THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF ECONOMICS

THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF ECONOMICS ARE MAJOR LEAGUE BASEBALL PLAYERS PAID THEIR MARGINAL REVENUE PRODUCT? BRIAN SCHANZENBACH Spring 2014 A thesis submitted in partial fulfillment of the requirements for a baccalaureate degree in Economics with honors in Economics Reviewed and approved* by the following: Ed Coulson Professor of Economics Professor of Real Estate Economics Jeffrey and Cindy King Fellow in Real Estate Thesis Supervisor Russell Chuderewicz Senior Lecturer in Economics Honors Advisor * Signatures are on file in the Schreyer Honors College.

i ABSTRACT This thesis studies whether Major League Baseball players are paid their marginal revenue product. In other words, the goal is to determine whether the players are paid the amount of money they make for their franchise. Major League Baseball wants a competitive league because a competitively balanced league makes the most amount of money. In order to have a competitively balanced league, the players must be paid their marginal revenue product. Thus, it is in the league s best interest for the players to receive their marginal revenue product as compensation. In order to calculate the marginal revenue product, I ran winning regressions and attendance regressions. The winning regressions calculated what factors into a team s winning percentage, while the attendance regressions calculated what factors into attendance at a ball game. The winning regressions gave me the marginal product and the attendance regressions gave me the marginal revenue. I was then able to calculate the marginal revenue product, as it is simply the marginal revenue multiplied by the marginal product. The next step was to regress the player salary on MRP, so that I could determine whether players are paid their marginal revenue product. I found that, on average, all Major League Baseball players are underpaid. Therefore, my recommendation to the league would be to increase the average salaries of each position accordingly to create a more competitively balanced league.

ii TABLE OF CONTENTS List of Tables... iii Acknowledgements... iv Chapter 1 Introduction... 1 Chapter 2 Literature Review... 5 Chapter 3 Data and Methodology... 13 Chapter 4 Results... 22 Chapter 5 Conclusion... 28 Appendix A Data... 30 BIBLIOGRAPHY... 91

iii LIST OF TABLES Table 1. Winning Regression Data... 17 Table 2. Attendance Regression Data... 20 Table 3. Winning Regression... 22 Table 4. Attendance Regression... 23 Table 5. Salary and Marginal Revenue Product Regression Data... 26 Table 6. Determination of Whether a Player is Paid Their MRP... 27 Table 7. Team Data... 30 Table 8. City Population and Team Attendance Data... 31 Table 9. Player Salary Data... 32 Table 10. Field Player Statistics Data... 60 Table 11. Pitcher Statistics Data... 75

iv ACKNOWLEDGEMENTS Professor Edward Coulson, For your advice throughout the completion of this thesis. Professor James Tybout, For your wisdom and help through the duration of the Honors Program in Economics.

Chapter 1 Introduction Professional athletes are paid incredibly high salaries to play a game that is typically reserved for children. Some people believe athletes are paid far too much since their occupation is nothing more than entertainment. Others believe their salaries are perfectly just given the utility of entertainment for each individual can be substantial. The fact of the matter is professional sports franchises are cash cows. They make a huge amount of money, create many jobs, and are responsible for a great deal of cash flow, whether it is advertising campaigns during games or internal financing. The goal of this paper is to attempt to determine whether each position in major league baseball is paid, on average, the amount they make for their team. In a competitive market, as professional sports intend to be, a player will be paid the amount they make for their team given complete free agency. However, complete free agency does not exist because players sign contracts that are longer than one year. However, we will assume that when each player signs their contract they were provided with a salary equal to their marginal revenue product. If they are paid less than their marginal revenue product then they are underpaid, while if they are paid more they are overpaid. In order to go about solving this problem, first I did research to discover what work had already been completed in this area and what models were used. The major piece of literature was Scully s paper on how performance influences salaries in Major League Baseball. He wrote the first major article on pay and performance in baseball and

2 his model has been used in various papers (Scully 1974). I based my model on Scully s with a few changes. The other major literature I used was a thesis written by Brian Fields entitled Estimating the Value of Major League Baseball Players. His paper is an analysis similar to Scully s paper, but uses more recent data (Fields 2001). My paper is similar as I am attempting to determine a player s marginal revenue product to compare it to his salary. I will then be able to determine whether they are overpaid, underpaid, or paid at the margin by comparing these two values. However, there are a few major differences that make my study unique and interesting. First, my paper looks at the 2011 Major League Baseball season. Since it is an analysis of the 2011 season, it is the most recent analysis of this kind. This is important, as salaries, statistics, and franchise values have exploded in recent years. Second, my paper uses attendance to measure marginal revenue product. I believe that this will give a more accurate value because it is easier to measure attendance, since those numbers are readily available, while revenue numbers are not. However, there are a few problems with using attendance to measure marginal revenue product. First off, there are things that affect attendance that players do not have any control over. A few examples of these would be the weather, other events going on in the area, and promotional giveaways. I attempted to account for these as best I could in the regression model, but not everything was accounted for. Another major issue with using attendance is there is a maximum capacity at each stadium. There will be some bias when calculating the affect of different statistics on attendance because there are a finite number of fans capable of viewing the game. There may be more fans that want to see a given game, but we cannot account for that because they were unable to purchase tickets.

3 The paper will begin with a literature review of all relevant information that was used to write this thesis. That includes the two sources discussed above, as well as many other resources. The next step is the data work. I have run many regression models to determine the marginal product, marginal revenue, and affect of salary on MRP. I analyzed the data from the regressions to further understand which statistics matter and how much they matter. I analyze the data and explain the calculations. I then perform the marginal revenue product and salary calculations to get the numbers I will compare. Next, I compare those numbers to determine whether players are paid effectively or not. I then am able to determine which positions are overpaid and which are underpaid. The other interesting thing about this analysis is it is not simply a sports paper, but can be used to understand the labor market economically. It is difficult to measure the marginal revenue product of employees because so many factors do not have numbers associated with them. For example, the only true way to measure someone s marginal revenue product is by looking at how much work they do. However, this leaves out a lot of factors including the work performed, the value of each project, and various intangibles that have no measurable data. Thus, one of the few occupations that can be analyzed to see whether the workers are underpaid or overpaid is professional athletics. There are data and statistics that can show how valuable a player is to the team and how much the team benefits from said player. Therefore, the analysis of Major League Baseball players is essentially a representation of the labor market in the economy. The Sports Business as a Labor Market Laboratory goes into detail about how professional athletics are a perfect way to analyze the labor market because the employees performance grades are so readily available to see. He is able to examine monopsony in

4 the labor force, discrimination, how ownership does not have any impact on the allocation of resources and instead only affects how wealth is distributed, and the impacts of supervision and incentives on behavior. Lawrence M. Kahn states, However, taken as a whole, this line of research produces additional evidence that making the labor market more competitive leads to higher salaries than would be the case under monopsony. Nonetheless, during the 1980s there still appeared to be widespread monopsonistic exploitation in baseball. Whatever the cause of segregation, it can have long-term consequences. In baseball, for example, managers are drawn from the middle infield positions, which have been disproportionately white. The mobility evidence appears to contradict the stereotype that while in the old days (before free agency), players stayed with one team, but now players are mercenaries and will move at the drop of $50 million. However, we often forget that there were many trades before free agency, and once a player moves nowadays to a team offering him a long-term contract the mercenary stereotype that player then typically becomes relatively immobile. In the major team sports that have been the primary focus of this paper, free agency has brought with it an increased incidence of long-term contracts, a finding Lehn (1990) argued was consistent with wealth effects, as players in essence buy long-term income insurance. He noted that as the incidence of longterm contracts went from virtually zero during the days of the reserve clause to 42 percent of baseball players with at least two years pay guaranteed as of 1980 (Kahn, 2000). The article is a good examination of professional athletics as a representation of the labor market.

Chapter 2 Literature Review Major League Baseball is a game driven by statistics. This makes it easier to analyze when compared to other sports, as you can truly understand what is going on and account for almost everything. There has also been an abundance of research done previously on baseball statistics. This has given me a great database of research I am able to use to pursue my goal of determining whether Major League Baseball players are paid their marginal revenue product. Gerald Scully wrote the first important paper in 1974 (Scully 1974). He attempted to estimate the marginal revenue product for players to determine how much they should be paid. He used a model with two equations. The first equation is a team revenue function that attempts to relate the winning percentage of a team and the characteristics of the market in the team s area to the revenues for that team. The second equation that goes into the model is a production function that attempts to relate team winning percentage and output to various team inputs. Scully then analyzed a season in the late 1960 s to determine player s wage compared to their MRP. He determined, through his model, players were paid about 10-20% of their MRP, which shows the reserve clause did cause a large economic loss to the players. This leads me to Anthony Krautmann s paper entitled What s Wrong with Scully-Estimates of a Player s Marginal Revenue Product (Krautmann 1999). Krautmann claims that Scully s assertion that even the highest paid athletes are grossly

6 underpaid compared to their marginal revenue product cannot possibly be correct. He cites the huge bidding wars during free agency as the main reason he finds it difficult to believe owners are swimming considerably below the marginal revenue product line for player salaries. Thus, in this paper he suggests an alternative method to estimate a player s economic value. Krautmann explains Scully s approach is proportional, where if a player accounts for a given percentage of the team s at bats you multiply that by their slugging percentage to determine their MRP. However, Krautmann uses an approach that he terms the free market returns approach. This method utilizes the belief that intense free agent bidding wars cause salaries to grow until they reach the MRP. The main difference in Krautmann s model is he only looks at free agents. He is not concerned with every single player in Major League Baseball. He believes only incorporating free agents will allow the model to truly determine whether players are paid their marginal revenue product because the only instance where this is a possibility is when a bidding war ensues. This theoretically pushes the salary higher and higher until it reaches the player s marginal revenue product, where the bidding will cease. The only time this theory exists is when a player is a free agent. Thus, Krautmann estimates the competitive return to performance based on this intuitive notion. Krautmann s results show players are underpaid, but less than by the amount Scully claims. His results show players that are considered journeymen are paid a salary about 85% of their marginal revenue product. Journeymen s salary is closest to their marginal revenue product since they have moderate production and have substantial negotiating rights, since they have been around a while. Thus, the other players are paid a salary that is less than 85% of their MRP.

7 In order to represent Scully s method fairly, a paper that supports his model will also be analyzed. The paper is written by John Bradbury and is entitled What's Right with Scully-Estimates of a Player's Marginal Revenue Product (Bradbury). Bradbury claims while Scully s approach is not perfect; it is not as far off as Krautmann claims. He feels Krautmann s method is no better as it eliminates the problems from Scully s method only to create new issues. The major difference between Scully s method and Krautmann s method is Scully examines all players, while Krautmann only examines free agents. Krautmann argues Scully s method cannot possibly measure marginal revenue product accurately because there is not pure competition to sign every player every year. Many players sign contracts for more than one year, so there is not a bidding war after every season to accurately measure their new marginal revenue product every year. Krautmann believes Scully s model underestimates marginal revenue product because of the lack of competition to sign each player every year, so he examines only free agents to account for this. He believes he will more accurately measure marginal revenue product through this method because of the constant bidding war for these players. The first supposed problem of Scully s method is the marginal revenue product estimates are far too high. Scully initially claimed they were well above salaries due to collusion among the owners through the reserve clause, which was a major problem when Scully first created his model. Krautmann claims the model was wrong because when it was run again about a decade later the salaries were still much lower. However, Bradbury claims the numbers were so unrealistic due to a unique sample or improper specification, as when he used a Scully-inspired approach the numbers were much more realistic. Another problem with the Scully-estimates was the correlation between them and salaries were

8 not strong. Bradbury proved this was not the case, and the correlation was strong. However, Bradbury claims Krautmann s method is fundamentally wrong. He believes competition in the free-agent market will not cause wages to effectively approximate the marginal revenue products. Krautmann does state a lack of competition would cause salaries to not equal the marginal revenue products, but he believes the free-agent market is competitive. However, Bradbury claims substitutes cause salaries to fall. There are so many good players that can fill a role it brings down everyone s salary. The other main salary depressant is when there are exceptionally talented young athletes that are free agents. They do not have the experience when first entering the league to garner a huge wage, thus creating cheap substitutes that are just as good as the expensive players if not better. Another issue is players often sacrifice a higher salary for other benefits. These benefits could be playing on a better team, playing for a hometown team, getting a guaranteed salary to protect them if they get injured, or various other reasons. Another issue with the free agent pool is there are very few free agents signed each year compared to the amount of players in the league. Thus, the small number of observations magnifies any problems. Therefore, Bradbury claims, while Scully s model does have some issues, it is the best model to estimate marginal revenue products for each Major League Baseball player. I will examine a paper from 1994 that studies whether baseball players are paid their marginal revenue products. The paper is called Are Baseball Players Paid their Marginal Products? and is written by Don MacDonald and Morgan Reynolds (MacDonald and Reynolds 1994). MacDonald and Reynolds note that previously researchers have concluded players are not paid their marginal revenue product, but they

9 wonder if the new contractual system of free agency and arbitration has pushed the salaries closer to the MRP. They use data from 1986 and 1987 and determine players are paid much closer to their marginal revenue product. However, they claim there is variation and it appears as though the more experienced players are paid close to their marginal revenue product, while younger players are not. MacDonald and Reynolds blame this fact on the market structure existing in professional baseball. I will begin to look into literature that explains which pieces of the data are most useful in reaching my goal. The first paper I will examine is Which Baseball Statistic Is the Most Important When Determining Team Success? by Adam Houser (Houser 2005). Houser attempts to determine the most important statistic for winning percentage prediction. Houser explains theory would suggest the best team in the league has the best statistics in the league, which means they must have the best players in the league leading to the highest team salary. However, this has not been the case on most occasions. Houser wants to determine which statistic is the most important to winning to see if that is the cause for Major League Baseball not aligning with the human capital theory, which states players will be paid for their productivity. He used mostly offensive statistics because, according to his literature review, offensive statistics are by far the best way of finding significant test statistics. He also used a few pitching and defensive statistics. Houser ran regressions of winning percentage on a variety of offensive statistics to determine which had the most importance. The three statistics that were significant were on-base percentage, slugging percentage, and WHIP (WHIP = (walks+hits)/innings pitched). This is an interesting revelation, as it seems from the fan perspective home run

10 hitters and flashy players are paid the most because they are the most exciting. In reality, if you want more wins these are not the players necessary according to Adam Houser. The next study observed is What Makes a Winning Baseball Team and What Makes a Playoff Team? by Javier Lopez, Daniel Mundfrom, and Jay Schaffer (Lopez, Mundfrom, and Schaffer 2011). This paper continues with the theme of determining what matters for the creation of a winning team. The data is from the 1995-2009 seasons. Lopez used 32 different statistics in a multiple linear regression and discriminant analyses. The intent of the regression was to determine what makes a winning team, while the discriminant analyses were used to discover the components of a playoff team. Batting, fielding, and pitching statistics were all used. Lopez ran a regression on wins with all 32 variables and eliminated the variable with the smallest, non-significant contribution to the explanation of the variance in order to remove multicollinearity from the data. They continued to do this until there were only significant values left. By the time the procedure was completed, the only variables remaining were OPS (on-base percentage plus slugging percentage) and ERA (earned run average). Lopez concluded that this made sense, as there was one variable to measure offense (OPS) and one variable to measure defense (ERA). Thus, they determined out of all statistics for a team, the most important statistics for determining wins are OPS and ERA. Continuing with determining what contributes most to winning, I will briefly address The Numbers Behind the MLB by Kevin Rader (Rader). The data that Rader used is from the 2010 season, which is the most recent season someone has performed data analysis. Rader first ran simple linear regression models, and then ran a multiple regression model he based his analysis and conclusions on. After running all of the

11 regressions, the significant variables were batting average, strikeouts, quality starts, and errors. Rader states the fact these statistics were significant was not a surprise, but it was surprising that payroll, home runs, and the league each team plays in were not significant determinants of the winning percentage. Rader also examines how these results will affect the future and what this could mean. Rader suggested in his conclusion teams should pursue players that have high batting averages and a low amount of errors committed. He also suggests teams should pursue pitchers with many quality starts and strikeouts. However, Rader determines quality starts and strikeouts are less important than high batting averages and low amounts of errors because batting average and errors were more significant. The next topic examined is the factors affecting attendance. Thus, Factors Affecting Attendance of Major League Baseball by John Marcum and Theodore Greenstein was the next paper analyzed (Marcum and Greenstein 1985). This study was performed on one National League team and one American League team for the 1982 season to determine what the major factors that contributed to attendance at a professional baseball game. The two teams were the St. Louis Cardinals and the Texas Rangers. Multiple regression analyses were performed to discover the affects. The variables included day of the week, home team s record, away team s record, the last 10 results, weather, and promotions. Interestingly, attendance seems to be mostly based on opponent, day of the week, and promotions. Day of the week is the most important factor for attendance at Cardinals games, while promotions are the most important factor for attendance at Rangers games. Also, the opponent record is much more important for Rangers fans than it is for Cardinals fans. This is perhaps due to the fact that the Rangers

12 had a poor season in 1982 and suggests an interesting conclusion that fans with struggling home teams are more interested in a baseball game when their team plays a better opponent. If a home team is performing well, attendance will be strong no matter what, but if the home team is struggling there must be promotions or high caliber opponents to bring fans into the stadium.

Chapter 3 Data and Methodology My objective is to determine whether Major League Baseball players are paid their marginal revenue product. Thus, we must first understand what marginal revenue product is. According to Rodney Fort s textbook Sports Economics, the marginal revenue product is equal to the marginal product multiplied by the marginal revenue (Fort 2011). MRP(W) = MP(W) x MR(W) The marginal product is the player s contribution to winning percentage, while the marginal revenue, in this case, is the amount of attendance on the margin generated by the player s contribution to winning. Marginal revenue decreases with output because of the law of diminishing returns. Thus, the marginal revenue is downward sloping for the individual team at any level of W in the long run. Since marginal revenue product is the other side of the equation, it is the input s contribution to the revenues earned by the team owner. In order to calculate the marginal revenue product, we will use Scully s method (Scully 1974). The first step is to estimate the contribution of a player s statistics in the production of wins (the marginal product). Thus, Winning = f(h, P, F)

14 Winning for the team is the clear objective and it depends on H, which is the hitter performance, P, which is the pitcher performance, and F, which is the fielding performance. The model for winning will be as follows: Winning = α 0 +β 1 *R+β 2 *HR+β 3 *H+β 4 *ERA+β 5 *IP+β 6 *CG+β 7 *SHO+β 7 *SO+β 7 *FPCT+e where Winning = percentage of games won by a team R = runs scored during the season H = hits recorded by the team during the season ERA = team earned run average per 9-inning game over the course of the season IP = innings pitched during the season CG = number of complete games pitched by a team during the season SHO = number of shutouts recorded by a team during the season SO = number of strikeouts pitched by a team during the season FPCT = team fielding percentage during the season The winning percentage of a major league baseball team is obviously affected by many things over the course of the season. I have attempted to capture as many as seemed relevant to the regression. The hitting statistics I believed had the most affect on winning percentage were runs scored and hits recorded. My belief is the more runs a team records, the higher their team s winning percentage because to win a ball game you must score more runs than your opponent. Therefore, it makes sense that typically the teams scoring the most runs would have the best winning percentage. Hits should also positively influence winning percentage because a team needs to get on base to score runs. The most common way of getting on base is to get a hit, so I would think more hits would mean more runs. The pitching statistics I chose to use in my regression are team earned run average, innings pitched, number of complete games, number of shutouts, and number of strikeouts recorded. Earned run average is the statistic I expect to have the most impact on winning percentage because it is the calculation of how many runs a team s pitching stuff allows per nine innings. I expect the relationship between ERA and

15 winning percentage to be negative because I would expect that when a team allows more runs their winning percentage should decrease. I believe the innings pitched should positively affect winning percentage because a team pitches more innings when they are winning as the home team and do not need to take their final at bat or when they are in extra innings. If they are in extra innings they are in a close game where their chance of winning is decent. Thus, more innings should mean a higher winning percentage. However, I believe this affect will be small because the number of innings pitched over the course of the season does not differ much from team to team. There may be a slightly positive impact on winning percentage, but most games are completed in nine innings, meaning the difference between teams will be slim. The CG variable represents the number of complete games pitched for one team during the season. A complete game is when only one pitcher is used throughout the entirety of a game. The only way a pitcher is able to complete a game is if he has a low number of pitches thrown, which most likely signifies the other team is struggling against him. Therefore, I expect a positive correlation between complete games and winning percentage. The more complete games teams have, the higher their winning percentage. However, this may also be an ineffective variable because there are not many complete games over the course of a season. The variable SHO represents the number of shutouts a team earns over the course of the season. A shutout means the team wins the game because a game cannot end in a tie and they have allowed zero runs. Thus, shutouts should correlate positively with winning percentage because one extra shutout means one extra win. While, there tends not to be an abundance of shutouts over the course of the season, every extra shutout means an extra win. The variable SO represents the number of strikeouts a team pitches

16 over the course of the season. I expect there to be a positive correlation between strikeouts and winning percentage because a strikeout is an out where no runners are able to advance. When there are more strikeouts, it means that there are fewer batters capable of running the bases and advancing others along the base paths. Therefore, more strikeouts mean less possibility of scoring runs. The only fielding statistic that I am using in my regression is fielding percentage because I think that it is a broad statistic that is able to represent how well a team fields. I expect fielding percentage to affect winning percentage positively because a team that has a better fielding percentage does not allow as many runners on base. This means opposing teams are less likely to score than if they had more base runners, so the winning percentage of a good fielding team should be higher than the winning percentage of a poor fielding team. My study is modeled after Scully s examination of the pay for performance rate in Major League Baseball in the 1970 s. I have collected data from the 2011 Major League Baseball season to attempt to determine whether players are paid their marginal revenue product. I think it is interesting to do this study during the tail-end of the steroid era because there are so many stars in the game that seem to have inflated contracts. I will use the modified winning regression that includes logarithmic variables because it has a larger r-squared. This means that the regression explains more of what affects attendance than the regression that contains no logarithmic variables. The following table shows the results of the logarithmic winning regression: Winning 1 = α 0 +β 1 *R+β 2 *HR+β 3 *H+β 4 *ERA+β 5 *IP+β 6 *CG+β 7 *SHO+β 7 *SO+β 7 *FPCT+e

Winning 2 = α 0 +β 1 *R+β 2 *HR+β 3 *Log(H)+β 4 *ERA+β 5 *Log(IP)+β 6 *Log(CG)+β 7 *Log(SHO)+β 7 *Log(SO) +β 7 *FPCT+e 17 Table 1. Winning Regression Data Variable WP 1 WP 2 Intercept 0.5325 0.7987 p-value 0.808 0.851 R 0.0003 0.0004 p-value 0.061 0.016 HR 0.0007 0.0005 p-value 0.019 0.087 H 0.0000 p-value 0.853 Log(H) -0.0286 p-value 0.861 ERA -0.1017-0.1135 p-value 0.000 0.000 IP 0.0000 p-value 0.936 Log(IP) -0.0911 p-value 0.892 CG -0.0005 p-value 0.741 Log(CG) -0.0107 p-value 0.187 SHO 0.0030 p-value 0.142 Log(SHO) 0.0243 p-value 0.168 SO -0.0001 p-value 0.299 Log(SO) -0.0920 p-value 0.198 FPCT 0.0002 1.2906 p-value 1.000 0.570 R 2 0.9151 0.9309

18 The next step is to calculate the marginal revenue. I will be unable to get broadcast revenue because franchises do not readily give this information out, so the revenue gained will be understated. However, my model will attempt to circumvent this as best it can. Thus, the equation for the marginal revenue is: Attendance = f(w, OCF) Attendance will be the main contributor to revenue without broadcast revenue. Attendance will depend on W or winning, which was described above and OCF, which is other city factors. These include city population, whether the opponent is a contender, and whether the opponent makes the playoffs, among others. The model for attendance will be as follows: Attendance = α 0 +β 1 *POP+β 2 *W+β 3 *CONT+β 4 *PLAYOFFS+β 5 *PRICE+β 6 *GB+e where Attendance = the number of fans that attended all home games for each team POP = home team s city population W = winning percentage over the course of the 2011 season CONT = 1 if team finished within 3 games of first place in the division, 0 otherwise PLAYOFFS = opponent made the playoffs at the end of the season PRICE = the average price per ticket GB = number of games behind the division winner at the end of the season Attendance is an important measure of team success. It gives a decent idea of how much money an organization earns. Thus, attendance is increasingly important in determining how much a player is paid. There are a few variables that go into determining attendance. I have attempted to choose the statistics that I believe to be the most important determinants of attendance. The amount of people living in the city where the team plays should be positively associated with attendance because the more people in a given city means there are more potential attendees. Also, given that large population cities tend to win more games, more people will want to attend in order to see a good

19 team play. Winning percentage is an obvious foundation of attendance because people want to go to a game where their team wins, so I expect there to be a positive relationship with attendance. The variable CONT is a variable that determines whether each team was a contender based on their final winning percentage. A team that is three games or less behind the division winner is considered a contender. Presumably, the attendance will increase when the visiting team is a contender because people want to see better teams play. PLAYOFFS represents when the opponent was a team that ended up making the playoffs in 2011. I expect a positive correlation between PLAYOFF and Attendance because fans want to see the best players and ball clubs, even if it is not their home team. The PRICE variable is a measure of the average ticket price for each stadium. Obviously, one would think the lower a ticket price is, the higher the attendance. However, I believe lower ticket prices lead to lower attendance because there must have been a reason for the price dropping so much. Lastly, GB represents games behind the division winner the home team ends up at the end of the season. I expect a negative correlation because as a team gets further behind there is little to play for and the team is most likely not good. Thus, fans would not want to see the game as much because there is no excitement. The data I have used to analyze my question comes from a few different sources. I used the well-known sports network, ESPN, to get the wins and losses for every team during the 2011 season, as well as all of the team statistics (ESPN 2011). The average ticket prices for each team came from the daily sports list written by Getz (Getz 2012). I found data on the population of each city that has a baseball team from two different sources. The first source was from the Government of Canada, which gave me the population of the only Canadian city with a baseball team, Toronto (Government of

Canada 2014). The remaining population data came for the United States Census Bureau (United State Census Bureau 2012). Newsday was my source for all of the player salaries during the 2011 MLB season (Newsday 2014). Fielding statistics were gathered from the Sports Reference LLC. These statistics included fielding percentage, errors, and plays for each player (Sports Reference LLC 2013). I used a sports database created by The Guru to find data for various baseball statistics. This includes all major statistics of field players and pitchers. Games, at bats, runs, hits, homeruns, RBI, stolen bases, and walks among others were included in the statistics provided for the field players. Meanwhile, statistics provided for pitchers included wins, loses, complete games, strikeouts, walks, ERA, earned runs, and homeruns allowed among others. This data was the primary source for my calculations (The Guru 2014). The following table shows the results of the attendance regression. Attendance = α 0 +β 1 *POP+β 2 *W+β 3 *CONT+β 4 *PLAYOFFS+β 5 *PRICE+β 6 *GB+e Log(Attendance) = α 0 +β 1 *Log(POP)+β 2 *W+β 3 *CONT+β 4 *PLAYOFFS+β 5 *Log(PRICE)+β 6 *GB+e 20 Table 2. Attendance Regression Data Variable Attendance Log(Attendance) Intercept 1617491.00 14.225 p-value 0.000 0.000 POP 0.021 p-value 0.000 Log(POP) 0.014 p-value 0.000 W 2157348.00 0.835 p-value 0.000 0.000 CONT 62048.00 0.008 p-value 0.014 0.379

21 PLAYOFFS 3514.76 0.001 p-value 0.488 0.655 PRICE 3011.75 p-value 0.001 Log(PRICE) 0.005 p-value 0.000 GB -3603.77-0.001 p-value 0.000 0.000 R 2 0.3280 0.3171 We are able to calculate marginal revenue product since we have marginal product and marginal revenue.

Chapter 4 Results I have performed the winning regressions based on how a team s statistics affect their winning percentage. The regression that I will use for the remainder of this paper for winning is the second regression in Table 1 because it has greater coverage, which means that the second regression describes what affects winning percentage better than the first regression. The winning regression can be viewed in Table 3 and the estimated equation is: Winning = 0.7987 + 0.0004*R + 0.0005*HR 0.0286*Log(H) 0.1135*ERA 0.0911*Log(IP) 0.0107*Log(CG) + 0.0243*Log(SHO) 0.0920*Log(SO) + 1.2906*FPCT + e Table 3. Winning Regression wp Coefficient Std. Err. t P> t [95% Conf. Interval] r 0.0004 0.00 2.63 0.02 0.00 0.00 hr 0.0005 0.00 1.80 0.09 0.00 0.00 lh -0.0286 0.16-0.18 0.86-0.37 0.31 era -0.1135 0.02-6.56 0.00-0.15-0.08 lip -0.0911 0.66-0.14 0.89-1.48 1.30 lcg -0.0107 0.01-1.37 0.19-0.03 0.01 lsho 0.0243 0.02 1.43 0.17-0.01 0.06 lso -0.0920 0.07-1.33 0.20-0.24 0.05 fpct 1.2906 2.23 0.58 0.57-3.38 5.96 _cons 0.7987 4.20 0.19 0.85-8.00 9.59 There are three test statistics that are significant at the 10% level, as can be seen in the above equation. They are R, with a p-value of 0.02, HR, with a p-value of 0.09, and

23 ERA, with a p-value of 0.00. Thus, a one-run increase in the amount of runs the team scores increase the winning percentage by 0.0004 units. A one-homerun increase in the amount of homeruns the team hits increases the winning percentage by 0.0005 units. A one-run increase in the team s earned run average causes a decrease in the winning percentage of 0.1135 units. The next results that must be shown are the attendance regressions. I will use the non-logarithmic model from Table 2 because it has a greater r-squared value. The results of the regression can be viewed in Table 4 and the equation can be estimated as: Attendance = 1617491+0.021*POP+2157348*W+62048*CONT+3514.76*PLAYOFFS+3011.75*PRICE 3603.77*GB+e Table 4. Attendance Regression attendance Coefficient Std. Err. t P> t [95% Conf. Interval] citypop 0.02 0.00 6.61 0.00 0.01 0.03 w 2157348.00 147257.90 14.65 0.00 1868584.00 2446113.00 cont 62048.00 25102.32 2.47 0.01 12823.77 111272.20 playoffs 3514.76 5068.24 0.69 0.49-6423.78 13453.30 price 3011.75 889.02 3.39 0.00 1268.42 4755.07 gb -3603.77 539.04-6.69 0.00-4660.79-2546.75 _cons 1617491.00 81464.06 19.86 0.00 1457744.00 1777237.00 There are six test statistics that are significant at the 10% level as can be seen in Table 2. The variables are city population, with a p-value of 0.00, winning percentage, with a p- value of 0.00, contender, with a p-value of 0.01, ticket price, with a p-value of 0.00, and number of games back with a p-value of 0.00. Thus, a one-person increase in city population causes an increase of 0.02 in attendance. A one-unit increase in winning

24 percentage causes an increase of 2,157,348 in attendance. A team that is considered a contender causes an increase of 62,048 in attendance. A one-unit increase in ticket price causes an increase of 3,011.75 in attendance. A one-game increase in games back of the division winner in 2011 causes a decrease of 3,603.77 in attendance. We are able to calculate the average marginal revenue product for each position. The marginal revenue product is the player s individual contribution to winning percentage multiplied by the amount of attendance, on the margin, generated by the individual player s contribution to winning. In order to find the MRP, we calculate the change in winning divided by the change in player statistics to determine how a change in an individual player s statistics will change the winning percentage of their team. The difference between marginal product for pitchers and hitters comes in the statistics included in each marginal product calculation. The marginal revenue includes all variables that were significant in the winning regression. This includes runs, homeruns, earned run average, and the amount of walks allowed by each pitcher. Essentially, the coefficient of each variable from the regression is multiplied by the individual statistic for each player and combined with all of the other variables. The marginal revenue equation is calculated below: MR = 0.0004 * Player R + 0.0005 * Player HR 0.1135 * Player ERA We can see from the attendance regression equation that a one-point increase in the winning percentage of a team raises the season attendance by 2,157,348. The marginal revenue is the affect winning has on attendance. In this model, the marginal revenue is

25 the change in attendance over the change in winning percentage, which is the coefficient for winning in the attendance regression. This value is above, 2,157,348. However, we must multiply the winning coefficient in the attendance regression by the average ticket price for each team. The reasoning behind this calculation is that when we compare attendance to salary, they must have equivalent units. In order to make the MRP a dollar value, we must multiply the calculation by the average price per ticket. The marginal revenue product is the marginal revenue multiplied by the marginal product. In addition, the marginal revenue must be multiplied by 81 for hitters because the MR is a single game calculation and there are 81 home games that a hitter could play. For pitchers, the MR must be multiplied by half of innings pitched because half of the games that teams play are at home. Thus, the MRP of hitters is: MRP Hitters = 81* (0.0004 * Player R + 0.0005 * Player HR) * (2,157,348 * Avg. Ticket Price per Team) Similarly, the MRP of pitchers is: MRP Pitchers = 0.5*(innings pitched) * ( 0.1135 * Player ERA) * (2,157,348 * Avg. Ticket Price per Team) Now that I have the MRP for pitchers and hitters, I can calculate whether players are paid their MRP. In order to calculate this, I will run a regression model where player salary is regressed on MRP. The model is:

26 Salary i = α + β*mrp i + e i where Salary i is the salary of player i, MRP i is the MRP of player i, and e i is the error of player i. In order for players to be paid their MRP, β must be equal to one after the regression is run, assuming that MRP is estimated accurately. This states that for every one-unit increase in MRP there is a one-unit increase in salary. I ran regressions using this model for every position to calculate whether the average player at each position is paid their marginal revenue product. The regression results can be seen in Table 3. Table 5. Salary and Marginal Revenue Product Regression Data Variable Pitcher Catcher First Base Second Base Third Base Shortstop Outfield Intercept 387357.60 491000.20 156651.00 870610.40 108121.60-545980.30 787845.70 p-value 0.04 0.06 0.87 0.201 0.85 0.48 0.05 MRP 0.01 0.01 0.03 0.01 0.03 0.03 0.02 p-value 0.00 0.00 0.00 0.00 0.00 0.00 0.00 R 2 0.2274 0.2607 0.3791 0.1835 0.3594 0.3823 0.2027 We see that all position s β values are smaller than one. Also, every β, which is the coefficient of the marginal revenue product, is statistically significant. This means that they are statistically different from the hypotheses. Thus, every position is underpaid according to my MRP calculation. We have the regression data from the model that compares salary to marginal revenue product. I can compare the coefficients to the hypotheses to determine whether a position is overpaid, underpaid, or paid what the average player should make for a salary. In order to determine whether a position is overpaid, underpaid, or paid at the margin, we simply compare the marginal revenue product coefficient to the hypothesis. If the marginal revenue product is larger than the hypothesis then the position is overpaid. If the

27 marginal revenue product is smaller than the hypothesis then the position is underpaid. If the marginal revenue product is equal to the hypothesis then the position is paid at the margin. The value comparison can be viewed in Table 31. Table 6. Determination of Whether a Player is Paid Their MRP Position MRP Coefficient Comparison Catcher 0.01 Underpaid First Base 0.03 Underpaid Outfield 0.02 Underpaid Shortstop 0.03 Underpaid Second Base 0.01 Underpaid Third Base 0.03 Underpaid Pitcher 0.01 Underpaid! We can see in Table 6 that all positions are grossly underpaid. This is unsurprisingly similar to the literature outlined throughout this paper, as the other papers have consistently found that players are underpaid. The major difference is that the previous papers were written based on data from the early 1990 s and the early 1970 s, while my paper uses the 2011 Major League Baseball season. There has been a huge increase in player salaries over recent years, including a contract signed this past week where a player is paid over $30 million dollars per year. Thus, it is surprising that the average player is so substantially underpaid.

Chapter 5 Conclusion This study determines whether Major League Baseball players are paid their marginal revenue product. I estimated a winning regression, an attendance regression, and a salary regression. I was able to calculate the marginal revenue product by using the data gathered from the winning regression and attendance regression. I then compared it to the salary regression to determine whether players were paid their marginal revenue product. The data suggests that all Major League Baseball players are substantially underpaid. The goal of professional sports leagues is to be competitive. When they are competitive they make the most money, which is obviously the ultimate goal. In order to be as competitive as possible players must be paid their marginal revenue product. This is how much they make for the team, and is how much the team should pay them. If teams overpay or underpay their players, then the league is not as competitive as it could be and is not maximizing their profits. Thus, not paying the players correctly harms the whole of the league. Major League Baseball should use this information to increase the salaries of their players in all positions. This study reveals that players are underpai based on their value to their teams. Therefore, if Major League Baseball wants to maximize their profits they must adjust the salaries of their players to the margin. When players are paid their marginal value the league is at its most competitive state. The league will have the most

29 revenue when it is at its highest level of competition. Thus, it is in the interest of Major League Baseball as a whole to use this study to justify adjusting player salaries as described.

Appendix A Data Table 7. Team Data TEAM GP WP AB R H HR ERA CG SHO IP SO FPCT Arizona 162 0.580 5421 731 1357 172 3.8 5 12 1443.1 1058 0.985 Atlanta 162 0.549 5528 641 1345 173 3.48 3 16 1479.2 1332 0.987 Baltimore 162 0.426 5585 708 1434 191 4.89 3 7 1446.2 1044 0.982 Boston 162 0.556 5710 875 1600 203 4.2 2 13 1457.1 1213 0.985 Chicago Cubs 162 0.438 5549 654 1423 148 4.33 4 5 1434.1 1224 0.978 Chicago Sox 162 0.488 5502 654 1387 154 4.1 6 14 1460 1220 0.987 Cincinnati 162 0.488 5612 735 1438 183 4.16 4 5 1467.2 1112 0.985 Cleveland 162 0.494 5509 704 1380 154 4.23 2 4 1453.1 1024 0.982 Colorado 162 0.451 5544 735 1429 163 4.43 5 7 1447.2 1118 0.984 Detroit 162 0.586 5563 787 1540 169 4.04 4 14 1440 1115 0.983 Florida 162 0.444 5508 625 1358 149 3.95 7 11 1459.2 1218 0.985 Houston 162 0.346 5598 615 1442 95 4.51 2 6 1435 1191 0.981 Kansas City 162 0.438 5672 730 1560 129 4.44 2 6 1451.1 1080 0.985 LA Angels 162 0.531 5513 667 1394 155 3.57 12 11 1465 1058 0.985 LA Dodgers 161 0.509 5436 644 1395 117 3.54 7 17 1432 1265 0.986 Milwaukee 162 0.593 5447 721 1422 185 3.63 1 13 1441.2 1257 0.982 Minnesota 162 0.389 5487 619 1357 103 4.58 7 8 1421.2 940 0.98 NY Mets 162 0.475 5600 718 1477 108 4.19 6 9 1448 1126 0.981 NY Yankees 162 0.599 5518 867 1452 222 3.73 5 8 1458.1 1222 0.983 Oakland 162 0.457 5452 645 1330 114 3.71 6 12 1447.2 1160 0.979 Philadelphia 162 0.630 5579 713 1409 153 3.02 18 21 1477 1299 0.988 Pittsburgh 162 0.444 5421 610 1325 107 4.04 5 11 1449.1 1031 0.982 San Diego 162 0.438 5417 593 1284 91 3.42 0 10 1449.1 1139 0.985 San Francisco 162 0.531 5486 570 1327 121 3.2 3 12 1468 1316 0.983 Seattle 162 0.414 5421 556 1263 109 3.9 12 10 1433 1088 0.982 St. Louis 162 0.556 5532 762 1513 162 3.74 7 9 1462 1098 0.982 Tampa Bay 162 0.562 5436 707 1324 172 3.58 15 13 1449 1143 0.988 Texas 162 0.593 5659 855 1599 210 3.79 10 19 1441.1 1179 0.981 Toronto 162 0.500 5559 743 1384 186 4.32 7 10 1458.2 1169 0.982 Washington 161 0.497 5441 624 1319 154 3.58 3 10 1449.1 1049 0.983

31 Table 8. City Population and Team Attendance Data Team City Population Total Attendance in 2011 Season ARI 1,469,471 2,579,486.00 ATL 432,427 2,687,942.00 BAL 619,493 2,520,803.00 BOS 625,087 3,055,879.00 CHC 2,707,120 3,038,530.00 CHW 2,707,120 2,143,991.00 CIN 296,223 2,629,012.00 CLE 393,806 2,426,549.00 COL 619,968 2,934,723.00 DET 706,585 2,745,765.00 FLA 408,750 2,459,238.00 HOU 2,145,146 2,113,016.00 KC 463,202 2,439,250.00 LAA 3,819,702 3,186,165.00 LAD 3,819,702 2,954,891.00 MIL 597,867 3,103,203.00 MIN 387,753 3,187,863.00 NYM 8,244,910 2,395,863.00 NYY 8,244,910 3,669,242.00 OAK 395,817 2,595,923.00 PHI 1,536,471 3,681,112.00 PIT 307,484 2,530,065.00 SD 1,326,179 2,522,361.00 SEA 620,778 2,549,055.00 SF 812,826 3,476,259.00 STL 318,069 3,106,066.00 TB 346,037 2,436,946.00 TEX 373,698 2,958,327.00 TOR 5,841,100 2,696,057.00 WAS 617,996 2,388,538.00