Do Major League Baseball Players Earn Their Marginal Revenue Product?
David Oliger
Dr. Byun/Howland
5/9/2014
Abstract
When it comes to determining a Major League Baseball player’s marginal revenue product, many statistics are factored in. In this paper, I will be discussing the statistics I feel have the greatest effect on a player’s salary, and whether each player earns their marginal revenue product, which is determined by their statistics. I will run two different regressions that determine a player’s success. One regression I will run is the relationship between team revenue and team winning percentage. The other regression will show the relationship between winning percentage and statistics. The results show that for the most part, players are underpaid in relation to their marginal revenue product.
Introduction
The purpose of my paper is to determine if Major League Baseball players earn their marginal revenue product or not. As my samples, I have come up with four different tables. Those tables are: 1) the top 10 RBI leaders of the 2012 season, 2) the top 10 highest paid players in 2012, 3) rookies in the 2012 season, and 4) veterans in the 2012 season. I would like to which of these groups of players earns closest to what their productivity level suggests their MRP should be. From running regressions on the previously mentioned variables, I will determine each of these players’ MRP. I will compare this to their actual salary to determine if they earn their marginal revenue product.
Literature Review
The foundation for my research on whether Major League Baseball players are paid their marginal revenue product comes from work done by Fields (2001). Fields examined the work done by Scully (1974) as the basis for his paper. Scully is considered the pioneer of the econometric study on pay versus performance of Major League Baseball players. Although Scully’s approach has been highly scrutinized by many, it is still one of the primary methods in determining a player’s marginal revenue product. Scully’s estimate of a player’s MRP is broken down into a two equation model. The first equation is a team revenue function that relates the team’s revenue to the team’s win-loss record and market characteristics of the area in which the team plays. The second equation, a production function, relates team output and win-loss percentage to many different team inputs. Scully’s results showed that players were only paid 10-20% of their marginal revenue product in the 1968-1969 seasons.
MacDonald and Reynolds (1994) did research to determine if the new contractual system of free agency and final-offer arbitration allowed for players’ salaries to be equal to their marginal revenue product. They used public data from the 1986-1987 seasons including all players who were on a major league roster as of August 31, 1986 and August 31, 1987. First they analyzed whether any economic evidence of owner collusion existed during the 1986-1987 seasons. Next, they used a systematic analysis of final-offer arbitration in baseball and found it has a stronger independent effect on salaries than free agency. They also use two different equations in their research. The first examines the baseball production function. This is what that equation looks like:
WP=a0+a1RUNS+a2ERA+a3CONT+a4OUT+e1,
where WP is winning percentage, RUNS is the number of runs scored for the season, ERA is the team’s earned run average, CONT is a dummy variable that is 1 if the team finished within five games of first place in the division and 0 if not, and OUT is a dummy variable that is 1 if a team finishes 20 games or more out of first place in the division and 0 if not.
The Data
In order to retrieve the data for my paper, I have done a replication of the data found by Fields in his work from 2001. Fields extracted his data from the 1990-1999 MLB seasons. For my paper, I am going to use statistics from the 2012 MLB season. I have used the same equations for my regressions that Fields used for his regressions.
In baseball, the definition of a player’s marginal revenue product is the performance that he contributes to the team and the effect of that performance on team revenue (Scully 1974). When a player performs well on a personal level, it will help the team win more games. When the team wins more games, more fans go to the games. When more fans go to the games, the team’s total revenue increases. Therefore, a player’s marginal revenue product can be attributed to the amount of team revenue produced by his contribution to the team and giving fans a reason to come out and watch games (Scully 1974).
A player’s MRP is based on their contribution to team performance variables. These performance variables effect winning percentage and winning percentage effects team revenue. Just like Fields wrote it, the team production function is written as follows:
WINPCT= β₀ + β₁RC + β₂ERA + β₃NATLG
WINPCT= percentage of games won
RC= total runs created for the season
ERA= team earned run average per 9 inning game
NATLG= dummy variable that is 1 if team is in National League, 0 if otherwise
I believe that the runs created variable is the best indicator of a player’s personal performance throughout a season. Not only does it take into account a player’s batting average, on base percentage, and slugging percentage, which are arguably the most important stats in determining a player’s worth, but it also takes into account stats like walks, stolen bases, sacrifice hits, and others. The more runs a player creates for his team, the better chance his team has of winning games. Therefore, this is a better measure of a player’s offensive performance than just simply batting or one of the other statistics mentioned earlier. Team ERA is the best defensive measure of a team. The lower your team’s ERA is, the fewer amount of runs your team has to score in order to win. The only bad thing about ERA is that it doesn’t take errors into account. If a run is scored on an error, it does not raise the player and team’s ERA. However, it is still a team’s best defensive measure. The NATLG variable is a dummy variable added to compensate for quality of play. In the American League, they are allowed to use a designated hitter for the pitcher, whereas in the National League, there is no such thing. Therefore, the quality of batting lineups in the American League is better. Because of the higher quality of teams’ batting lineups in the American League, the value of their runs created variable should be higher.
The second equation explains total team revenue as a function of win percentage, and is shown as follows:
TOTREV= β₀ + β₁WINPCT + β₂NATLG
TOTREV= total team revenue in millions of dollars
WINPCT= team winning percentage
NATLG= dummy variable that is 1 if team is in National League, 0 if otherwise
As explained earlier, this equation suggests that total team revenue is positively affected by the team’s winning percentage. The more games a team wins, the more fans will show up to games. Once again, the dummy variable NATLG is there to compensate for the difference in level of play between each league.
The Marginal Revenue Product for each player is calculated by multiplying the estimated increase in total revenue resulting from a one point increase in win percentage, the estimated increase in win percentage resulting in a one point increase in runs created, and the annual runs created for that player.
For each my data tables I have used a variety of different samples. The goal of the tables was to see what group of players was closest to earning their MRP. The first table is of the top RBI leaders of the 2012 season, the second is of the 10 players with the highest salaries in 2012, the third is of the top producing rookies, and the fourth is of the top producing veterans, which is a mixture of guys that are still early in their careers and guys that have been in the MLB longer. For each of the tables, I have calculated their MRP based on the regressions I have run to see which group of players is closest to earning their MRP.
Results
First regression, a regression of total team revenue with respect to team winning percentage and the National League dummy variable to compensate for difference in level of play:
Coefficients / Standard Error / t Stat / P-value / Lower 95% / Upper 95% / Lower 95.0% / Upper 95.0%Intercept / 164.049 / 78.35392 / 2.093692 / 0.045812 / 3.28004 / 324.818 / 3.28004 / 324.818
Team Win % / 137.392 / 151.2828 / 0.908181 / 0.371818 / -173.015 / 447.7986 / -173.015 / 447.7986
NATLG / -10.2719 / 21.96272 / -0.4677 / 0.643753 / -55.3357 / 34.79184 / -55.3357 / 34.79184
Second regression, which is a regression of team winning percentage with respect to total team runs created, total team ERA, and the National league dummy variable to compensate for difference in level of play:
Coefficients / Standard Error / t Stat / P-value / Lower 95% / Upper 95% / Lower 95.0% / Upper 95.0%Intercept / 0.603651 / 0.061321 / 9.844052 / 2.94E-10 / 0.477603 / 0.729698 / 0.477603 / 0.729698
Team RC / 0.000546 / 6.7E-05 / 8.14314 / 1.27E-08 / 0.000408 / 0.000684 / 0.000408 / 0.000684
Team ERA / -0.12069 / 0.008581 / -14.0653 / 1.15E-13 / -0.13833 / -0.10305 / -0.13833 / -0.10305
NATLG / -0.01719 / 0.008626 / -1.993 / 0.056854 / -0.03492 / 0.000539 / -0.03492 / 0.000539
As you can see from the results of the first regression, a one point increase team winning percentage will raise the team’s total revenue by about $137,392. From looking at the results of the second regression, you can see that a one run increase in total team runs created for a season increases team winning percentage by 0.000546 points.
The first of the data tables previously mentioned in this paper that I will talk about is the one of the top 10 RBI leaders in the 2012 season. The table is as follows:
RBI Leaders 2012 / RBI / RC / Salary / MRPMiguel Cabrera / 139 / 133.6 / $21,000,000 / $10,022,142
Josh Hamilton / 128 / 111.9 / $17,400,000 / $8,394,294
Chase Headley / 115 / 115.5 / $3,475,000 / $8,664,352
Ryan Braun / 112 / 135 / $6,000,000 / $10,127,164
Edwin Encarnacion / 110 / 118.3 / $3,500,000 / $8,874,397
Josh Willingham / 110 / 98 / $7,000,000 / $7,351,571
Alfonso Soriano / 108 / 85.7 / $19,000,000 / $6,428,874
Adrian Gonzalez / 108 / 99.2 / $21,000,000 / $7,441,590
Prince Fielder / 108 / 123.1 / $23,000,000 / $9,234,474
Billy Butler / 107 / 109.6 / $8,000,000 / $8,221,757
When you look at a table of RBI leaders in any given season, you can expect that about half of the names on the list are regulars. By that I mean they are people that are among the leaders in RBI every single season. Those people that are among the leaders are what we refer to as ‘superstars’. In every single case, we find that superstars are severely overpaid in terms of their marginal revenue product. Out of the five people on this list with salaries of $17,000,000 and above, every single one of them has a salary that is at least double what the MRP calculation suggests their salary should be. If a player is considered a superstar, they will get paid a lot more money than the league average salary, but not a single one of these ‘superstars’ plays to a performance level that suggests they deserve to be paid that much money.
For the other five players in this list, they are not considered superstars yet because they have not consistently been among the leaders in RBI every season. Because of this, their actual salaries are much lower than the salaries of the superstars. But when it comes to these players’ salary compared to their marginal revenue product, every single one of them makes right at or less than what their MRP value suggests they should be making.
The next table that I put together is of the players with the 10 highest salaries of the 2012 season. I wanted to do a table like this because players with the highest salaries are the ones who are considered to be ‘superstars’. I wanted to see if I could come up with more proof that superstars are overpaid. The table is as follows:
Top 10 Salaries 2012 / Salary / RC / MRPA-Rod / $30,000,000 / 72.1 / $5,408,656
Vernon Wells / $24,187,500 / 26.9 / $2,017,931
Mark Teixeira / $23,125,000 / 72.3 / $5,423,659
Prince Fielder / $23,000,000 / 123.1 / $9,234,474
Joe Mauer / $23,000,000 / 99.2 / $7,441,590
Adrian Gonzalez / $21,857,142 / 99.2 / $7,441,590
Miguel Cabrera / $21,000,000 / 133.6 / $10,022,142
Carl Crawford / $20,357,142 / 18.2 / $1,365,292
Ryan Howard / $20,000,000 / 31.2 / $2,340,500
Carlos Lee / $19,000,000 / 68.4 / $5,131,097
As you can tell, every single one of these players is overpaid. And not just that, they are overpaid by a lot. It is proven by these values that none of the superstars of sports deserve the ridiculously big contracts they get. They definitely still deserve a lot of money, as they are the players with the most player production (in most cases), but they receive more money than they should.
The next table is of rookies in the 2012 season and how their MRP compares to their salary. I picked 10 rookies who played consistently and played in a large percentage of their team’s games. I left out rookies who played in less than have of the team’s games for the year. The table is as follows:
Salaries / RC / MRPMike Trout / $500,000 / 129.8 / $9,737,081
Matt Carpenter / $480,000 / 48.9 / $3,668,284
YoenisCespedes / $9,000,000 / 86.9 / $6,518,893
Norichika Aoki / $1,000,000 / 85 / $6,376,363
Yonder Alonso / $1,400,000 / 76.1 / $5,708,720
Jordan Pacheco / $480,000 / 65.6 / $4,921,052
Bryce Harper / $500,000 / 87.5 / $6,563,903
Todd Frazier / $500,000 / 67.7 / $5,078,585
Steve Lombardozzi / $481,000 / 44.9 / $3,368,220
Wilin Rosario / $480,000 / 61.7 / $4,628,489
One important piece of information to know when looking at this data table is that the league minimum salary for rookie players in 2012 was $480,000. With the exception of three of the players in this list, every player was right at or very near this league minimum salary. The reason why they have such low salaries in their rookie season is because they have not yet proved themselves. Most teams will not pay a player a lot of money until they have proven they can be consistent producers for the team. However, every single player in this list of rookies proved that they have the capability to produce in the MLB. Only 3 of the players in the table have a salary of at least $1,000,000 but every single player has an MRP estimate of at least $3,000,000. Based on this information, we can make the conclusion that rookies are underpaid in the MLB. Since they haven’t proven themselves on a consistent basis, they don’t make as much money as others. However, all players in this sample have proven that they have the ability to perform at a high level and should have made more money than they did in their rookie season.
The final table that I made was of a group of 10 veterans who were in the middle of the pack in terms of production in the 2012 season. I wanted to see how the results of veterans compared to that of the rookies. The table is as follows:
Salary / RC / MRPIan Kinsler / $7,200,000 / 91.1 / $6,833,961
AJ Pierzynski / $6,000,000 / 76.8 / $5,761,231
Chris Davis / $3,000,000 / 81.5 / $6,113,807
Rafael Furcal / $6,500,000 / 56.5 / $4,238,406
Howie Kendrick / $4,850,000 / 64.7 / $4,853,537
Coco Crisp / $6,000,000 / 67.8 / $5,086,087
Erick Aybar / $5,075,000 / 69.8 / $5,236,119
Jay Bruce / $5,041,666 / 96.5 / $7,239,047
Rickie Weeks / $11,000,000 / 81.8 / $6,136,311
Ben Zobrist / $4,687,300 / 101 / $7,576,619
. With the exception of one outlier, Rickie Weeks, every player in this table has a salary that is within about $3,000,000 of their estimated MRP. A couple of the players have salaries that are almost spot on with what their estimated MRP is. It is split 50/50 between players who are earning more than their MRP and players who are earning less than their MRP. The outlier, Rickie Weeks, has a much higher salary because he had a very productive 2011 season, so they raised his salary significantly.
Based on all of these results, there are some conclusions that we can make. First off, we are able to accept the ‘superstars’ model of Rosen (1981). This model says that the salaries of the very highest players in the MLB disproportionately exceed their relative productivity advantage. The original superstars model used data from the 1970’s to come to their conclusion. We find this to be true of players in the 2012 season as well. All of the players with the highest salaries in Major League Baseball earn a very large amount more than what their productivity level suggests they should earn.
When it comes to the players who were top 10 in RBIs that season, we see some similar results. Half of the players in the top 10 for RBI are consistently in the top 10, therefore we can consider them ‘superstars’. They consistently show that they are capable of a high level of production year in and year out. These players, as discussed in the previous paragraph, earn a salary much higher than their MRP. The other five players in this list are players who have not yet proven that they can be in the top 10 in RBI every season. Therefore, they do not earn a ‘superstar’ salary. These players all have salaries that are lower, and in some cases significantly lower, than their MRP. If these players continue to have high levels of productivity every year in the future, they will most certainly receive a hefty pay raise. But for now, they have lower salaries because they are not solidified as some of the best players in the league.
When it comes to rookies, we see that for the most part, they are highly underpaid. For my sample, I took rookies who played in a high majority of their team’s games in the 2012 season and left out those who played less than 60% of the games. This gives me the best idea of their estimated MRP because they had the opportunity to produce for their team almost every game. Every rookie with the exception of one, YoenisCespedes, was severely underpaid in their rookie season. Teams are reluctant to pay rookies a lot of money from the beginning because they don’t know how their production will be year in and year out. The reason YoenisCespedes had a much higher salary in his rookie season than the rest in because he played professional baseball in Cuba and was very successful. He proved himself in Cuba so his team thought that he deserved a large amount of money.