ATHENS UNIVERSITY OF ECONOMICS AND BUSINESS SCHOOL OF ECONOMIC SCIENCES DEPARTMENT OF ECONOMICS

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1 ATHENS UNIVERSITY OF ECONOMICS AND BUSINESS SCHOOL OF ECONOMIC SCIENCES DEPARTMENT OF ECONOMICS THE DETERMINANTS OF NBA PLAYER SALARIES: A REGRESSION ANALYSIS ANDREAS MARGONIS Dissertation submitted in partial fulfilment of the necessary prerequisites for the acquisition of the MSc Degree Athens, January 2017

2 We approve the dissertation of Andreas Margonis Aikaterini Kyriazidou Signature Athens University of Economics and Business Theodore Palivos Signature Athens University of Economics and Business Stylianos Arvanitis Signature Athens University of Economics and Business Date 2

3 Table of Contents Abstract... 4 Introduction... 5 The NBA... 6 Literature Review Data Models Results Results of the model which contains career average performance statistics Result of the model which includes the performance statistics from the season before signing the contract Forward selection model Time effect on the NBA players salaries Violating the assumptions of the classic linear regression model Conclusions References Appendix

4 Abstract In this thesis an effort has been made to find the determinants of NBA players salaries. A unique dataset is consisted by panel data of contracts, personal characteristics and on-court performance statistics of 1895 NBA players, which are collected by hand, from to NBA season. Multiple regressions will be run including a shirking model so that the statistical significance and the sign of coefficients are found in order to observe the influence they have on the NBA players salaries as well as the time horizon, in which the factors that are considered by the NBA teams are consisted. In the last part, there is an attempt to examine if there is an exogenous time effect on the salaries of the NBA players with the use of the models which come of the research. The results show that NBA teams consider only the players performance from the season before they sign their contracts while there is no sign of salary discrimination based on nationality or position. 4

5 Introduction One of the most widely debated subjects in sports is the wages of players and if they deserve them. Conversations are more intensified about the contracts of NBA players since the average wage of NBA players is the highest between all professional team leagues in the world. In addition, a raise to the gap is expected because of the rapid rise of the salary cap which was announced by the NBA authorities. Players are criticized by the fans that they put their maximum effort just in the year before they become free agents. In addition, they show selfish behavior in order to boost their performance statistics. NBA teams are also accused that they reward this kind of behavior by offering large contracts to players who have briefly shown a high level of performance. The purpose of the thesis is to research and reach to conclusions, with regard to data from NBA contracts from the season to the season, about the criteria which influence wages that will be offered to basketball players. The goal of the thesis is to test if wage determinants are statistically significant and create a reliable and accurate model which will reflect NBA players wages by using econometrics theory and tools. Structure In this chapter we analyze the way in which we examined the subject of the determinants of the NBA players salaries using the proper econometric tools. At first, we will observe the form of the NBA market along with the rules and the restrictions which govern it. After that, we will review the historical background of the sports economics which is the field where this particular subject belongs to. In addition we will sort out and examine the books, articles and the essays which concern our subject. Afterwards, we will conclude on the models that came as a result of the literature review. In order to estimate the given models we will use the method of the Ordinary Least Squares so that we quantify the relationship between our variables and then, we will comment the results. Thereafter, we will conduct the forward selection method so that we end up to a more accurate model. Thereupon, we will test if there is a sign of time effect in all our models. Finally, we will check whether the assumptions of the Ordinary Least Squares method are violated and consequently, we will make the necessary corrections. In the last part of the thesis, we will mention the conclusions we will have reached and recommend an amount of subjects that can be examined taking the essay into account. 5

6 The NBA The National Basketball Association (NBA) is the men s professional basketball league in North America. It is consisted by 30 teams of which 29 are established in the United States of America and 1 in Canada. The NBA has the players with the highest average annual salary in the world. NBA teams are categorized in 2 conferences (East and West) and in 6 divisions (Atlantic, Central, Southeast, Northwest, Pacific and Southwest). From the previous divisions the first 3 belong to Eastern Conference and the other 3 to the West Conference. A NBA season is consisted by the regular season and the playoffs. During the regular season each team participates in 82 games of which 41 are played home and 41 are played away. Each team has 4 matches against all teams of its own division (16 games in total). Also, it plays against six of the teams from the other two divisions of its conference 4 times (24 games in total) and the remaining four teams three times (12 games in total). Finally, each team faces all teams from the other conference two times (30 games in total). It is understood that there an unsymmetrical season schedule. The eight teams with the best winning records of each conference are promoted to the NBA playoffs. The NBA playoffs have a tournament format. Each team plays against an opponent in a bestof-seven series, with the first team to win four games advancing into the next round, while the other team is eliminated from the playoffs. In the next round, the successful team plays against another advancing team of the same conference. All but one team in each conference are eliminated from the playoffs. The final round known as NBA Finals is a bestof seven series between the remaining teams of the two conferences. The winner of this round is proclaimed champion and receives the Larry O'Brien Championship Trophy. The NBA market NBA teams can acquire their players via two ways: NBA draft, free agency and trade. The NBA draft is an event taking place every year at the start of the NBA season. In this event teams draft players who wish to join the league. The NBA teams choose by order which is determined by last season teams winning record. The team with the worst winning record chooses a player first and the team with the best chooses last. This procedure is repeated one more time (total two rounds, 60 picks).from the 2006 NBA draft the players, who have the right to participate in the NBA draft, must be at least 19 years old during the 6

7 calendar year of the draft, they must have graduated high school and at least one year must have passed after their high school graduation. First round rookie contracts are standard, according to draft position. The first overall pick receives more than the second pick, the second more than the third, and so on. Second round picks are not standard, but they are offered overwhelmingly minimum contracts. As a result, rookies contracts depend on college and high school championships or the international ones. So, the data set does not contain rookies salaries. A big difference between the NBA and other international leagues is that NBA teams have not the possibility to transfer players. The only way NBA teams can acquire players under contract is via trade. Trades are limited by salary cap. Specifically, teams below the salary cap may trade without regard to salary, as long as they do not end up with more than $100,000 above the cap following a trade. In addition, teams above the cap (or teams below the cap that would end up with more than $100,000 over the cap following a trade) cannot acquire more than 125% plus $100,000 of the salary they trade away. Under the 2011 CBA, teams that remain below the luxury tax threshold even after the trade can acquire the lesser of 150% plus $100,000, or 100% plus $5 million, of the salary they trade away. There is no lower limit teams may divest themselves of as much salary as they wish (or can convince another team to take on) in a trade. Trade does not affect either the player s salary or the duration of the contract. There are two types of free agency: unrestricted and restricted. If a player is an unrestricted free agent, they have the right to sign with any team. If a player is a restricted free agent, they have the right to sign with any team, however their last team is able to match the other team s offer and keep the player to its roster. In order for a player to become a restricted free agent, they must have been offered a Qualifying Offer by their team. For first-round draft picks, restricted free agency is only allowed after a team exercises its option for a fourth year, and the team makes a Qualifying Offer at the Rookie-scale amount after the fourth year is completed. For any other player to be a restricted free agent, they must be at most a three-year NBA veteran, and their team must have made a Qualifying Offer for either 125% of their previous season salary or the minimum salary plus $200,000, whichever offer is higher. NBA salary cap and Exceptions NBA salary cap is the maximum of one team s payroll. Its purpose is the maintenance of competitive balance between the NBA teams and the control of their costs. The amount of the salary cap changes from season to season. It is determined by CBA and it is calculated based on league s last season revenues. Salary cap was first introduced in the first NBA season in and it was equal to $5000 ($60,775 in 2016 prices), but it was removed 7

8 until the season. In it was $ 30,000,000 ($42,680,000 in 2016 prices), for the season, the salary cap was $70,000,000 and for the season, the salary cap will be equal to $94,140,000. This rapid rise of salary cap is caused by the $24 billion nine-year length media-rights agreement between NBA, ESPN and Turner Sports. $ ,00 Figure 1: Salary Cap History $ ,00 $ ,00 $ ,00 $ ,00 $ ,00 $ ,00 $ ,00 $ ,00 $ ,00 $0, In order to ensure NBA players contracts CBA defines an amount of money that must be spent on NBA players salaries. From the season until the season salaries were capped at 57% of BRI (basketball-related income) and from season at 51.2%. Every team must spend 90% of the salary cap each year. NBA salary cap is characterized as a soft cap, namely, teams are able to surpass the limit with the use of some existing exceptions which are the following: Mid-level exception, where teams are able to sign a contract with a player for a specified maximum amount which depends on the team s cap status. Before the season the mid level exception was independent from the cap status. Bi-annual exception, where teams are allowed to sign a contract with any player at $1,672,000 for up to two years. 8

9 Rookie exception, where teams are able to sign contracts with the players chosen in the NBA draft. Larry Bird exception, where teams are able to exceed the salary cap to re-sign their own free agents, at an amount up to the maximum salary. The length of the contract can be up to five years. Between the season and the season, the maximum length was 6 years and between the season and the season, 7 years. In order for a player to be considered as a Bird free agent, they must have played in the NBA for at least three years, they must not have been waived and must not have changed teams. Non-Bird exception, where a team is allowed to re-sign its own free agent for either the 175% of his last season s salary, or the NBA's average salary, whichever is greater. In order for a player to be considered as an Early Bird free agent, they must have played for the same team for at least two seasons. Minimum Salary exception, where teams are able to sign a limitless number of free agents for the NBA s minimum salary for two years maximum. The NBA teams, whose payroll is over the salary cap, must pay a dollar for dollar luxury tax. The revenues from these taxes are collected by the NBA authorities and then divided among teams which do not surpass salary cap. Lockout A lockout is started by the owners of NBA teams because of the discrepancy between them and the National Basketball Players Association (NBPA) about the negotiations for the league's collective bargaining agreement (CBA). During the lockout, players cannot access NBA team facilities, trainers, or staffs and teams cannot sign, trade or waive players. The NBA lockout The NBA lockout lasted from July 1, 1998 to January 20, 1999.NBA owners requested a new CBA by asking for a maximum players contact allowed to sign and changes to the salary cap. Those demands were rejected by NBPA and the lockout began. The major issue was the existence of loopholes which allowed teams to exceed the payroll limit. The most known one was the Larry Bird Exception which enabled NBA teams to spend an unlimited amount of money to re-sign their own players. The lockout ended on January with the agreement between NBA owners and NBPA. Consequently, the Larry Bird Exception was retained, though maximum annual pay raises 9

10 were capped. Also, it capped players' salaries at between $9 million and $14 million, depending on how long they had played in the NBA. A rookie pay scale was introduced, with salary increases tied to how early a player was selected in the NBA Draft. The league's minimum salary was increased by $ 15,000. The most important result of the NBA lockout is the introduction of a luxury tax that imposed a dollar-for-dollar payment for teams whose payrolls were over the salary cap. Because of the changes stated above, the data before season cannot be utilized. 10

11 Literature Review This essay does not fully belong to only one field of economics however the main base is provided by the field of sports economics. In the next section we will review the historical background of this particular field. Historical Background The economics of professional team sports is a young and relatively small field of academic research. Simon Rottenberg and Walter Neale are considered to be the founders of economics of professional sports. The pioneer of sports economics Simon Rottenberg, is an economist at the University of Massachusetts at Amherst with his article published in the Journal of Political Economy in 1956 which examined the baseball player market. This article is still considered as very up to - date, even though 60 years have passed from its publication. The other founder of sports economics is considered to be Walter Neale with the publication of his paper The peculiar Economics of Professional Sports, published in the Quarterly Journal of Economics in Instead of the expected growth of this specific field by the two economists, surprisingly none of them published any other essay with significant contribution to the field. On the other hand, other economists took over and continued publishing regularly on the subject, such as Gerald Scully, James Quirk and Roger Noll in the USA, Peter Sloane in the UK, Braham Dabscheck in Australia and Colin Jones in Canada. Roger Noll achieved a great milestone with the publication of the book Government and the Sports Business in 1974, which contained a great number of very important papers from the first ever conference on sports economics held at the Brookings Institution in December of 1971.Roger Noll s book caused the start of a rapid growth of the sports economics field in the USA, as more and more studies of the subsidies of sports arenas and stadiums, the demand for sports and sports sponsorship and broadcasting were conducted. The fist monographs on sports economics are Baseball and Billions, written by Andrew Zimbalist and Pay Dirt, written by James Quirk and Rodney Fort. Both of them were published in In the early 2000 s the International Association of Sports Economists (IASE) was founded in France. Also, at the same time, a new journal started in California, that was called The Journal of Sports Economics, which mainly publishes studies and papers related to professional team sports. Also, a book edited by Andrew Zimbalist, which contains a 11

12 collection of papers between 1950 and 2000, was published in In addition, the book Handbook on the Economics of Sport edited by Wladimir Andreff and Stefan Szymanski includes 86 contributions covering the most important topics of sports economics written by 65 sports economists. Finally, in 2007 Stefan Késenne from the University of Antwerp and KU Leuven in Belgium wrote the book The Economic Theory of Professional Team Sports which analyzed some of the most important topics of sports economics, such as the players and sports product market, the transfer system and the revenue sharing to teams. As we can notice the subject which we examine in our thesis does not fully belong to the field of sports economics as this field is mostly concerned with winning prediction, demand of the sports product and the teams motives effect on the league and consumers( fans). The only reference we can find is from some independent studies especially from The Journal of Sports Economics. However these researches are empirical ones and based on the examination of factors which researchers considered that they had study value. As we stated before, this does not belong into the field of sports economics only but also in the field of contract theory and we will examine past papers and theories which seem to have a major effect on NBA players salaries. In this chapter we review essays, studies and articles which researched the NBA players salaries and the factors that affect them. Competitive Balance One of the most important elements of the NBA championship which puzzles every sports league in the world is the maintenance and improvement of the competitive balance. Competitive balance is the balance between the sporting capabilities of teams. The reason why competitive balance is so important for a league is that the proper one creates uncertainty of the championship s outcome which leads to a raise of demand for the league s product. In sports economics, there are two kinds of teams, profit maximizing teams which target is to maximize their profits and win maximizing teams which target is to maximize the wins regardless of profits. American teams in general are considered win maximizing ones by the sports economics and our analysis will take for granted that NBA teams are win maximizing ones. There are two key points in order to improve the competitive balance, the revenue sharing and the demand for young talent To begin with, in sports economics, there are two models, Walras equilibrium model and Game Theory model which reflect the effect of share revenue both models conclude that in 12

13 a win - maximization league revenue sharing improves competitive balance and increases the player salary level. About demand for young players, in a win maximization league such as the NBA there is more demand for talented young players and higher average salaries than in a profit maximization league however the distribution of talent is more unequal and the total revenue of the league is lower than in a profit maximization league. According to Kesenne [26], transfer system leads to many unwanted results. First of all, with the transfer system, managers are paid separately in order to contribute to a player s transfer which teams spend a significant larger amount of money in order to acquire a player. Furthermore, the competitive balance of the league worsens as richer teams are able to obtain the best players from smaller and poorer teams. As a result a few teams are able to compete for the championship while the small teams survive only by selling their best players and gain the transaction fees. In addition, transfer system causing the undevelopment of youth talent as teams prefer to invest to players who have already shown a great performance level and avoid acquiring young players whose potential is uncertain and need a significant amount of time to reach the level of the older players. In order to the teams and the league not suffer from these consequences and to improve the competitive balance, Kesenne suggest some alternative measures. These are the abolishment of transfer system, the introduction of hard caps in contracts duration and the banning of players release. In addition, Kesenne proposes the introduction of a special league where only youth players will participate in order to youth players have the opportunity to develop their skills. The NBA seems to accept the sports economics theory for win maximization leagues and take into account the Kesenne s criticism on the transfer system and accept the alternative measurements which he proposed. NBA has a number of mechanisms which try to improve the competitive balance. These are the salary cap, the NBA draft, the NBA Development League and the prohibition of transfers. To begin with, salary cap defines the amount of money that can be spent on free agency. As we stated earlier, salary cap is determined by the leagues total revenues. The revenues are equally distributed to all teams. In addition, the NBA has not a transfer system. Each player has the right to sign with any team he wants to without any restrictions. Furthermore, the contracts length and the amount of money that they offer are capped according to the statutory regulation of the CBA. In addition, contracts are respected. Even if a team waives a player and as a result he becomes an unrestricted free agent, he receives the amount of money which is stipulated in the contract. For the protection of both the young players and the teams which are not able to compete for the championship because of lack of talent in their rosters, the NBA has created the NBA draft and the NBA Development League. In the NBA draft weaker teams are able to pick the most talented young players relatively cheaply as the rookie contracts are fixed. In addition, 13

14 the players who are not able to find a contract in a NBA team can be assigned to a NBA Development League team. These teams are subsidiary to the NBA teams and they have very close connections. Thus, because of the restriction on the NBA teams roster (each team can only have fifteen players) each NBA team can assign a player who does not earn a position to the team s roster to the NBA Development Team in order to develop his basketball skills. Also NCAA can be considered as a league designed for the training and the development of youth players. It should be remembered that our thesis does not examine the efficiency of the NBA measurements on improving the competitive balance of the league but their impact on NBA salaries. In order to find if these measurements affect the NBA players salaries, our model will include a variable which will state the duration of the contract and a variable which will show the amount of salary cap when the contract is signed. Salary Discrimination There are plenty of studies which examine the existence of discrimination in professional sports. To begin with, Eschker, Perez and Siegler [12] (2004) collected all the NBA players performance and wages data from the season and monitored their progress until the season and created a semi-log model. The result of the research was that, except from the and seasons, there is no sign of salary discrimination based on nationality. Yang and Lin [6] (2010) scrutinized a dataset of NBA players between the season and the season and they used the technique of two - stage double fixed - effect model. They conclude that NBA players coming from overseas sign smaller contracts than the American players. They also stated that international players, whose countries have a strong economy, get better labor market treatment. However, Yang and Lin examined mainly non-basketball variables such as the countries of the international players and their market labor characteristics. Hill and Groothuis [13] (2013) examined whether there is a wage discrimination or a wage premium in the NBA with a dataset which included players from the season to the season. A dummy variable for international players who had not applied for an US college and another dummy variable for international players who played for an US college are included in their model. They conclude that there is not either a wage discrimination or a wage premium. Bodvarsson and Fuess [21] (2006) examined whether there is a wage discrimination based on nationality and race in Major League Baseball (MLB) by using a dataset with 557 observations from the and the season. They used dummy variables in order to check both cases. The results show that there is not any evidence of race discrimination, however, foreign players are given better salaries. 14

15 Wen-Jhan Jane, Sheng-Tung Chen and Min-Hua Kuo [27] (2013) examined if there is salary discrimination caused by nationality in the Nippon Professional Baseball (Japanese baseball league) by regressing a dataset which included 663 observations from the to the season. They conclude that there is a significantly large premium wage for foreign players. As we can see these researches lead to different results. In the model, a dummy variable, that will notify if a player is non-american, will be included aiming to examine whether there is salary discrimination based on nationality. Another topic which is widely debated is salary discrimination based on position. In the game of basketball there are 5 positions: point guard, shooting guard, small forward, power forward and center. A player s position is depended on their height and which basketball skills they have, such as their ability to shoot from long and short distance, rebound pass the ball et cetera. Many studies refer to salary discrimination based on position and in the next chapter we will review a few of them. To begin with, Brown, Spiro, and Keegan [4] (1991) ran a research about salary discrimination of the NBA players. They used performance data and a dummy variable for the players race. They deduce that there is a wage discrimination based on the players race. However, Matthew Dey [11] (1997) criticized the results by using the same data and regression model but he included a variable for the position. The salary discrimination was based on position in Dey s essay. Specifically he stated that there is a premium wage given to players who played in the center position. James Richard Hill [16] (2004) conducted a research similar to one of Brown, Spiro, and Keegan. He searched for a wage discrimination based on the race in the NBA. He created a model which included variables for the height and the performance statistics and a dummy variable for the race. At first, he ran the regression without the variable for the height.as a result, the dummy variable for the race was statistically significant and showed a salary premium for the white players. Nevertheless, when he ran the same regression including the variable for the height, it was statistically significant and the dummy variable was not. Hill stated that the race discrimination was a result of the correlation between the race and the height. He found that there is a salary premium for the players height and no evidence of wage discrimination based on the race in the NBA. Yang and Lin [6] (2010) in their research find that height and position are statistically significant determinants of the NBA players wages. Masi, Ksiazek and Clarke [22] (2015) searched for salary discrimination in the NBA. They took into account the players performance, their race and their position. The results show existence of race discrimination. Also, there is evidence of a premium wage for players who play at the center position. Vincent and Eastman [7] (2009) made a research about NHL (National Hockey League) players. They ran a regression which contains position height and performance indicators in 15

16 order to test if players wages are affected by those factors. They conclude that position is statistically significant, however, height is not. As we can see, many researches have shown evidence of salary discrimination based on the position of the players. In our regression model we will include 5 dummy variables which will state the players position. Age One key factor of the players performance is their age. There are many opinions of which age is the golden age of a basketball player. Many researchers claim that a basketball player s prime lasts from their 25 years until their 30 years [24] [25], while others insist that a player s performance is dropping continuously from the age of 25 [8] [10]. The element on which all researchers agree is that the players performance has a reversed U-shape. For that reason, a variable which signifies age and a variable which signifies age squared will be included in the regression model. College Attendance and Early Entry to the NBA One of the most widely debated issues in the NBA is the age that players have, when they enter in the NBA. Many people think that players are not physically and mentally ready to begin their professional career without attending college. On the other hand, many people insist that many players have the required skills to play for a NBA team and college basketball will not help them develop their basketball ability and that they will stay stagnant. In this thesis, we will not examine the results of college in the players spiritual cultivation. The fact that concerns us is if players who have attended college are capable of signing better contracts over time than those who have not. Groothuis, Hill, and Perri [14] (2007) examine the phenomenon of entering in the NBA straight out of high school for young players. First of all, they hypothesize that NBA teams scouts use NCAA as a reliable signaling mechanism. They state that, thanks to players attendance to college, NBA teams are taking less risky decisions about the players who they will draft. Furthermore, with the induction of the rookie pay scale from the NBA season, teams have an important motive to draft players as soon as possible, because their cost is less than the marginal revenue product given by the young players. Also, teams are able to obtain very good players with superstar potential with low wages for multiple years before the rival teams. In addition, teams are able to renew their players contracts or give them qualifying offers and, as a result, they can keep their players for many years and not necessarily seek for talented free agents in the offseason. Even if their decisions are wrong, their bad choices can be waved without large cost. On the other hand, players prefer to start 16

17 their professional career early. Because of the existence of the rookie pay scale, new NBA players are committed to low wages for 3-4 years and then they are allowed to sign a multimillion-deal. So it is obvious that players want to join the league as early as possible in order to work under limited contracts at a very young age and claim a contract with a large wage in a relatively young age maybe before their basketball prime. Groothuis, Hill, and Perri estimated that the average age of the first round picks dropped from 22.3 years to 20.5 years between 1994 and 2004 confirming the previous statement. The authors tried to estimate a wage model, which included performance statistics, a dummy variable, which shows if a player is under a rookie scale contract, and an interaction variable, which combined the previous dummy variable with the player s experience. It is occurred that the first two years of a contract are beneficial for players, however, the rest of them are unbeneficial. Moreover, the authors observed first round picks performance between the season and the season. They concluded that players who skip college or college freshmen have a lower performance in the first two seasons comparing to players who stayed for more years in college, but in the third and the fourth season they outperformed college juniors, seniors and graduates. This means that very talented players believe that college does not help them improve their basketball skills and they skip college or leave it early. In our model a dummy variable, which will show if a player attended college, will be included and test if there is a premium wage for college or high school players. Shirking and Contract Year effect Every contract in the real world is not complete. When a player signs a multi-year contract, they have the motive to drop their effort and performance, since the contract is guaranteed and there is no risk of losing their salary. On the other hand, when players enter to their contract year namely in the year when their contracts expire, they will put their best effort in order to raise their performance statistics and find a more attractive contract. This phenomenon is called contract year effect. In the contract theory there are some essays written by Holmstrom [3], and Alchian and Demsetz [2] (1979, 1972). In these essays it is claimed that there is a correlation between the years of contract signed and shirking. The free agent tends to maximize their effort before they sign a contract and decrease their effort after they sign the contract. There are some researches looking for the contract year effect. To begin with, Berri and Krautmann [9] (2006) found evidence of shirking effects in the NBA players. However, these effects are very sensitive to the specification of productivity. If NBA efficiency score is used, there are shirking effects, but, if marginal products of the NBA players are used as productivity indicators, the shirking disappears. 17

18 Stiroh [19] (2007) created a dataset with the performance stats and salaries of the NBA players from the season to the season plus the performance statistics of the teams they belonged to. He stated that players performance in contract year is statistically significant and there is evidence of shirking. Krautmann and Oppenheimer [1] (2002) searched for a correlation between the wages and the contract length. They used performance statistics and salaries from MLB players from the season to the season. They found a positive statistically significant coefficient of the interaction of years of the contract on salary, however, a negative statistically significant coefficient of the impact between the years of the contract and the performance was found. Link and Yosifov [5] (2011) used the same model as Krautmann and Oppenheimer, but they used a larger dataset and winshares as a new independent variable. The results of their research are exactly the same as the results of Krautmann s and Oppenheimer s essay. Stankiewicz [18] (2009) tested if contracts length of the MLB (Major League Baseball) players has an effect on their productivity. She created a dataset of 50 players who signed one-year contracts and 50 players who signed multi-year contracts. Surprisingly, the study concludes that players who signed multi-year contracts are more productive than players who signed one- year deals. As we can see contract year effect is a subject worth studying. In order to check if there is this effect and its magnitude to salaries, except for the players career average statistics, the last season s performance statistics will be included to our model. Players Performance and Efficiency The most important factor of a player s contract is their on-court performance personal statistics. The most used statistics are: Points per Game (ppg), Rebounds per Game (reb), Assists per game (ast), Steals per game (stl) and Blocks per Game (blk). The statistics ppg and ast point out their offensive performance while stl and blk point out their defensive performance. Rebounds are part of the offense and the defense in the game of basketball. For this reason rebounds are separated into two different statistics: offensive rebounds (orb) and defensive rebounds (drb). One of the unique characteristics of basketball in general is that there are not offensive and defensive positions. So a player must play offense and defense at the same time. Consequently, both offensive and defensive performance stats reflect a player s basketball ability. In basketball, points are used to keep track of the score in the game. If a player makes a shot from outside the 3-point line, they score 3 points. If a player makes a shot from inside the 3- point line, they score 2 points. If a player makes a free throw, they score 1 point. 18

19 In basketball, a rebound is a statistic awarded to a player who successfully collects the ball after a missed field goal attempt. Rebounds determine which team will have ball possession after a missed shot or free throw. An offensive rebound occurs when an offensive player retrieves the ball after a missed field goal attempt or free throw and the offensive team retains possession of the ball. A defensive rebound occurs when a defensive player retrieves the ball after a missed field goal attempt or free throw and the defensive team gains possession. The vast majority of the rebounds are defensive, because the defensive team is closer to the basket. The most important qualities a player should have in order to be a great rebounder are strength, height and great versatility. This is the reason why rebounds are collected mostly by power forwards and centers. However, there are some shorter players who have shown great rebounding ability. An assist is attributed to an offensive player who passes the ball to a teammate in a way that leads to a score by field goal. Only the pass directly before the score counts as an assist. A pass leading to a shooting foul and scoring by free throws does not count as an assist. Point guards usually have the most assists per game, as their role is organizing the offense, passing and ballhandling. However, there are some players - especially small forwards- who record a great number of assists per game. A player gets a steal when they legally force another player to commit a turnover. This can be succeeded by defecting and controlling or by catching an opponent s pass or dribble without touching opponents hands. Also, a steal is earned by a defensive player even if they do not deflect or tip the ball, but they end up with the ball. Stealing the ball requires great on-ball defense, defensive awareness, quickness, speed and good reflexes & position on the court. As a result there is no position which helps players get more steals. While point guards and shooting guards have the edge of getting more steals because of their quickness and speed, many players from the other positions have exceptional stealing abilities. In basketball, a player gets a block when they legally deflect an opponent s field goal attempt. The defensive player must not touch the opponent s hand, otherwise a foul will be called. Furthermore, the ball must travel upward or be at its apex, when it is deflected, otherwise it is ruled as a goaltend namely, the block does not count and the field goal attempt is automatically considered as made and provides to the opposing team 2 or 3 points, depending on if it was a 2-point or 3-point attempt. In addition, a goaltend happens if the ball touches the board and, then, is deflected by a defensive player. Also, a defensive player s block does not count if the opposing player is fouled by the same or another defensive player while attempting a field goal. Moreover, if a shot gets deflected and still the ball gets into the basket, the shot counts and there is no block. Every block is counted as a missed field goal attempt for the opposing player. 19

20 Blocking shots requires great versatility, defensive awareness, good jump timing. Also, it is obvious that tall players with large wingspan have the edge in this statistical category. Hence, in contrast with steals, blocks seem to be recorded mostly by power forwards and centers. However, there are few players who play in the guard position and are exceptionally good shot blockers. The previous statistics show the positive performance of players. Nevertheless, it is necessary to take into account the undesirable production of players. The most common statistics concerning the players undesirable production are turnovers and fouls. In basketball, a foul is a transgression of the rules more serious than a violation. Most fouls are a result of illegal personal contact with an opponent or unsportsmanlike behavior. Fouls can have a negative influence on a team as a player can foul-out, namely, they disqualify from the game, or allow the opponents to shoot free throws for easy points. A player commits a turnover when their team loses possession of the ball before one player of their team attempts a field goal. This can happen from player s mistakes such as letting the ball get stolen, travelling, three second violation, five second violation, backcourt violation, throwing the ball out of bounds, stepping out of bounds, receiving a technical foul and committing an offensive foul. All the previous statistics reflect players performance. It is obvious that, for example, if a player had 20 points and took 10 shots, they had a better performance than someone who had 20 points and took 15 shots. In addition, if a player scores 10 points in 20 minutes, they have a better performance than one who scored 10 points in 30 minutes. So it is understood that players efficiency is equally important as performance statistics. PER (Player Efficiency Rating) is a statistic which measures players per minute performance. This statistic is standardized in a way that its league mean is 15 across seasons. It is created by the ESPN writer and analyst John Hollinger and its purpose is rating players statistical performance. The formula of PER is: uper = (1 / MP) * [ 3P + (2/3) * AST + (2 - factor * (team_ast / team_fg)) * FG + (FT *0.5 * (1 + (1 - (team_ast / team_fg)) + (2/3) * (team_ast / team_fg))) - VOP * TOV - VOP * DRB% * (FGA - FG) - VOP * 0.44 * ( (0.56 * DRB%)) * (FTA - FT) + VOP * (1 - DRB%) * (TRB - ORB) + VOP * DRB% * ORB + VOP * STL + VOP * DRB% * BLK - PF * ((lg_ft / lg_pf) * (lg_fta / lg_pf) * VOP)] 20

21 Where: factor = (2 / 3) - (0.5 * (lg_ast / lg_fg)) / (2 * (lg_fg / lg_ft)) VOP = lg_pts / (lg_fga - lg_orb + lg_tov * lg_fta) DRB% = (lg_trb - lg_orb) / lg_trb tm, the prefix, indicating of team rather than of player lg, the prefix, indicating of league rather than of player min for the number of minutes played 3P for the number of three-point field goals made FG for the number of field goals made FGA for the number of field goals attempted FT for the number of free throws made FTA for the number of free throws attempted VOP for the value of possession (but in reference to the league, in this instance) RB for the number of rebounds: ORB for the offensive rebounds, DRB for the defensive ones, TRB for (the total) combined, RBP for percentage of the offensive or the defensive rebounds AST for the assists STL for the steals BLK for the blocks TOV for the turnovers PF for the personal fouls Also it is needed to adjust pace: pace adjustment = lg_pace / team_pace Where: Pace= Possessions per game For missing values: estimated pace adjustment = 2 * lg_ppg / (team_ppg + opp_ppg) The pace adjustment is made to uper( aper): aper = (pace adjustment) * uper Standarizing: PER = aper * (15 / lg_aper) 21

22 PER has been criticized a lot. It is insisted that PER cannot reliably value defensive performance as it includes only steals and blocks as defensive performance statistics. However, we should keep in mind that basketball statistics in general have issues with reflecting defensive performance. Also, Berri [10] supported the opinion that PER rewards inefficient shooting. He quoted: "Hollinger argues that each two point field goal made is worth about 1.65 points. A three point field goal made is worth 2.65 points. A missed field goal, though, costs a team 0.72 points. Given these values, with a bit of math we can show that a player will break even on their two point field goal attempts if they hit on 30.4% of these shots. On three pointers the break-even point is 21.4%. If a player exceeds these thresholds, and virtually every NBA player does so with respect to two-point shots, the more they shoot the higher their value in PERs is. So a player can be an inefficient scorer and simply inflate their value by taking a large number of shots." Hollinger answered: Berri leads off with a huge misunderstanding of PER that the credits and debits it gives for making and missing shots equate to a break-even shooting mark of 30.4% on 2-point shots. He made this assumption because he forgot that PER is calibrated against the rest of the league at the end of the formula. Actually, if we took a player that was completely average in every other respect for the season rebounds, free throws, assists, turnovers, et cetera and gave them a league-average rate of shots, and all of them were 2- pointers, and they shot 30.4%, they'd end up with a PER of As long-time PER fans know, that would make them considerably worse than nearly every player in the league. To end up with a league-average PER of 15.00, the actual break-even mark in this case is 48.5%, which is exactly what the league average is on 2-point shots this season. Despite the criticism PER is considered as the best statistic for efficiency and we will include it in our model. Nevertheless, we will not completely reject Berri s criticism and we will include in our model field goal percentage, three-point field goal percentage, free throw percentage and effective field goal percentage. Effective field goal percentage (Efg) is a statistic that adjusts field goal percentage with regard to the fact that a 3-point field goal is worth one more point than a 2-point field goal. The formula is: Efg = ( FG * 3P) / FGA where: FG = Field goal percentage 3P = 3-point field goal percentage FGA = Field goal attempts which includes both 2-point and 3-point field goal attempts The vast majority of the articles, the essays and the studies have researched the causality between the NBA players wages and their on-court performance. This is a natural fact given that the on-court performance of a player is the most important aspect they can offer to their team. For this reason it is worthless to refer to multiple researches based on players performance. However we would like to add some other researches results below. 22

23 Berri, Brook and Schmidt [10] (2007) stated in their book that PER is a statistic that leads to larger wages. Also, they argue that scoring a lot of points, even inefficiently, leads to good contracts. Lyons Jr., Jackson Jr. and Livingston [23] (2015) tried to find the determinants of the NBA players salaries based on their performance. Their dataset contain the salaries and the performance statistics of 243 NBA players in the season. By running multiple regressions they conclude that points per game, field goal percentage, rebounds per game, assists per game and fouls are statistically significant with good estimators. However, 3- point field goal percentage, free throw percentage and defensive statistics (steals and blocks) are statistically insignificant. We believe that the different results of the essays about the NBA players on-court performance are caused by the size of the sample, the years and the selection of other variables from the authors. Conclusions We believe that our thesis will help the expansion of the current bibliography of the field of sports economics. To begin with, the field of sports economics does not provide us with a consolidated theory about the factors that teams take into account when they offer contracts to free agents. The majority of our thesis references are mainly essays which are derived by the examination of a number of factors which arouse the researchers interest. We try to test all the findings of these researches with the use of a great number of variables which contain lots of information about a player s performance level and characteristics in order to minimize the risk of omission of a factor which has effect on NBA players salaries. No other essay examines such a large number of variables. In addition, our thesis will examine contracts from the past eighteen seasons. We did not find any essay which examines the determinants of players wages at any sport which contained contracts from so many seasons. Our dataset contains players contracts from all the NBA s recent history which will make our results consistent through time. Furthermore, many essays do not contain a shirking model while others do not include a model which contains career average performance statistics. We include both models in order to be able to compare in which one our data fits better, so that, we reach some very important conclusions about if NBA teams consider a player s performance through his entire career or just the performance he had shown just in the year before he signed his new contract. Finally, our essay contains a number of different contracts which are offered to the same player. So, there may be a cluster effect, unobserved by the OLS t statistic. Hence, cluster standard errors will be retrieved in order to conduct efficient t tests for the estimators statistical significance. In addition, we will test if the assumptions of the classic linear model 23