper talent level players can generally demand higher wages because they are unique, and there are very few, or no, other players like them available to teams. Conversely, players who are new, or relatively unproven, may not receive as high a salary as they could in a completely competitive market because the teams in the market know that there are relatively few other places for the players to go to prove their abilities. For this reason, 11 some newer players may end up being paid significantly more or less than the marginal revenue product they provide to the team. However, player contracts are limited to a certain number of years (7 is the max), and after that point teams will better know that player s true value6. This is the case of a bilateral monopoly. In this case, the players are the only suppliers of the labor to which the franchises are the only demanders. The graph below is a representation of the case of bilateral monopoly in a non-perfectly competitive market. Wage rate is on the vertical axis and employment is on the horizontal axis. In the graph, MCL is the marginal cost of labor curve, SL is the supply of labor curve, and VMP is the value of marginal product or demand for labor, and MRP is the Marginal Revenue product curve. 6 It must also be noted that in the case of the NBA there is uncertainty in the outcome of signing a player. This will generally lower a player s prospective salary because the team incurs the risk of signing the player and having him be injured or simply not play to his potential. 12 In the graph above, the area between W1 and W2 is sometimes referred to as the contract zone. This is the area of potential negotiation in the instance of a bilateral monopoly. Applying this graph to the situation of the NBA is quite simple. Players will ask for a salary of W1 and the teams will offer a bid of W2. The two sides will then negotiate to some point between W1 and W2. The more power the player or players have over the market, the closer the final salary will be to W1. Likewise, the more power the franchises have in the free agent market, the closer the final salary will be to W2. It can be seen that a situation such as this could possibly be the reason we have such wide descrepencies between players salaries. Some players have more market power than other players, and are thus able to earn even higher wages. Lastly, it should also be noted that because the players are unionized, they do have an added advantage in the market7. Because teams do not set a single wage like firms in the real world, but instead negotiate with each player individually, it follows that a team s decision to sign a player is done individually as well. A player will be signed as long as the marginal revenue product the team receives from signing him is greater than or equal to value of the contract. In other words, they will be willing to offer up to the amount of the marginal revenue product as the value of the contract. Si  MRPi Where Si equals the salary of the ith player and MRPi is the marginal revenue product of the ith player. It is also generally the goal of the player to receive the most money he can for his services. This generally results in a bargaining process between the team and the player. Because of this bargaining process, teams sometimes overpay for players in 7 Reynolds et al (1991, pp.440) 13 terms of their monetary value to the franchise. It must also be remembered that unlike firms (workers) in the real world, professional sports teams (players) may not always act as profit (wage) maximizing entities. The main reason for this because they are also concerned with winning, which does not necessarily go hand in hand with short run profit (wage) maximization. Sometimes teams will knowingly overpay for very high profile players, and try to compensate by paying other players less than their true worth, or they will simply view overpaying for players as the price of winning. Likewise, players will sometimes take less money to play for a team they think has a better chance of winning. In other words, winning is included in the short run marginal revenue product not just the monetary value. So, while teams may knowingly monetarily overpay for a player, they will not knowingly overpay the total value they place on that player (including intrinsic values) over many periods. Clearly, NBA teams must be careful with how much they pay players. In an era such as today, where upper echelon player can make upwards of 25 million dollars per year, overpaying for such players can cripple a franchise for years. As stated earlier, one of the best ways for teams to analyze veteran free agents is to examine players stocks of athletic human capital. Certainly teams examine player s physical attributes, such as height, weight, strength, overall physical fitness, but they must also analyze how those attributes are utilized on the basketball court. While a player that is 7 4 is appealing to most NBA franchises, if that player can not move up and down the court in a timely fashion there is no use for him on the basketball court. Other examples of the player s athletic human capital may be age, career statistics, and intangible basketball attributes like desire, hard work, or clutch playing. Most of these are things a player can invest 14 time, effort, and money on, in order to raise his future salary. Obviously each team will analyze a given player differently, and this is why some teams are willing to pay more for certain players, while other teams or not. Teams may not necessarily investigate every attribute a player has, but they are certainly aware of what they feel that player s basketball abilities are, and how they fit or do not fit with their team. In doing so, they are analyzing what they feel that players stock of athletic human capital is, and what it is worth to them. 15 CHAPTER 4: LITERATURE REVIEW While the issue of salary determination in normal labor markets is not a new issue, its application to the world of professional sports is a relatively new and untapped field of research compared to other more conventional fields of economics. There are a few papers that have been written on topics similar, but not the same as the one discussed in this paper. Because this area of econometric analysis is fairly new, using the knowledge and findings of the few published papers dealing with issues similar to this paper s is an integral part of understanding and developing a working model for the issue at hand. In addition to the articles dealing with salary determination in professional sports, some other works were utilized for back ground information regarding the human capital approach to salary determination. Perhaps the most influential piece of economic literature on the human capital approach to wage determination is Gary Becker s Human Capital. Becker won the Nobel Prize in 1992 for his work on the human capital approach to wage determination and is still considered today to be the foremost authority in this field of economic analysis. Becker accomplished two major feats with this work. The first was to lay many of the theoretical foundations for the human capital approach to wage determination, and the second was to analyze the effect of education on earnings. Becker s findings were as important then as they are today and have been one of the major catalysts for the increasing interest in labor economics, and wage determination in particular. 16 While Becker s original purpose had been to estimate the money rate of return on college and high-school education, in the end he also established the theoretical framework for investment in human capital and its effects on wages. He found that his analysis offered important insight into a wide array of empirical phenomena which had, before this point, been virtually unexplained. Three of these phenomena that are of particular importance to this model are: (1) Earnings typically increase with age at a decreasing rate. Both the rate of increase and the rate of retardation tend to positively related to the level of skill. (2) Unemployment rates tend to be inversely related to level of skill (6) Abler persons receive more education and other kinds of training than others8. These and other findings of Becker s answered many previously unanswered or unexplained findings in previous economic analyses. Becker also used the first section of his book to analyze the effects of three different types of training, on-the-job, general, and job-specific as well as schooling, other knowledge, and increased productivity, on wages. Becker also used this section to cover the relationship between earnings, costs and rates of return for different persons. Lastly, Becker used the first section to analyze various incentives to invest in human capital as well as some of the effects of human capital. In the end, this section gave critical insight into how certain aspects of a player, like age, experience, previous output, and so forth might affect a player s salary. While the first part of Becker s book deals with the theoretical framework of investment in human capital, the second part is purely an econometric analysis focusing on the effects of education on wages. This section provided an excellent example of an in-depth econometric analysis of a real world problem that has stood the test of time. For 8 Becker (1975, p.16) 17 example, Becker found that the rate of return on a college education was about 10 to 12% per year, and that this had remained surprisingly constant through the years9. Becker also found that other factors of individual s human capital had an affect on their wages as well. Attributes such as intelligence, physical condition, race, sex, age, skill level all had vital effects on the earnings profiles of individuals. In short, Becker s Human Capital provided an excellent understanding of the human capital approach to wage determination, and provided a basis for how this theory might be adapted to fit the issue at hand. In addition to Becker s work on the human capital approach to salary determination, three papers in particular were vital in understanding the nature and processes of testing a model of the NBA: Eshcker s et al (2004), Matthew Dey s (1997), and Kahn and Shah s (2005). In addition to these three papers, three other papers on salary determination in Major League Baseball were also important to our study. The primary usefulness of these papers was background information on sports economics in general, and information on how factors such as age and experience might affect salary. In total, these papers provided and excellent foundation for the model and employed in this paper and its application to the world of professional sports, and the NBA in particular. Almost all the literature on salary determination in the NBA revolves around testing for racial discrepancies in the salaries of white versus non-white players. For example, Hill (2004), Kanazawa (2001), McCormick (2001), and Jenkins (1996) all focused on racial discrimination in professional basketball. Generally speaking, almost 9 Becker (1975, p. 232) 18 all of these papers found that in the period during the 80 s there existed some discrepancies in salaries for black versus white players. However, almost all the papers have found that this discrimination has all but dissipated during the mid 1990 s and into today. Also, almost all the literature in this genre uses the human capital approach to wage determination. Nearly every paper uses basketball related statistics along with other player attributes to estimate a model. Other commonly used variables are age, position variables, all-star or superstar variable, and, as mentioned above, race. These variables are then analyzed to measure their effect on salaries and results have generally been fairly consistent, with only a few exceptions. Thus it can be seen the human capital approach to wage determination is very popular for models regarding professional sports. In Eshcker s et al (2004), the main purpose is to determine if there exists a statistically significant difference between salaries of foreign players compared to American players. Similar to the current study, Eshcker uses the human capital approach to analyze the existence of an international player premium in the NBA, but instead of individual data pooled across years, he uses yearly data to analyze his question. Like this paper, Eshcker s model also uses on-court characteristics, off-court characteristics, and other measures of the players human capital. Eshcker found that there was a premium for international players in the first few years of his data, but that it disappeared after a few years. He believed the main reason for this was because NBA franchises better learned how to scout and analyze international talent. In doing so, they reduced the number of international players they overpaid, and the premium disappeared. Eshcker also found that the four on-court characteristics used in this paper were significant for 19 almost every year in his data. However, he found no evidence to support the existence of an all-star premium, which is something that will be tested in this paper. Similarly, Dey (1997) also used the human capital approach to test his hypothesis. Dey s main question was the issue of race and how it affected the salaries of players with basically the same ability levels but different races. Dey s model also used the on-court characteristics and off-court characteristics to measure each player s level of human capital and allow him to test for differences in the salaries of players with similar stocks, but different races. Like Eshcker, Dey also used an all-star variable to capture the premium for elite players, but unlike Eshcker he found it to be significant. Dey also found that although there might have existed some discrepancy between the salaries of similarly able white and black players before the late 1980 s, that this had dissipated by early 1990 s. He pointed to mass fan acceptance of non-white players after the mid 1980 s as the reason teams were more comfortable paying non-white players comparable salaries. The NBA is and always will be, a fan oriented sport, and right or wrong, the owners will generally succumb to the desires of the fans. Lastly, in Kahn and Shah s (2005) the major focus was again to test for discrepancies between white and non-white players salaries. Again, they employed a human capital type model to test their query. Like Eshcker and Dey, they also used basketball statistics to measure each players stock of human capital as well as other off- court measures. They used these variables to test if their significance levels changed when they were applied to players of different races. They found little to no evidence to support the existence of a racial discrepancy for players under the rookie salary scale or 20 free agents. They did however find that there was some evidence to support the existence of a racial inequality between marginal white and non-white players. In total these articles on the NBA were invaluable in providing real world examples of how the human capital approach to wage determination should be applied to the NBA. In general the articles supported on some level each others findings about the effects of different skills or attributes on player s salaries. However, the variable of primary interest in this paper, all-star, was found to have differing levels of significance between the papers. 21 CHAPTER 5: DATA AND METHODOLOGY The model chosen in this paper to determine NBA players salaries is a simple ordinary least squares (OLS) salary determination model. The empirical model is based upon the application of the human capital approach to wage determination to the NBA, and also upon the literature. In the model, log of average per year salary is the dependent variable with four on-court characteristic variables: points per minutes (PPM), rebounds per minutes (RPM), assists per minutes (APM), and blocks per minutes (BPM), four interaction variables of the on court characteristics variables with a dummy variable for post player (POSTPPM, POSTRPM, POSTAPM, POSTBPM), as well as one variable to measure a player s experience level in the big game (PLAYOFFM), the player s age (AGE) and age squared (AGE2) and lastly a dummy variable all-star (ALL-STAR). The general form of the model is thus: Log Salary= B0+B1(PPM)+B2(RPM)+B3(APM)+B4(BPM)+B5(AGE)+B6(ALLSTAR))+ B7(PLAYOFFM)+B8(AGE2)+B9(POSTPPM)+B10(POSTRPM)+B11(POSTAPM) +B12(POSTBPM)+t. For the model chosen, average per year salary has been selected as the dependent variable. In actuality most contracts signed today in the NBA have different specifications that allow teams and players to negotiate on a total value and length of a contract as well as the yearly payout. In general there are two major types of contract structuring, back loading and front loading. Back loading is when a team makes the last 22 few years of a contract worth more than the first years, and this is primarily done for salary cap reasons. An example of a back-loaded contract might be, a player signs a 40 million dollar four year contract and does not receive 10 million dollar per year, but instead receive 5 million the first year, 5 million the second year, and 15 million per year for the remaining two years. Front-loading is much more favorable for the players because they receive more money sooner, and is often a request of elite players. Clearly this presents a problem in salary determination because a player s contract is generally not evenly weighted throughout the length of the contract. Thus for the purposes of this paper, salary will be computed as total contract value divided by the number of years for the contract10. Because this paper focuses on the elite players in the NBA, the population of the model consists of every player whose average per year salary is worth at least 5 million dollars per year. The main reason for this limit to the dependent variable is that NBA franchises are most concerned with those players that they sign to large contracts because those players represent a much more significant financial investment than the lower level players. From this population, a random sample of 79 players was chosen and a model was regressed. To compress the scale, the log of salary was used. This is generally found to be how most salary determination models are specified and it seemed to fit the data in this case. It also makes interpretation of the coefficients of the explanatory variables more easily interpretable. Next, the four on court characteristic variables used in the model measure a provide insight into each players stock of athletic human capital, as it applies to 10 Contract values are not published. These values were taken from www.nationwide.net/~patricia/ and www.nba.com. 23 basketball. It was found by Dey (1997) and Eschker et al (2004) that these variables where the best judge of a players on-court abilities and talents. All on-court variables were calculated for the player s career up until the year his most recent contract was signed. For this reason, only veteran players where chosen because calculating rookie on-court statistics would be impossible because they would not have any statistics from the NBA. To calculate rookie contracts would require a different model all together. In other words, franchises would be required to use clairvoyance to form an expectation about a rookie s potential instead of using prior experience as they can with veteran players. These four variables will be tested for individual significance and joint significance at the five percent level. Generally these four statistics are kept per game so that a player s points per game or rebounds per game is what is most commonly kept. However for this model, it was found that many of the players in the data set had played in large numbers of games, but very few minutes, as is common with young players with only a few years experience. Thus the statistics were converted to a per minute basis to get a truer measure of the player s prior on court abilities. Points per minutes is calculated by summing all points scored by a player throughout his career in the NBA and dividing it by the total number of minutes played. This is the most popular of all on court statistics and is generally thought of as the best determination of a player s offensive abilities. Because there is an interaction term between this variable and a dummy variable for post, this variable can be interpreted as PPM effect on salary for guards only11. Because scoring is always considered an 11 Post dummy is a 1 for all centers and forwards, and a 0 for all gaurds. 24 important part of an upper echelon player s abilities, especially for guards, this variable is expected to have positive effect on salary. Rebounds per minute is calculated by summing all rebounds gathered by a player throughout his NBA career and dividing it by the number of minutes played. Again, because there is an interaction term between this variable and a dummy variable for post, this variable can be interpreted as RPM affect on salary for guards only. Because the variable only measures the effects of rebounds on the salary of guards, and rebounding is not generally expected from guards, it is expected have only a minor positive effect on salary of guards. Assists per minute is calculated by summing all assists by a player throughout his NBA career and dividing it by the number of minutes played. Because there is an interaction term between this variable and a dummy variable for post, this variable can be interpreted as APM affect on salary for guards only. Passing is almost always considered a vital part of a guard s abilities, and it is therefore expected to have a positive effect on salary for guards. Lastly, blocks per minute is calculated by summing all blocks by a player throughout his NBA career and dividing it by the number of minutes played. Because there is an interaction term between this variable and a dummy variable for post, this variable can be interpreted as BPM affect on salary for guards only. Guards are generally shorter than post players, and are not expected to get many, nor do they get many, blocks. It follows that although blocks would usually be expected to have a positive effect on salary, in this instance where it is only for guards, the sign could be positive or negative. 25 Next are the interaction variables. These variables are included to show how different types of players are paid to do different things on the basketball court. In general, a point guard is not counted on to rebound. He is counted on to distribute the basketball, and provide scoring when needed. Therefore, you would not expect to find that rebounding is a highly significant factor in the determining of a point guard s salary, but that assists would be. The variable POSTPPM is equal to points per minute multiplied by a dummy variable for post. The dummy variable is a one for a post player, and a zero for a guard. Therefore this variable tests for the affect of PPM on salary for post players only. While offense may not always be expected of every post player, it is generally expected that every player on the court can score points if needed. Thus, this variable is expected to a have a positive, significant effect on a post player s salary. Next, the variable POSTRPM is equal to rebounds per minute multiplied by a dummy variable for post. As before, the dummy variable is a one for a post player, and a zero for a guard. Therefore this variable tests for the affect of RPM on salary for post players only. Because almost every post player is expected to rebound, this variable is expected to be positive. Next, the variable POSTAPM is equal to assists per minute multiplied by a dummy variable for post. Again, dummy variable is a one for a post player, and a zero for a guard. Therefore this variable tests for the affect of APM on salary for post players only. The expected sign of this variable is not determinable. While assists may not be expected of most post players, it is not absurd to think that post players who pass the ball well get paid more than those who do not. 26 Lastly, the final post interaction variable is POSTBPM, and it is equal to blocks per minute multiplied by a dummy variable for post. Again, dummy variable is a one for a post player, and a zero for a guard. Therefore this variable tests for the effect of BPM on salary for post players only. Blocks are generally considered to be the best measure of a player s defensive abilities, especially for post players. Therefore, this variable is expected to have a positive effect on salary. The two general characteristics of AGE and AGE2 are the next variables in the model. The first, AGE, is the player s age at the time the contract was signed. The second is simple the square of AGE. Often it is the case in salary determination models that age takes a parabolic shape; therefore, age squared is used. Both these variables are considered to be vital variables in any salary determination model. The two variables will be tested for joint significance at the five percent level. In most salary determination models, it is expected that salary increases in the first part of ones career, reaches a peak, and then decreases from that point on. Lastly, the special variables, Playoff minutes played and All-star were included in the model. They were included to capture those aspects of player s abilities or attributes that are not necessarily captured by the player s statistics. These variables will be tested for individual significance at the five percent level. The variable PLAYOFFM is equal to the total number of minutes the player has played in the playoffs for his career. This variable will capture the experience factor that is often associated with tenure in other salary determination models. It is also likely to capture some of the intangible factors such as clutch performance or winning attitude that is so often talked about. To understand this, it must be understood that the final goal of 27 every franchise is to win an NBA title and to do this requires teams to play well in the playoffs. It seems obvious that teams would be highly interested in a player s experience level in this type of high pressure situation. Thus it follows that this variable is also expected to have positive effect on the player s salary. Finally, ALL-STAR is a dummy variable noting if a player has been an NBA all- star in the five years prior to his contract signing. It is only taken back to five years before the contract because if a player s was an all-star in his second year in the league and he has not been one in the last 6 years, teams will generally not consider him an all- star caliber player. This variable is used to set apart those players that are considered to be the best players each year in the NBA. Although results have been mixed in the past, the all-star variable is expected to be significant and positive for the time period collected. Applying the human capital approach to the world of professional basketball through using different basketball related statistics and characteristics has brought us to this point. Next, a model will be regressed using the empirical form set forth in this section and the results will be analyzed. 28 TABLE 1 VARIABLE DESCRIPTIONS AND SUMMARY STATISTICS Variable Definition Mean Standard Deviation Log Salary Log of the player s average per year salary 15.948 .393393 PPM Total career points/total minutes played .4225 .099558 RPM Total career rebounds/ total minutes played .2031 .071747 APM Total career assists/total minutes played .07882 .052886 BPM Total career blocks/total minutes played .02964 .023319 AGE Players age at time of contract signing 26.39 3.023 ALLSTAR Denotes if player was an All-star in the last 5 years .2532 .4376 PLAYOFFM Total number of Playoff minutes played 1116.14 1248.21 AGE2 Players age at time of contract signing squared 705.59 168.90 POSTPPM Total career points/total minutes played*Dummy variable for post player .2588 .215108 POSTRPM Total career rebounds/ total minutes played*Dummy variable for post player .1520 .123721 POSTAPM Total career assists/total minutes played*Dummy variable for post player .3395 .031712 POSTBPM Total career blocks/total minutes played*Dummy variable for post player .2521 .026144 29 CHAPTER 6: RESULTS I estimated the previously specified model in LIMDEP using OLS. The results have been recorded in TABLE 2(A) on page 33. The overall model was found to fit the fairly well with and R2 of .65 and an adjusted R2 of .58. This suggests that 65% of the variation in player salaries is explained by the model. The data has a total of 79 observations which results in the model having 66 degrees of freedom which is more than enough for confident results. Also, the F statistic for the whole model is 10.30, which is higher than the critical value of 2.45, suggesting all the variables are jointly different from zero. In general the model had the expected signs and significance levels for almost all of the variables. Also the model was tested for the presence of potential problem such as multicollinearity, heteroskedasticity, and specification or omitted variables error. Because the model does not use time-series data, there is no potential problem of auto- correlation. The existence of multicollinearity in a model such as this is expected because there is an inter-relationship between some variables. This can easily be seen by considering the case of rebounds and blocks. It is likely that players who get a high number of blocks also get a high number of rebounds, hence there will be multicollinearity between these two variables. Despite this it is at worst near-extreme multicollinearity which only affects the efficiency of the estimates. Thus the existence of multicollinearity actually results in larger variance and smaller t-statistics. This model 30 has a fairly high R2 but more than half of the variables are significant which is generally not the case with high multicollinearity. Therefore it is a non-issue for the model12. Second, heteroskedasticity was tested for using the Breusch-Pagan test. The 2 statistic for the Breusch-Pagan test for the model is 8.84 which is well below the critical value of 21.0313. Therefore, it can be concluded that heteroskedasticity is not a problem in the model. In spite of this, the program for White corrected standard errors was applied to the model to test if it provided more accurate results. If no heteroskedasticity exists in the model then the white standard errors will be the same as the normal standard errors. In this case, the adjusted standard errors were different which suggests there was some small level of heteroskedasticity. Therefore the model is regressed using the White Standard errors. Lastly, specification error and omitted variables bias was tested for using the Ramsey RESET test. The F-test for the Ramsey RESET was calculated to be .34 which is well below the critical value of approximately 2.70. Also, the for the RESET test, the lower your F-statistic is, the more certain you can be that specification error or omitted variables test is not a problem. Therefore, we can be highly certain that these problems cannot be proven to exist in the model. The results of the tests for the on court characteristics were generally as expected. As stated in the variable description section, the four on court characteristics are the effects of those variables for guards only. Therefore, an increase in one unit of PPM can be expected to increase salary by 147%. While this seems high, it must be remembered 12 The existence of Multicollinearity was analyzed using the correlation matrix in Appendix 2. 13 Bruesch-Pagan test is only asymptotically justified, however the value of 8.84 is well below the critical value. 31 that an increase of one unit in PPM would mean increasing point per minute by 1, and the largest value this variable took on in the data was .67. Therefore increasing the persons PPM by one unit would mean increasing this to 1.67 PPM which would be extremely high. Therefore it is probably best to consider this variable is to say an increase in .1 units of PPM, which would mean increasing PPM by .1, would result in increasing salary by 14.7% for a guard. Likewise, APM was also found to be significant, and positive. From the model it can be interpreted that a .1 unit increase in APM would increase salary of salary for a guard of 15.7%. Also, BPM was found to be significant and negative. At first it seems odd that increasing blocks per minute would decrease salary, but it must be remembered that this coefficient is for guards only. A guard s main purpose on the court is to score and distribute the basketball. Hence guards that get a large number of blocks are very rare and therefore this result is inflated because of the low number of blocks for guards in the data. In general it would not be expected that blocks would be a significant statistic that a team would look at when negotiating a contract with a free agent guard. On a related note, RPM was not found to be significant, but this was expected for guards, as their main purpose on the court is to score and distribute the basketball. Lastly all four variables were tested for joint significance using the F-test and were found to an F-value of approximately 3.65 which is greater than the 99% critical value of 3.60. Therefore we can be 99% certain that these four coefficients are jointly different from zero. On the contrary, the results of the post interaction variables were fairly weak. Only one of the post interaction variables was found to be individually significant. This is somewhat surprising, but not entirely. POSTBPM was found to be significant at the 1% level, and it was positive. It can thus be interpreted that a .01 unit increase in BPM 32 (scaled down more because its values were very low) can be expected to raise a post player s salary by 18.3%. Also, the four variables were tested for joint significance, and were not found to be jointly significant with an F-value of 1.88 which is less than the critical value of 2.40. However, it was found that removing the variables resulted in a slight omitted variables bias, so the variables were left in the model. This correlated with the fact there is generally a position or position interaction term in most other models found in the literatures led to the inclusion of these variables in the model14. In contrast to the post interaction variables, both general variables were found to be individually significant, but the signs were somewhat counter-intuitive. AGE had a negative sign, and AGE2 had a positive sign which seems to be opposite of what would be expected in a general salary determination model. However, this model is special because it deals with athletes and professional sports. AGE is downward sloping because the model only includes players who have played at least a few years in the league, thus the early years of a players career are not included. Therefore data for the age variable generally starts at a player s peak age, and decreases from there. AGE2 seems to include what could be called the Shaq effect. Shaquille O neal is the second highest paid player in the data set, with perhaps the best overall stats, and is also one of the oldest. Likewise, several of the higher paid players are older which results in having an upward sloping tail to the end of the data. These two variables were also tested for joint significance using the F-test and were found to have an F-value of 8.90, which is significantly higher than the 99% critical value of 4.63. 14 Because of the lack in joint significance of the post interaction variables, a second regression was run that does not include them. The results of this regression can be seen in TABLE 2(B) on page 34. 33 Likewise, the two special variables included in the model were highly significant. The dummy variable all-star was found to be statistically significant at the 1% level with a t-value of 4.121. Although this result was different from the results found by Eschker et al (2004) in his model, it is not completely unexpected. In addition to this the coefficient for the All-star variable was .3696. A simple interpretation of this would suggest that being an all-star increases a player s salary by approximately 36.96%. Therefore it can be seen that being an All-star has a significant positive effect on that player s salary. This is an important finding and its implications, as can be seen in the following chapters, can be quite interesting15. Also, the variable for playoff minutes was also a positive and significant at the 1% level. It can be interpreted from the coefficient that a 100 unit increase in playoff minutes (100 minutes played) would result in a .7% increase in salary. Although the effect is somewhat small it must be remembered that several players have 5000 or more playoff minutes in their career. Therefore it can be seen that this can be a large factor in player salaries for the more experienced veteran players. 15 To assure that the result found for all-star was correct a Chow Test was run on the model. The unrestricted model was set as the complete model minus the post interaction terms, and plus 7 interaction terms for each of the other explanatory variables multiplied by ALLSTAR. The restricted model was this model above without the 7 ALLSTAR interaction terms. A Chow test was performed and the F-value found was .80 which is lower than the critical value of approximately 2.95. Thus we can be fairly certain the effect of ALLSTAR is its own individual significance and not caused by its correlation to other variables in the model. 34 TABLE 2(A) OLS RESULTS Independent Variables Coefficient (Standard Error) ***PPM 1.4689 (.44953) RPM 1.91452 (1.36897) **APM 1.57819 (.54814) **BPM -13.51896 (6.03295) ***AGE -.410700 (.12769) ***ALLSTAR .36962 (.08968) ***PLAYOFFM .00007081 (.0000253) ***AGE2 .006788 (.002292) POSTPPM -.682765 (.615240) POSTRPM -1.49284 (1.338907) POSTAPM 1.97220 (2.29282) ***POSTBPM 18.32113 (6.506644) ***CONSTANT 20.96965 (1.73149) OBSERVATIONS R2 79 .65184 ***1% Confidence Level, **5% Confidence Level, *10%Confidence level 35 TABLE 2(B) OLS RESULTS Independent Variables Coefficient (Standard Error) ***PPM .87883542 (.36602443) RPM -.25639820 (.59783453) ***APM 1.64305616 (.69774396) *BPM 2.48818139 (1.41169020) ***AGE -.31073562 (.11650264) ***AGE2 .00491279 (.00205509) ***ALLSTAR .44329138 (.09203425) ***PLAYOFFM .0000722014 (.0000257155) ***CONSTANT 19.9680805 (1.63914682) OBSERVATIONS R2 79 .60867 36 CHAPTER 7: FAILED VARIABLES This section gives a discussion of some of the variables that were tried in the model, but failed for one reason or another. In total, more than 50 variables were attempted in the model, but in the end, only the twelve variables used added some significant predictive power to the model. The first variable that was removed from the model was years in league (YIL). YIL is calculated by totaling the total number of years a player has been in the league at the time his contract was signed. This type of experience variable is almost always seen in salary determination models. However, in this model it was found to present a major problem, while simultaneously not adding much predictive power. It was found to be highly correlated with AGE and AGE2, and this near perfect multicolinearity presented a problem for the model. In the end, the significance level lost on other variables in the model when YIL was included, was too high, and thus it was dropped to provide more efficient predictions. Also, dropping the AGE variables and substituting in YIL was also tried. However, it was not a better fit than AGE for the model, and thus AGE was included but not YIL. Likewise, height was also a failed variable for much the same reason. It was highly correlated with both rebounds and blocks and this prevented any of these variables from being statistically significant. Also, it added little to the model in terms of predictive power and was therefore dropped. 37 Next, dummy variables for the year of contract signing were also attempted in the model. Their purpose was to catch any time trend that may exist in the data. While this is not generally a problem with pooled data, such as is used in this model, this paper deals with a period of eight years and testing for a trend is a vital part of finding reliable results. Therefore, it was tested to see if any trend existed. When added, none of the dummies were found to be individually significant. In addition to this, they were not found to be jointly significant either. Thus, these variables were dropped because they added little to the model. After this, a set of variables that included only the player s previous season s statistics was included in the model. This was intended to test if teams pay more attention to a player s entire stock of statistics, or if they focus instead on their most recent performance. Therefore, these statistics were gathered for approximately 40 of the 79 observations in the model and the variables were included in the original regression. None of these variables were found to be individually significant, and they were also found to not be jointly significant either. It follows, that the evidence suggests that teams focus more on a player s entire career, rather than their most recent accolades. Clearly this is the safest route for a team to take. As stated earlier, teams do not want to be stuck with a winner s curse, and this is probably one of the best ways for them to reduce the likelihood of it happening. Next, a dummy variable for a player re-signing with his previous team was included. This was included to see if the result found for all-star was truly significant. It was believed that perhaps the all-star variable was capturing this effect, and thus, its significance was artificially inflated. However, when the variable was included in the 38 model, the significance of all-star was not affected. Also, the dummy variable for re- signing was not individually significant and thus it was dropped from the model16. Lastly, a variable for perennial all-star was included in the model as well. It is a dummy variable for players having more than three all-star selections to their name. Undoubtedly, if there exists a premium for one time all stars in general, then there might also exist a premium for perennial all-stars, since they will certainly be the most popular of all players. Once the variable was gathered, it was then multiplied by each of the other explanatory variables in the model to test if a perennial all-star player s salary is determined differently from other players. Unfortunately for this model, there were only nine perennial all-stars and this presented a major problem. There were simply not enough observations of the perennial all-star variable to establish a reliable result, and thus this variable was dropped as well. As it can be seen, potential variables in a model such as this are not hard to come by. However, it is vital that we include only those variables that fit the data best and provide confident results, while using previous literature to guide us as well. 16 This dummy variable was also attempted in the reduced version of the model found in TABLE 2(B). When the post interaction variables are left out and this variable is included, this dummy becomes individually significant. However, it is not found to affect the significance of the ALLSTAR variable even in this instance thus the conclusion regarding this result is valid even in the reduced model. 39 CHAPTER 8: CRITIQUE AND CONCLUSION As is always the case with econometric studies, variables have certainly been left out17. In a case as complicated as that of professional player salaries there are several other possible variables that were left out or omitted in this model. One of the major variables that might have been left out of the model is player popularity. This variable seems like it could potentially be a big factor in some player s salaries. In spite of this, the all-star variable is actually a popularity rating of sorts because some of the all-stars (starters) are selected by the fans18. The second reason this variable was left out, is because it would be very difficult to measure. Another factor that might have some effect on player salaries is the franchise s salary cap room. This means that teams who have more cap room would be more willing to offer more money to players than those teams without the cap room. However, it is likely that this effect will be quite small, because as discussed in Chapter 2, the NBA has a soft cap, and the exceptions allow for teams to pay players practically whatever they desire. Lastly, another variable that was potentially left out of the analysis was a preference variable on the part of the athletes themselves. It is sometimes the case that a player prefers to stay in a certain city or area of the country, for reasons such as family, and is willing to take less money to stay in those areas. This 17 However none of the omissions were significant enough to be found using the RESET test. 18 A ballot of 120 players, 60 from each league, is established by an expert panel of basketball media members. Fans are then allowed to vote for 2 gaurds, 2 forwards, and 1 center from each league. The top 5 vote getters (2 highest guards, 2 highest forwards, and the highest center) from each conference are then declared the starters for the All-star Game. Next, all the coaches in each conference are given seven votes. They are not allowed to vote for players from their own team. The seven players from each league that receive the highest number of votes are then selected for the All-star team as reserves. 40 might mean that this player is worth more to the local franchise; however, this is still debatable. It might also be the case the player mentionedwishes to play for a certain coach or with a certain player and that those factors affect the salary that is accepted. In addition to these variables, other variables were tried in the model, to see if they expanded its predicting abilities but were found to be insignificant. The main variable that was tested and left out was years in league. It was found to not increase the predictive power of the model, and simply added more multicolinearity to the model. After dropping the YIL variable the model was tested for omitted variables bias using the RESET test, and passed. Therefore, there is no reason to include the variable. In conclusion, the human capital model that was chosen was the model that best fit the data, and was the best, linear, unbiased, estimator of player salaries of all the models tested. In addition to this, the model s predictive power was as great as any other model dealing with player salary determination researched. The null hypothesis that the All-star variable was not significant was rejected. It thus follows that there did exist a premium in the NBA for all-star players during this time period. The model has shown that the fact that a player is an all-star increases his salary over other players by 36.96% ceteris paribus. Conversely, in Eschker s et al (2004) paper, he found that this was not the case. Eschker s et al (2004) paper was based on contracts signed from 1996 to 2002. However, Dey s (1997) model which was based on contracts signed between 1987-1993, found that the all-star variable was significant. It is the opinion of the author that the change in significance of the all-star variable occurred because of a shift in how the NBA advertises and the type of players that were present in the league at the time the study was performed. At the time Dey s (1997) test was performed, the NBA was in the its prime 41 with Michael Jordan, Larry Bird, and Magic Johnson being the center of focus for fans and franchises alike. These players were extremely exciting, and the unique basketball style they played was something fans were drawn to. Thus teams in this period were paying the upper echelon players, they hoped might one day become a superstar, the big bucks hoping they too might draw the crowds like Michael and Magic did. In contrast, at the time Eschker wrote his paper, the NBA had just recently come out of a nasty labor dispute. Fans were fed up with superstar athletes complaining about how much they made, and wanted to see teams that played together and won. Seemingly cyclical, in recent years it seems as though the NBA has focused on individual players (Kobe Bryant, Shaquille O Neal, and LeBron James, to name a few) and this is perhaps why the all-star variable has become significant once again. Yet again, fans have in recent years have become more drawn by players that are exciting, than by teams that win. In the most recent time period it seems as though teams have shifted their focus to getting those players that are most exciting to the fans as opposed to finding those players that will make them better. Admittedly, these are sometimes one in the same, but oftentimes they are not. This change in focus by fans and franchises alike has caused the all-star variable to become significant in the last few years. Thus, it follows that significance of the all- star variable is most likely influenced greatly by the attitude of fans towards the NBA and its players as well as how the NBA advertises. 42 BIBLIOGRAPHY Becker, Gary S. Human Capital. Second edition. National Bureau of Economic Research. Chicago: The University of Chicago Press. 1975. Bender, Patricia. Patricia s Various Basketball Stuff . http://www.nationwide.net /patricia/. 2006. Bowles, Samuel et al. The Determinants of Earnings: A Behavioral Approach . Journal Of Economic Literature. December 2001. v. 39, iss. 4, pp. 1137-76. Burger, John D and Stephen JK Walters. Market Size, Pay, and Performance: A General Model and Application to Major League Baseball . Journal of Sports Economics. vol. 4. no. 2. 2003. Coon, Larry et al. NBA Salary Cap FAQ . http://members.cox.net/lmcoon/ salarycap.htm.November 2005. Dey, Matthew S. Racial Difference in National Basketball Association Players Salaries: A New Look . The American Economist. Fall 1997. vol. 41. iss. 2. pp. 84-90. Eschker, Erick et al. The NBA and the Influx of International Basketball Players . Applied Economics. vol. 36. 2004. Faurot, David J. Equilibrium Explanation of Bargaining and Arbitration Major League Baseball . Journal of Sports Economics. vol. 2, no. 1. 2001. Hamilton, Jean Catherine. Salary Determination in Professional Sports. Dissertation. The University of California Berkley. 1995. Hill, James Richard. Pay Discrimination in the NBA Revisited . Quarterly Journal of Business and Economics. Winter-Spring 2004, v. 43, iss. 1-2. pp.81-92. Jenkins, Jeffery A. A Reexamination of Salary Discrimination in Professional Basketball . Social Science Quarterly. September 1996, v.77, iss. 3. pp. 594-608. Jewell, R Todd et al. Testing the Determinants of Income Distribution in Major League Baseball . Economic Inquiry. vol. 42, no.3. July 2004. 43 Kahn, Lawrence M and Malav Shah. Race, Compensation, and Contract Length in the NBA: 2001-2002 . Industrial Relations. Vol. 44, no.3. July 2005. Kanazawa, Mark T and Jonas P. Funk. Racial Discrimination in Professional Basketball: Evidence from Nielsen Ratings . Economic Inquiry. October 2001, v. 71, iss. 6. pp.599- 608. Long, James E. et al. Salary Vs. Marginal Revenue Product Under Monopsony and Competition: The Case of Professional Basketball. Atlantic Economic Journal. vol. XII. September 1985. 50-59. McCormick, Robert E. and Tollison, Robert D. Why Do Black Players Work More for Less Money? . Journal of Economic Behavior and Organization. February 2001, v. 44, iss.2. pp.201-19. Reynolds, Lloyd G. et al. Labor Economics and Labor Relations. 10th ed. Prentice Hall. New Jersey. 1991. www.nba.com. Copyright 2005 NBA Media Ventures, LLC. 44 APPENDIX 1: DATA PLAYER AVG Per year Salary Year Signed PPG RPG APG BPG Abdur- Rahim 5860000 2005 19.84821429 8.145833333 2.748511905 0.82738095 Allen 16000000 2005 20.87057011 4.708782743 3.987673344 0.17873651 Artest 7000000 2002 12.31527094 4.300492611 2.743842365 0.6059113 Battie 5500000 2006 6.539473684 5.67481203 0.706766917 1.06390977 Bender 6800000 2002 5.211180124 2.105590062 0.602484472 0.5093167 Bibby 11500000 2002 14.45918367 3.292517007 7.068027211 0.15986394 Billups 5616666 2002 11.34343434 2.37037037 4.161616162 0.16161616 Blount 6416667 2004 5.852398524 4.47601476 0.638376384 0.99261992 Boozer 11666667 2004 12.64102564 9.397435897 1.628205128 0.67307692 Brown 8333333 2005 7.699604743 5.454545455 0.996047431 0.68379446 Brown 8500000 2003 9.181102362 7.900262467 1.54855643 1.15879265 Bryant 19485714 2004 21.77361854 5.021390374 4.260249554 0.62032085 Cassell 5666666 2002 15.27739726 3.186643836 6.200342466 0.15753424 Cato 7000000 1999 3.700854701 3.435897436 0.358974359 1.28205128 Chandler 10666667 2005 7.586206897 7.287356322 0.835249042 1.4674329 Collins 5900000 2004 5.389830508 4.529661017 1.360169492 0.62288135 Crawford 7920000 2004 11.21721311 2.422131148 3.831967213 0.29918032 Currie 10000000 2005 11.81314879 4.892733564 0.577854671 0.88581314 Daniels 6000000 2005 7.78330373 1.785079929 3.269982238 0.11545293 Davis 12000000 2005 10.27357392 7.621653085 1.159487776 1.02328288 Davis 5783333 2002 7.797814208 2.278688525 1.68852459 0.21857923 Duncan 17429672 2003 22.89135255 12.30155211 3.208425721 2.50332594 Dunleavy 9000000 2004 8.554140127 4.178343949 2.076433121 0.20382165 Fisher 6100000 2004 7.404411765 2.058823529 2.974264706 0.08088235 Fortson 5428571 2000 9.648648649 7.540540541 0.740540541 0.30810810 Foster 5000000 2002 4.412790698 5.680232558 0.627906977 0.38953488 Francis 14166666 2002 19.68691589 6.369158879 6.476635514 0.39719626 Gadzurick 6000000 2005 6.273170732 5.936585366 0.326829268 1.28292682 Ginobili 8666667 2004 10.35616438 3.45890411 2.938356164 0.22602739 Hamilton 8857142 2003 16.7414966 3.06462585 2.418367347 0.14625850 Hardaway 12382142 1999 19.01897019 4.74796748 5.536585366 0.51761517 Harrington 6000000 2001 6.436241611 3.88590604 1.161073826 0.19463087 Haywood 5000000 2004 6.15 5.059090909 0.459090909 1.40909090 Horn 12166667 1999 20.52884615 7.365384615 1.644230769 0.75 Howard 6150000 2003 17.89522342 7.454545455 3.1201849 0.37904468 Hughes 12000000 2005 15.20045045 4.673423423 3.286036036 0.36486486 James 6000000 2005 4.914179104 3.492537313 0.384328358 1.28731343 Jaric 6666667 2005 8.494252874 2.850574713 4.465517241 0.27586206 45 PLAYER AVG Per year Salary Year Signed PPG RPG APG BPG Jones 13268571 2000 16.19951923 3.956730769 3.319711538 0.71394230 Kidd 17262000 2003 14.77989822 6.454198473 9.291348601 0.29770992 Kirilenko 14333333 2004 13.02916667 6.045833333 1.983333333 2.2875 Lafrentz 9996250 2002 12.97590361 6.899598394 1.208835341 2.47389558 Lewis 9285714 2002 11.84169884 5.405405405 1.243243243 0.47104247 Maggette 7500000 2003 11.45054945 4.201465201 1.384615385 0.25641025 Magliore 6750000 2003 7.894957983 6.218487395 0.613445378 1.15546218 Marion 13166667 2002 16.28436019 9.398104265 1.853080569 1.17061611 Marshall 5500000 2005 12.37634409 8.259408602 1.577956989 0.99865591 Martin 13000000 2004 15.08480565 7.586572438 2.360424028 1.36395759 Mason 7233333 2003 10.9055794 4.819742489 1.416309013 0.33905579 McDyess 5625000 2004 17.60180995 8.696832579 1.56561086 1.67194570 McGrady 21000000 2004 21.3963039 6.396303901 4.121149897 1.17043121 Miles 8000000 2004 9.770226537 5.346278317 2.009708738 1.15857605 Miller 8500000 2003 14.25538462 4.107692308 7.852307692 0.27692307 Miller 9571428 2003 10.5451505 6.866220736 1.735785953 0.58528428 Nash 11000000 2004 12.34608379 2.551912568 6.045537341 0.05828779 Nesterovic 7000000 2003 7.452531646 5.414556962 1.037974684 1.18037974 Nowitzki 13216666 2001 17.08056872 6.862559242 2.004739336 0.92890995 Okur 8333333 2004 8.223776224 5.286713287 0.979020979 0.71328671 Olowakandi 5408700 2003 9.941176471 7.978328173 0.761609907 1.63157894 Oneal 18084000 2003 10.96825397 6.798185941 0.968253968 1.6439909 Oneal 20000000 2005 26.73582766 11.95124717 2.878684807 2.57709750 Paterson 5672500 2001 11.02209945 4.320441989 1.596685083 0.48618784 Pollard 5116666 2000 7.064 4.48 0.448 0.696 Prince 9600000 2005 10.60194175 6.650485437 2.242718447 0.74757281 Redd 15016667 2005 17.69230769 4.224358974 1.814102564 0.10897435 Richardson 7250000 2004 11.96441281 4.932384342 1.355871886 0.20284697 Rose 13268571 2000 10.7716895 3.0456621 3.668949772 0.35844748 Rose 6000000 2002 6.561307902 4.280653951 0.643051771 0.49046321 Simmons 9400000 2005 9.634517766 4.248730964 1.715736041 0.20812182 Smith 5672500 2001 14.17169374 7.415313225 1.236658933 1.09512761 Stojacovic 7500000 2000 10.48360656 3.43442623 1.459016393 0.11475409 Swift 6000000 2005 9.011363636 4.96875 0.579545455 1.44602272 Szcerbiac 10833333 2005 15.00502513 4.376884422 2.708542714 0.29145728 Terry 7500000 2003 16.07142857 3.055900621 5.568322981 0.15217391 Walker 8833333 2005 21.27947598 8.679767103 4.11790393 0.60262008 Wallace 5000000 2000 3.99122807 6.276315789 0.460526316 1.10964912 Watson 5800000 2005 5.720394737 1.9375 3.654605263 0.1875 Williamson 5250000 2001 11.96551724 4.194581281 1.369458128 0.37931034 Wright 6000000 1999 7.74742268 7.412371134 0.706185567 0.94329896 46 PLAYER AVG Per year Salary PPM RPM APM BPM Abdur- Rahim 5860000 0.536632 0.220237 0.074311 0.02237 Allen 16000000 0.55608 0.125462 0.106248 0.004762 Artest 7000000 0.400449 0.139837 0.08922 0.019702 Battie 5500000 0.293562 0.254746 0.031727 0.04776 Bender 6800000 0.356869 0.144194 0.041259 0.034879 Bibby 11500000 0.395001 0.089946 0.193087 0.004367 Billups 5616666 0.413171 0.086338 0.151582 0.005887 Blount 6416667 0.298232 0.228093 0.032531 0.050583 Boozer 11666667 0.424908 0.31588 0.05473 0.022624 Brown 8333333 0.33955 0.240544 0.043925 0.030155 Brown 8500000 0.288995 0.248678 0.048744 0.036476 Bryant 19485714 0.633788 0.146163 0.124008 0.018056 Cassell 5666666 0.59272 0.318521 0.083075 0.064818 Cato 7000000 0.278995 0.259021 0.027062 0.096649 Chandler 10666667 0.320026 0.307419 0.035235 0.061904 Collins 5900000 0.230143 0.193414 0.058079 0.026597 Crawford 7920000 0.432112 0.093306 0.147616 0.011525 Currie 10000000 0.510848 0.211582 0.024989 0.038306 Daniels 6000000 0.353102 0.080983 0.148348 0.005238 Davis 12000000 0.33885 0.251382 0.038243 0.033751 Davis 5783333 0.452872 0.132339 0.098064 0.012694 Duncan 17429672 0.582421 0.312987 0.081632 0.063692 Dunleavy 9000000 0.368855 0.18017 0.089536 0.008789 Fisher 6100000 0.312345 0.086849 0.125465 0.003412 Fortson 5428571 0.437071 0.341577 0.033546 0.013957 Foster 5000000 0.250992 0.323082 0.035714 0.022156 Francis 14166666 0.506797 0.16396 0.166727 0.010225 Gadzurick 6000000 0.338154 0.320011 0.017618 0.069156 Ginobili 8666667 0.409645 0.136819 0.116229 0.008941 Hamilton 8857142 0.56348 0.103148 0.081397 0.004923 Hardaway 12382142 0.511479 0.127687 0.148896 0.01392 Harrington 6000000 0.330007 0.199243 0.059532 0.009979 Haywood 5000000 0.289103 0.237821 0.021581 0.066239 Horn 12166667 0.547296 0.19636 0.043835 0.019995 Howard 6150000 0.479858 0.199893 0.083667 0.010164 Hughes 12000000 0.490373 0.150767 0.106009 0.011771 James 6000000 0.323032 0.229581 0.025264 0.084621 Jaric 6666667 0.308238 0.103441 0.162044 0.01001 Jones 13268571 0.456541 0.11151 0.093557 0.020121 Kidd 17262000 0.394398 0.172229 0.247938 0.007944 Kirilenko 14333333 0.430776 0.19989 0.065574 0.07563 Lafrentz 9996250 0.417766 0.222136 0.038919 0.079648 Lewis 9285714 0.436584 0.199288 0.045836 0.017367 Maggette 7500000 0.492283 0.18063 0.059528 0.011024 Magliore 6750000 0.369373 0.290938 0.028701 0.054059 Marion 13166667 0.475505 0.274426 0.05411 0.034182 Marshall 5500000 0.438247 0.292466 0.055875 0.035362 47 PLAYER AVG Per year Salary PPM RPM APM BPM Martin 13000000 0.442109 0.222349 0.06918 0.039975 Mason 7233333 0.378971 0.167487 0.049217 0.011782 McDyess 5625000 0.52882 0.261283 0.047036 0.050231 McGrady 21000000 0.636336 0.190229 0.122565 0.034809 Miles 8000000 0.357405 0.195572 0.073517 0.042382 Miller 8500000 0.425945 0.122736 0.234624 0.008274 Miller 9571428 0.426254 0.277545 0.070164 0.023658 Nash 11000000 0.43183 0.089258 0.211455 0.002039 Nesterovic 7000000 0.312293 0.226893 0.043496 0.049463 Nowitzki 13216666 0.513317 0.206238 0.060248 0.027916 Okur 8333333 0.399185 0.256619 0.047522 0.034623 Olowakandi 5408700 0.326454 0.261997 0.02501 0.053579 Oneal 18084000 0.454264 0.281555 0.040101 0.068088 Oneal 20000000 0.714901 0.31957 0.076974 0.06891 Paterson 5672500 0.463953 0.18186 0.067209 0.020465 Pollard 5116666 0.46182 0.292887 0.029289 0.045502 Prince 9600000 0.353684 0.221862 0.074818 0.024939 Redd 15016667 0.572792 0.136765 0.058732 0.003528 Richardson 7250000 0.465909 0.192073 0.052799 0.007899 Rose 13268571 0.427278 0.120811 0.145535 0.014218 Rose 6000000 0.411835 0.268685 0.040363 0.030785 Simmons 9400000 0.387663 0.170956 0.069036 0.008374 Smith 5672500 0.449614 0.235259 0.039234 0.034744 Stojacovic 7500000 0.461067 0.151045 0.064167 0.005047 Swift 6000000 0.428533 0.236287 0.02756 0.068765 Szcerbiac 10833333 0.453799 0.132371 0.081915 0.008815 Terry 7500000 0.469388 0.089252 0.16263 0.004444 Walker 8833333 0.549132 0.223988 0.106265 0.015551 Wallace 5000000 0.201729 0.317225 0.023276 0.056085 Watson 5800000 0.299466 0.101429 0.191321 0.009816 Williamson 5250000 0.476882 0.167174 0.054579 0.015117 Wright 6000000 0.292526 0.279875 0.026664 0.035617 48 PLAYER AVG Per year Salary MPG AGE YIL ALLSTAR Minutes Height Abdur- Rahim 5860000 36.98660714 27 9 1 24855 81 Allen 16000000 37.53158706 30 9 1 24358 77 Artest 7000000 30.75369458 23 3 0 6243 79 Battie 5500000 22.27631579 30 8 0 11851 83 Bender 6800000 14.60248447 21 3 0 2351 84 Bibby 11500000 36.60544218 24 4 0 10762 74 Billups 5616666 27.45454545 26 5 0 8154 75 Blount 6416667 19.62361624 29 4 0 5318 84 Boozer 11666667 29.75 23 2 0 4641 81 Brown 8333333 22.67588933 23 4 0 5737 83 Brown 8500000 31.76902887 34 10 0 24208 83 Bryant 19485714 34.35472371 26 8 1 19273 78 Cassell 5666666 38.62084257 33 9 0 17418 75 Cato 7000000 13.26495726 25 2 0 1552 83 Chandler 10666667 23.70498084 23 4 0 6187 85 Collins 5900000 23.41949153 26 3 0 5527 84 Crawford 7920000 25.95901639 24 4 0 6334 77 Currie 10000000 23.12456747 23 4 0 6683 83 Daniels 6000000 22.04262877 30 8 0 12410 76 Davis 12000000 30.31897555 37 12 1 26044 81 Davis 5783333 17.21857923 23 4 0 3151 79 Duncan 17429672 39.3037694 27 6 1 17726 83 Dunleavy 9000000 23.1910828 24 2 0 3641 81 Fisher 6100000 23.70588235 30 8 0 12896 73 Fortson 5428571 22.07567568 24 3 0 4084 80 Foster 5000000 17.58139535 25 3 0 3024 83 Francis 14166666 38.84579439 25 3 1 8313 75 Gadzurick 6000000 18.55121951 27 3 0 3803 83 Ginobili 8666667 25.28082192 27 2 0 3691 78 Hamilton 8857142 29.71088435 25 4 0 8735 79 Hardaway 12382142 37.18428184 28 6 1 13721 79 Harrington 6000000 19.5033557 21 3 0 2906 81 Haywood 5000000 21.27272727 25 3 0 4680 84 Horn 12166667 37.50961538 24 2 0 3901 82 Howard 6150000 37.29275809 30 9 0 24203 81 Hughes 12000000 30.99774775 26 7 0 13763 77 James 6000000 15.21268657 30 5 0 4077 85 Jaric 6666667 27.55747126 27 3 0 4795 79 Jones 13268571 35.48317308 29 6 1 14761 78 Kidd 17262000 37.47455471 32 11 1 29455 76 Kirilenko 14333333 30.24583333 23 3 1 7259 81 Lafrentz 9996250 31.06024096 26 4 0 7734 83 Lewis 9285714 27.12355212 23 4 0 7025 82 Maggette 7500000 23.26007326 24 4 0 6350 78 Magliore 6750000 21.37394958 25 3 0 5087 83 Marion 13166667 34.2464455 24 3 0 7226 79 49 PLAYER AVG Per year Salary MPG AGE YIL ALLSTAR Minutes Height Marshall 5500000 28.2405914 32 11 0 21011 81 Martin 13000000 34.12014134 27 4 1 9656 81 Mason 7233333 28.77682403 26 3 0 6705 77 McDyess 5625000 33.28506787 28 7 1 14712 81 McGrady 21000000 33.62422998 25 7 1 16375 80 Miles 8000000 27.33656958 23 4 0 8447 81 Miller 8500000 33.46769231 27 4 0 10877 74 Miller 9571428 24.73913043 27 5 1 7397 84 Nash 11000000 28.59016393 30 8 1 15696 75 Nesterovic 7000000 23.86392405 27 5 0 7541 84 Nowitzki 13216666 33.27488152 23 3 0 7021 84 Okur 8333333 20.6013986 25 2 0 2946 83 Olowakandi 5408700 30.45201238 28 5 0 9836 84 Oneal 18084000 24.14512472 25 7 1 10648 83 Oneal 20000000 37.39795918 33 13 1 32985 85 Paterson 5672500 23.75690608 26 3 0 4300 77 Pollard 5116666 15.296 25 3 0 1912 83 Prince 9600000 29.97572816 25 3 0 6175 81 Redd 15016667 30.88782051 26 5 1 9637 78 Richardson 7250000 25.6797153 24 4 0 7216 78 Rose 13268571 25.21004566 27 6 0 11042 80 Rose 6000000 15.93188011 28 6 0 5847 79 Simmons 9400000 24.85279188 25 4 0 4896 78 Smith 5672500 31.51972158 26 6 0 13585 82 Stojacovic 7500000 22.73770492 23 2 0 2774 82 Swift 6000000 21.02840909 26 5 0 7402 81 Szcerbiac 10833333 33.06532663 28 6 1 13160 79 Terry 7500000 34.23913043 26 4 0 11025 74 Walker 8833333 38.7510917 29 9 1 26622 81 Wallace 5000000 19.78508772 26 4 0 4511 81 Watson 5800000 19.10197368 26 4 0 5807 73 Williamson 5250000 25.091133 28 6 0 10187 79 Wright 6000000 26.48453608 24 3 0 5138 83 50 PLAYER AVG Per year Salary Playoff Games Playoff Minutes Perennial All- star post Abdur- Rahim 5860000 0 0 0 1 Allen 16000000 37 1510 1 0 Artest 7000000 26 1003 0 1 Battie 5500000 26 656 0 1 Bender 6800000 34 304 0 1 Bibby 11500000 45 1762 0 0 Billups 5616666 68 2511 0 0 Blount 6416667 22 371 0 1 Boozer 11666667 0 0 0 1 Brown 8333333 3 60 0 1 Brown 8500000 71 2314 0 1 Bryant 19485714 119 4556 1 0 Cassell 5666666 103 2871 0 0 Cato 7000000 17 249 0 1 Chandler 10666667 6 172 0 1 Collins 5900000 52 1150 0 1 Crawford 7920000 0 0 0 0 Currie 10000000 0 0 0 1 Daniels 6000000 59 1247 0 0 Davis 12000000 93 2647 0 0 Davis 5783333 11 363 0 1 Duncan 17429672 105 4308 1 1 Dunleavy 9000000 0 0 0 1 Fisher 6100000 117 3028 0 0 Fortson 5428571 11 105 0 1 Foster 5000000 44 720 0 1 Francis 14166666 5 222 0 0 Gadzurick 6000000 1 9 0 1 Ginobili 8666667 57 1712 0 0 Hamilton 8857142 65 2662 0 0 Hardaway 12382142 63 2640 1 0 Harrington 6000000 25 570 0 1 Haywood 5000000 10 296 0 1 Horn 12166667 43 1292 0 1 Howard 6150000 13 520 0 1 Hughes 12000000 18 599 0 0 James 6000000 17 369 0 1 Jaric 6666667 0 0 0 0 Jones 13268571 71 2558 0 0 Kidd 17262000 77 3210 1 0 Kirilenko 14333333 9 267 0 1 Lafrentz 9996250 35 921 0 1 Lewis 9285714 16 548 0 1 Maggette 7500000 0 0 0 0 Magliore 6750000 31 705 0 1 Marion 13166667 34 1337 0 1 51 PLAYER AVG Per year Salary Playoff Games Playoff Minutes Perennial All- star post Marshall 5500000 9 284 0 1 Martin 13000000 56 23 0 1 Mason 7233333 16 607 0 0 McDyess 5625000 29 641 0 1 McGrady 21000000 25 1076 1 1 Miles 8000000 0 0 0 1 Miller 8500000 10 358 0 0 Miller 9571428 32 882 0 1 Nash 11000000 66 2295 0 0 Nesterovic 7000000 45 840 0 1 Nowitzki 13216666 53 2241 0 1 Okur 8333333 39 575 0 1 Olowakandi 5408700 15 224 0 1 Oneal 18084000 64 1801 1 1 Oneal 20000000 171 6813 1 1 Paterson 5672500 18 309 0 0 Pollard 5116666 53 649 0 1 Prince 9600000 63 2200 0 1 Redd 15016667 1 15 0 0 Richardson 7250000 15 564 0 0 Rose 13268571 58 1875 0 0 Rose 6000000 18 1432 0 1 Simmons 9400000 0 0 0 0 Smith 5672500 21 457 0 1 Stojacovic 7500000 57 2088 0 1 Swift 6000000 7 122 0 1 Szcerbiac 10833333 29 918 0 0 Terry 7500000 13 501 0 0 Walker 8833333 37 1507 1 1 Wallace 5000000 75 3033 0 1 Watson 5800000 8 136 0 0 Williamson 5250000 63 1088 0 1 Wright 6000000 11 277 0 1 52 APPENDIX 2 Correlation Matrix PPM RPM APM BPM AGE ALL* PLAY AGE2 PPM 1.0000 -.10041 .19313 -.16190 .06325 .50223 .36154 .05699 RPM -.10041 1.0000 -.69204 .67150 .06554 -.03895 -.01113 .07746 APM .19313 -.69204 1.00000 -.57954 .17080 .25204 .24375 .15574 BPM -.16190 .67150 -.57954 1.00000 .07905 -.00854 .00973 .08238 AGE .06325 .06554 .17080 .07905 1.00000 .33097 .44528 .99681 ALL* .50223 -.03895 .25204 -.00854 .33097 1.00000 .36536 .32546 PLAY .36154 -.01113 .24375 .00973 .44528 .36536 1.00000 .45129 AGE2 .05699 .07746 .15574 .08238 .99681 .32546 .45129 1.00000 PPM RPM APM BPM AGE ALL* PLAY AGE2 POSTPPM .15624 .61058 -.54087 .48672 -.19986 .01711 -.05609 -.19044 POSTRPM -.19542 .83864 -.68427 .63969 -.15957 -.12571 -.12319 -.15523 POSTAPM .12921 .38804 -.31320 .24464 -.19807 .08763 -.03272 -.18584 POSTBPM -.22178 .65286 -.60929 .93544 -.06755 -.04623 -.08112 -.06968 POSTPPM POSTRPM POSTAPM POSTBPM POSTPPM 1.00000 .85702 .86090 .64081 POSTRPM .85702 1.00000 .65934 .78166 POSTAPM .86090 .65934 1.00000 .39669 POSTBPM .64081 .78166 .39669 1.00000