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Estimating the Value of Major League Baseball Players
Brian Fields* East Carolina University Department of EconomicsMasters Paper July 26, 2001
Abstract This paper examines whether Major League Baseball players are paid their marginal revenue product. A two-step estimation technique is used with data from 1990 to 1999. First, I estimate a regression relating team revenues to the team’s winning percentage andother explanatory variables. The second regression estimates the relationship between winning percentage and team statistics. Given the estimates from these two models I can calculate player marginal revenue product by first predicting how his statistics will affect the team’s winning percentage and then relating the impact on winning percentage on team revenue. The results indicate that professional baseball players are underpaid inmarginal earnings per dollar of marginal revenue product. Players were paid more of their marginal product after the 1994-95 strike and older players appear to receive a salary closer to their marginal products than younger players.
- (^) The author would like to thank Dr. Ed Schumacher for his help and guidance in all phases of this paper
I. Introduction It is often debated whether or not professional baseball players are worth the large salaries they receive. Recent deals such as Alex Rodriguez’s $125 million contract with Texas and Manny Ramirez’s $96 million contract with Boston have caused many to speculate that baseball players are paid more than they are worth. A recent report from the Independent Members of the Commissioner’s Blue Ribbon Panel on Baseball Economics concluded that from 1995-99 only three teams (Cleveland, Colorado, and New York Yankees) achieved profitability (Levin et al. 2000). These factors have resulted in arguments for revenue sharing, a tax on clubs with payrolls over a fixed threshold, and other measures to attempt to lower players’ salaries. Baseball is a game of statistics that has proven to be an interesting labor market for economists, providing detailed measures of individual productivity. Unlike other professions, there are lots of data on individual performance and productivity. In addition, the fact that baseball players’ marginal revenue products are relatively independent, makes it easier to separate a particular player’s contribution to his team (Krautman 369). Thus, one can potentially estimate a players’ marginal revenue product and compare it to his actual salary. The purpose of this paper is to analyze pay-performance results of Major League Baseball players in a refined Scully model. I follow the work of MacDonald and Reynolds (1994) using data from 1990-1999, and examine whether professional baseball players are paid their marginal revenue product. The paper also examines if there was a significant change after the 1994-95 strike. The next section provides some background on labor relations in baseball. Section III provides a literature review. The team model
experience would still be free agents. However, a team would not sign them if doing so would put the team over the salary cap. Also part of the owners’ proposal was a guarantee to the players of 43 percent of revenue from ticket sales and broadcast contracts, which was about 82 percent of owners’ total revenue (Staudohar 1998). The purpose of the proposed salary cap was to protect teams in small markets from having their talented free agents brought up by big market teams. In theory, teams in large cities would be unable to dominate the free agent market because the cap would limit the players they could sign. Also, because teams spend large sums in developing young players, a salary cap would allow them to retain more of their young players because free agency opportunities would be more limited (Staudohar 1998). On December 31, 1993, baseball’s 4-year collective bargaining agreement expired. Baseball, as other sports, had its big market and small-market teams and economic disparities between clubs. Baseball teams share money from the sale of national broadcast rights equally but kept all sales from local broadcast rights. As a result, the owners decided to share some of their local revenues, but only if the players accepted the salary cap. The owners also proposed to share their revenues with the players, 50-50. Depending on the players’ share under the 50-50 split, no team could have a payroll of more than 110 percent or less than 84 percent of the average payroll for all teams. The Major League Baseball Players Association (MLBPA) rejected the salary cap and other major proposals. This set the stage for a strike that began on August 12, 1994 and lasted for 232 days – the longest strike ever in professional sports. In the end MLBPA accepted a modified version of the luxury tax. The early returns indicate that it
is having little if any effect on average player salaries (Staudohar 1998), although results in this paper suggest there has been a significant effect.
III. Literature review A number of previous studies have examined the marginal revenue product of professional baseball players. The pioneering econometric study on pay versus performance of Major League Baseball was provided by Scully (1974). While Scully’s approach has undergone much scrutiny, it remains one of the primary methods of estimating a player’s MRP. A number of studies have modified Scully’s basic model, used more recent data, and improved estimation procedures. Scully (1974) estimates MRP in a two equation model. The first is a team revenue function which relates team revenues to the team win-loss record and the principal market characteristics of the area in which the team plays. Then he estimates a production function, relating team output and win-loss percentage to a number of team inputs. Scully’s results show that players were paid only 10-20% of their marginal revenue product in data for the 1968- seasons. Scully found that the economic loss of professional baseball players under the reserve clause is of considerable magnitude (Scully 1974). Krautman (1999) revisits the Scully technique for estimating the MRP of professional baseball players. Using a sample of available free agents from 1990-1993, he attempts to show that the Scully technique is sensitive to the manner in which marginal product is measured. The approach estimates the market return on performance from a regression of free agent wages on performance. These market returns are then applied to the performance of reserve-clause players, giving estimates their market
my knowledge, no previous studies have utilized data over multiple seasons or as recent as the mid to late 90’s.
IV. Team Model and Marginal Revenue Product Employing one more unit of labor generates additional income for the firm because of the added output that is produced and sold. Thus, the marginal income generated with a unit of input is the multiplication of two quantities: the change in physical output produced (marginal product) and the marginal revenue generated per unit of physical output. Thus, the additional income created from hiring an additional worker is termed the marginal revenue product (MRP). In theory, a firm would be willing to pay a worker a wage up to his MRP. In a competitive labor market we would expect workers to be paid a wage equal to their MRP. The players’ marginal revenue product in baseball is the ability or performance that he contributes to the team and the effect of that performance on team revenue (Scully 1974). This effect can be direct or indirect. Ability contributes to team performance and victories raise gate receipts and broadcast revenues. Therefore a players’ market worth can be defined as the amount of team revenue produced by his contribution to attracting paying fans to see and hear the team compete (Scully 1974). Ignoring special appeal for ‘superstars’, a player’s MRP essentially is based on each player’s contribution to significant team performance variables, the effect of these performance variables on winning percentage, and, in turn, the effect of winning percentage on team revenue. I also assume that the team production function is linear and is written as:
WINPCT = α 0 + β 1 RC + β 2 ERA + β 3 NATLG + β 4 CONT + β 5 OUT + e (1)
where RC WINPCT = Total team runs created for the season = percentage of games won by a team NATLG^ ERA^ = teams earned run average per 9-inning game= 1 if team is in the National League, 0 otherwise OUT^ CONT = 1 if team finished 20 or more games out of first place in the division, 0 otherwise^ = 1 if team finished within 5 games of first place in the division, 0 otherwise As described below, runs created is a useful measure of offensive production because it not only gives weight to hitting and slugging averages, but also to offensive production like walks, stolen bases, sacrifices, and similar efforts. ERA is the best overall defensive measure because it reflects a pitcher’s ability to prevent runs from scoring. ERA is also a good defensive measure for team pitching, although it does not account for errors. However, more than just team hitting and pitching performance can determine winning. One or two runs win many games during the season. In this instance, pitching and hitting performance will make less difference in the outcome. The two dummy variables CONT and OUT , introduced by Scully (1974), adjust for these factors. The variable CONT captures team morale (hustle, quality of managerial and on the field decision making) which will substantially determine which team wins a higher share of these close games. The variable OUT captures the disheartenment of loosing and bringing up players from the minor leagues. The variable NATLG is specified to compensate for quality of play. The American League has a designated hitter to bat in place of the pitcher. This substitution, not allowed in the National League, should increases runs created in the American League. The second team equation explains variation in team revenue as a linear function of WINPCT and team characteristics, and is given as:
TOTREV = α 0 + σ 1 WINPCT + σ 2 NATLG + γ 1 TEAM + γ 2 YEAR + e (2)
each team between 1990-99, the data set contains 7,047 observations. Salaries and revenues have been adjusted to 1999 real dollars.
- Variable Creation Because hitters and pitchers differ in the kinds of variables used to measure individual performance, two different measures are used. For hitters, individual performance is measured by Runs Created ( RC). Runs Created is calculated by: ( ) AtBats Walks RC Hits Walks TotalBases
This formula reflects two important aspects in scoring runs in baseball. The number of hits and walks of a team reflect the team’s ability to get runners on base. The number of total bases of a team reflects the team’s ability to move runners that are already on base. This runs created formula can be used at an individual level to compute the number of runs that a player creates for his team. Baseball researchers have proposed ‘runs created’ measures to remove situation dependency (Grabiner). In other words, runs created allows a player to be evaluated for what he does, not for what his teammates or manager do. MacDonald and Reynolds (1994) view runs scored as the best offensive production variable. The problem with runs scored is that unless the batter hits a home run or steals home, he needs his teammates’ contribution to actually score a run, and he cannot do much to cause them to get hits once he is on base. Thus, if you bat in front of the best home-run hitters in the league, you will score a lot of runs, whether or not you have a good ability to score runs. Runs scored measures team offense very well, but it creates a problem when trying to measure individual contributions. RBI’s are commonly used as a measure of player’s offense, mainly because they are the only statistics easily available
that look like a complete measure. RBI’s however measure a lot of things that are not the player’s own contribution. You cannot drive in runners who are not on base (except home runs), but your own batting doesn’t put them there. If you bat behind good players you will get a lot of chances. In fact, leagues leaders in RBI are much more likely to be the players who batted with the most teammates on base or in scoring position (not the batter’s contribution) than those who hit the best with runners on base or in scoring position. Thus RBI’s are a better measure of who had the most chances to drive in runners than who was the best at driving in runners (Grabiner ). Table 1 compares the Runs Created ( RC ), RBI , and RUNS of the top ten RBI producers in 1990 and 1999. RBI hitters usually bat third or fourth in the batting order and are hitting with people on base. For example, in 1990 Ryne Sandberg had more Runs than RBI’s, and that is probably because he hit second and was driven in by other good hitters. It is clear that RBI’s and Runs scored are not the only determinants of Runs Created. As Bonds and Sandberg indicate, on base percentage and speed can increase your runs created. Runs Created shows more of the complete player in offensive characteristics. For pitchers, individual performance is measured by Earned Run Average ( ERA). Earned run average is calculated by:
InningsPit ched ERA = EarnedRuns *^9
ERA measures the average number of runs per nine innings pitched. For example, a pitcher with an ERA of 3.65 means that the pitcher gives up 3.65 earned runs per nine innings. An earned run is a run scored without any errors. In contrast, Scully (1974) and others claim a pitchers strikeout-walk ratio is the best measure of performance. The purpose of a pitcher, however, is to stop the other team from scoring. This could come in
VI. RESULTS
The team winning percentage function was estimated with team data from 1900-
- The estimated equation is:
WINPCT =. 547 +. 000235 RC −. 052 ERA −. 004 NATLG +. 046 CONT −. 043 OUT (3) (.021) (.000024) (.004) (.004) (.005) (.005) DF = 272, R^2 =. A one run increase in team runs created raises the team winning percentage by. points. Winning percentage is measured in thousandths. The effect of a 1 standard deviation increase in RC has a .026 ( 108. 53 *. 000235 )increase on WINPCT. A
reduction of one run in a team’s earned run average given up per nine innings raises winning percentage by .052. The effect of a 1 standard deviation decrease in ERA has a .031 (. 594 *. 05196 )increase in WINPCT. There is no significant difference in winning
percentage between leagues. Contenders and cellar teams finish .046 and .043, respectively, above or below other teams with equivalent player performance. All of the coefficients are significant at the 1% level except for NATLG. The team revenue function was estimated with team data from 1990-99 are shown in Table 5. The results indicate that raising the team winning percentage .1 point increases team revenue by 9.63 million dollars. A team who increases their WINPCT from .400 to .500 increases team revenue by 9.63 million dollars. The variable NATLG is not statistically significant indicating the difference in National and American League revenues are not significantly different. The team dummies show how the New York Yankees make $29.2 million more than the next highest team, the omitted variable Baltimore Orioles. Baltimore, Los Angeles, and the New York Mets have the same
revenues with the other teams making anywhere from $10-$49 million dollars less than Baltimore. The year dummies show that the year of the strike (1994-95) had an effect on team revenues. Team revenues were considerably lower the years of the strike, but quickly recovered so that 1999 revenues were $27 million more than revenues in 1990. To obtain player specific MRP , I assume that individual performance carries with it no externalities so that team performance is the linear summation of individual performance (MacDonald 1994). In other words, player productivities are independent, so that a good performance by one player does not affect the productivity of another. Determining whether major league baseball players are paid their marginal revenue product requires an independent calculation of individual MRP ’s derived from the previous equations 1 and 2. On offense, the purpose of a team and its player is to create runs. From equation (1) a one point increase in WINPCT is estimated to raise TOTREV $96,306 and from equation (2) a run created raises a team’s win percentage by .000235. Therefore the marginal revenue product of hitter is MRP hitters = .000235 * $96,306 * annual runs created (4)
For pitchers, ERA is the most popular statistic of performance. A pitcher can only prevent the other team from scoring runs against him. The lowest possible ERA is zero and an ERA of zero implies that a team’s winning percentage ( WINPCT ) would equal the intercept (.556 in Equation 3) plus any offensive production. To produce an equation for pitchers, note that a one-point increase in winning percentage ( WINPCT ) is worth $96,306 and each one-point decline in team ERA raises WINPCT by .054. A team’s ERA is not the sum of individual pitcher performances but a weighted average of individual ERA’s – weighted by each pitcher’s share of team innings pitched ( IP% ). Following
where salary (^) i is the salary of player i and MRPi is the estimated MRP. If baseball
players are paid their marginal revenue products and the estimate of MRP is accurate, the
estimate of μ should be equal to one: a one-dollar increase in MRP should result in a
one-dollar increase in salary. To the extent there is measurement error in the estimate of
MRP, estimates of μ will be biased downward.
Table 7 reports estimates of equation (6) for all major league baseball players from 1990-1999. The estimated MRP coefficient for all players is .493, which is significantly positive and different from zero. The coefficient suggests that baseball players receive .49 in marginal earnings per dollar of marginal revenue product. The
coefficient is significantly different from 1 since.^44. 014 −^1 =− 40. Thus, this literally
suggests that players are “underpaid” since the coefficient is significantly less than one, suggesting that players are paid in accord to their marginal revenue product. For hitters, the estimated MRP coefficient is .948, which is significantly positive and different from zero. However, the coefficient is significantly different from one at the 10% level. The coefficient suggests that hitters receive .948 in marginal earnings per dollar of marginal revenue product. The pitchers estimated MRP coefficient is .377, also significantly positive and different from one. A second model was estimated including an interaction term for the post-strike period (post-strike*MRP). For all players, the MRP coefficient was .399, which is significantly positive and different from one. The coefficient on POSTMRP is .183, implying that players made .183 more in marginal earnings per dollar of marginal revenue product after the strike than before the strike. For hitters, the estimated MRP coefficient is .773. The coefficient on POSTMRP , is .256. This coefficient indicates that
hitters received .256 more in marginal earnings per dollar of marginal revenue product after the strike than before the strike. For pitchers, the estimated MRP coefficient is .328 and is significant. The estimated POSTMRP coefficient is .097. Pitchers received .097 more in marginal earnings per dollar of marginal revenue product after the strike. Therefore the strike played a big role in the increase of major league players’ salaries, or at least increased the correlation between salary and MRP. The next regression included an interaction term including American League*MRP (ALMRP). All players had a MRP coefficient of .468. The coefficient on ALMRP was .051, which is significantly different from zero. Therefore players in the American League make .051 more per dollar of marginal revenue product. Pitchers have a MRP coefficient of .348 and a ALMRP coefficient of .050, which is significantly different from zero. Hitters have a MRP coefficient of .950, which is not significantly different from one, and an ALMRP coefficient of -.005. The coefficients on ALMRP show that pitching is more valued in the American League or that there is a higher premium placed on a given ERA. The final salary regressions are run with hitters and pitchers who have salaries above and below the average salary of $1,400,000. The results are found in Table 8. Beginning with the upper salary bracket, hitters have an estimated MRP coefficient of .637, which is significant. Hitters making above the average salary receive .637 more in marginal earnings per dollar of marginal revenue product. This coefficient suggests that hitters above the average salary are underpaid. Hitters who make below the average salary have an estimated MRP coefficient of .075. This suggests that hitters making below the average salary are much underpaid. For pitchers, the estimated MRP
If my MRP estimates are reasonable, there must be some explanations as to why owners are underpaying players as compared to his marginal revenue product. If my MRP estimates are correct, then exploitation of the players exists. The owners can misgauge a player’s worth. This could lead to the underestimating of player expectations by the owners. These could easily lead to the underpayment of professional baseball players. If my MRP estimates are wrong, it could be the result of econometric bias. Another problem could be the use of wrong variables. Runs Created and ERA may not be the best statistic to measure offensive and pitching performance. The Blue Ribbon Panel on Baseball Economics describes how the league needs to keep salaries low. They make suggestions to help out owners relative to the players. My results suggest the opposite. My results indicate that the league needs to raise the salaries. If my estimates are correct, the focus should be on helping players, relative to the owners, to help them receive their marginal revenue product.
References Grabiner, David, “The Sabermetric Manifesto,” The Baseball Archive , www.baseball.com. Krautman, Anthony C., “What’s Wrong with Scully-Estimates of a Player’s Marginal Revenue Product,” Economic Inquiry, Vol. 37, No.2, April 1999, 369- Levin, Richard C., George J. Mitchell, Paul A. Volcker, and George F. Will, The Report of the Independent Members of the Commissioner’s Blue Ribbon Panel on Baseball Economics , July 2000 MacDonald, Don N. and Morgan O. Reynolds, “Are Baseball Players Paid their Marginal Products?” Managerial and Decision Economics , Vol. 15, 1994, 443- Scully, Gerald W. “Pay and Performance in Major League Baseball,” Economic Review, Vol. 64, No. 6, December 1974, 915-930 The American
Staudohar, Paul D. “Salary Caps in Professional Team Sports,” Compensation and Working Conditions, Spring 1998, 3- Zimbalist, Andrew. “Salaries and Performance: Beyond the Scully Model,” Diamonds are Forever, The Business of Baseball. Sommers, Washington, D.C., 1992, 109-
