Final Thesis

Money Ball, Money Pit, or Money Misallocation?

A Thesis Presented to The Faculty of the Department of Economics Carthage College

In Partial Fulfillment of the Requirements for the Degree of Bachelor of Arts

Elena C. Kelsh December 2017



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ABSTRACT

This paper aims to address the following two issues as they pertain to the professional baseball industry: financial stability and pay equity. The continuously increasing salaries present in Major League Baseball (MLB) accompanied with the recent decline in ticket prices and attendance levels suggest that the business of baseball could be threatened, which recent literature has yet to address. At the same time, since the Reserve Clause was struck down in 1975, empirical work has yet to be done to test its effectiveness at removing player exploitation. Using performance statistics and salary data from the St. Louis Cardinals’ 2017 season, this paper attempts to target these shortcomings. While this study confirms baseball’s ability to financially stay afloat, it shows the increased level of pay discrimination and exploitation that still exists in the MLB today. If baseball is to remove this inefficiency, the current arbitration system needs immediate reconstruction.



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TABLE OF CONTENTS Introduction…………….……….……….……….……….……….…………...…..……..7 A Historical Overview…………….……….……….……….……….………….….…….9 The MLB Labor Market Today…………….……….……….……….……….………..10 Review of Previous Literature and Empirical Work…………….……….……...……11 Scully 1974……………………………………………………………………….12 Lackritz 1990……………………………………………………………....……..13 Howard and Miller 1993…………………………………………….……..……..14

Analytical Framework………….……….……….……….……….……….…….……..15 Issue #1: Franchise Financial Stability……………………………………..…….18 Evaluating Hitters’ MRP…………………………………………….….19 Evaluating Pitchers’ MRP………………………………………..……..21 Issue #2: Pay Equity………………………………………………...……………23 Data Description………………………………………………………...….…….24

Empirical Results……………….……….……….……….……….……….………..….24 Addressing Issue #1………………………………………………………….……24 Measuring Hitting and Pitching Contributions…………………………..24 Measuring Hitters’ MRP………………………………………...……….26 Deriving Marginal Costs………………………………………..………..28 Measuring Pitchers’ MRP………………………………………………..33 Evaluating the Team’s Financial Stability……………………….………37 Addressing Issue #2………………………………………………………………..38 Calculating the Lerner Index……………………………………….…….38 Evaluating Pay Equity……………………………………………………39 Comparative Analysis Using Scully’s 1974 Index Values……………….41

Policy Suggestions and Areas for Further Research………….….……….…………..44 Conclusion……………….……….……….……….……….……….……..…………….46 Appendix A: Variable Tables….……….……….……….……..….…….…..…………..49 Appendix B: Output Tables..…….……….……….……….……..….….………...……..51 Appendix C: Revenue and Expense Tables…....……….………....…………...………..53 Appendix D: MRP Results Tables…………….….……….…..…….……….……….…57 Appendix E: Lerner Index Results Tables………..…….……..……...…………………67 References…………….……….……….……….……….……….…………..………….71



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INTRODUCTION: Since the abolishment of the Reserve Clause, a stipulation in professional baseball players’ contracts that gave owners indefinite control over their services, the average player salary has risen from $208,448 to $4.4 million, adjusted for inflation.1 While the average salary has increased substantially, the salary range has also widened in scope over this 40 year period; in 1975, the minimum salary was $74,653 in 2017 dollars, with the highest salary sitting at almost $1.2 million – just a little over a $1 million range2. Comparatively, today, the salary gap has increased to over $30 million, with the minimum salary at $535,000, and the highest paid player, Clayton Kershaw, standing to make $33 million for the 2017 season as part of his 7 year, $215 million contract3. At the same time, these rising payroll costs have been accompanied by an almost 5% decrease in overall league attendance, a 33% decrease in ticket prices, and an aging fan base4. Although baseball has made up for these discrepancies with multi-million-dollar TV contracts, broadcasting rights, and merchandise sales, the facts at hand give rise to two competing questions regarding Major League Baseball’s (MLB) financial stability and pay equity in absence of the Reserve Clause. Can baseball afford these continual, exponential pay increases given the market characteristics, and if so, are the players truly being paid according to their performance?

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Average salary amounts extracted from https://www.baseball-reference.com and adjusted for inflation via http://www.bls.gov 2 Minimum salary amounts extracted from https://www.baseball-reference.com and adjusted for inflation via http://www.bls.gov. Highest salary information extracted from http://sabr.org 3 Minimum salary amounts extracted from https://www.baseball-reference.com. Highest salary information extracted from http://sabr.org 4 League attendance provided by http://www.espn.com/mlb/attendance, ticket pricing provided by http://www.kshb.com/sports/baseball/mlb-average-ticket-price-fan-cost-index-for-all-30-baseball-teams and https://www.forbes.com/sites/mikeozanian/2017/03/22/baseball-ticket-prices-for-every-team-cubs-top-mlb-at-151graphic/#35565e5f294a, and fan demographics information provided by https://www.wsj.com/articles/baseball-andits-aging-fans-1471534364?mg=prod/accounts-wsj



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Rising costs paired with shrinking revenue sources threatens the business of baseball from an efficiency and financial standpoint. Under any given market structure, the optimal decision for firms is to shut down if their total revenue is less than their variable costs. In this case, if clubs’ revenue fails to at least match player salaries, they will fold (Goolsebee and Levitt, 2016). This was seen when Jeffrey Loria sold the Montreal Expos in 2002 to the MLB after the organization was forced to sell their best players due to financial distress, causing a decrease in both consumer demand and team revenue (Armour and Levitt, 2015). Today, this same scenario has the potential to repeat itself in Miami, with same owner, Loria, who is currently looking to sell the franchise because of insufficient funds to compensate for the extreme team debt from an expensive new stadium and payroll.56 Moreover, the vast spread of player salaries suggests pay inequality within the league, even in the presence of the strongest union in professional sports, the Major League Baseball Players Association (MLBPA). Unless the wage differential is a result of difference in skill, productivity, or efficiency, price discrimination is observed, causing players to be either over or undercompensated and owners to exert market power over players’ labor services (Goolsebee and Levitt, 2016) (Pierenkemper, 2005) (Barbeza, 2005). If this is the case, it is questionable if the abolishment of the Reserve Clause has fulfilled its purpose in eliminating player exploitation. The inefficiencies at hand have the potential to wreak havoc on Major League Baseball, players, and fans, alike, emphasizing the importance of addressing the issue at hand. If the MLB is to operate at optimal levels, neoclassical theory proposes that marginal costs be equated to marginal

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Information on the Miami Marlins provided by https://www.forbes.com/sites/mikeozanian/2013/01/27/miamimarlins-have-become-baseballs-most-expensive-stadium-disaster/#40aa1b801d07 6 Stadium largely financed with tax dollars



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revenues, meaning that player salaries should be equated to the value of what they relatively contribute to their respective teams.

A HISTORICAL OVERVIEW: Prior to 1975, The Reserve Clause allowed team owners to exercise monopsony power over their players; once a player was signed to a team, they were at the mercy of the franchise and were wage takers in nature, allowing for owners to pay them less than their incremental contribution to the club (Scully, 2008). Bound to a team for the duration of their career, unless otherwise directed by the owner, players lacked the right to bargain and sell their services on the market to the highest bidding team. For these reasons, player salaries remained artificially low for decades (Borjas, 2013) (Haupert, 2002). Following the 1972 player strike, the first league-wide labor strike in professional sports history, and in the presence of, arguably, the strongest labor union in the world, the Major League Baseball Players’ Association (MLBPA) eventually won the war against the Reserve Clause. In 1975, they forever changed the labor market structure for professional baseball players and accomplished the ultimate goal of unions: ‘more’ (Haupert, 2005). Through monopoly unionism and collective bargaining, they were able to demand increased salaries, benefits, and improved working conditions. Although this resulted in the maximization of every MLBPA members’ utility, it remained inefficient in nature due to the decrease in total value of player contributions to the league, the deadweight loss, and the increase in outright expenses that came with wage increases above market equilibrium (Borjas, 2013) (Doeringer, 2005) (Haupert, 2002). Players were now given the right to engage in direct negotiation, bargain for long term contracts (LTC), and become free agents in absence of a salary cap (Haupert, 2002). Those



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freedoms are still enjoyed by players, today, contributing to free agents’ and even arbitration players’ exponentially increasing salaries. The system of arbitration and free agency restricts players from becoming free agents until 6 seasons of play, however, their contracts are available for final offer arbitration after 3 years. Until then, player salaries are determined by the team (Haupert, 2002).

THE MLB LABOR MARKET TODAY: The three levels of market structure that can be observed in the professional baseball market today are as follows: a monopsony market, a dual or bilateral monopoly market, and a monopoly market, respectively. The monopsony market prevails during the first 3 years after a player is brought up to the major leagues; players are bound to their unnegotiable contracts for 3 seasons, giving owners little incentive to raise those players’ salaries above the minimum. Owners are able to earn economic rents off of these players, since they are paying them less than the value of their relative output. Between the 3 and 6 year periods of service, a dual monopoly is observed, with players being eligible for final offer arbitration. The player is still bound to a singular team; however, he is given the right to bargain, with the threat of taking his contract to an independent arbitrator if a deal is not settled on. This market phenomenon raises player salaries by a substantial amount compared to the monopsony market, with the goal being to settle on a contract of fair market value, i.e., compensating players according to their expected performance. Once a player reaches year 6 of service in the majors, he is considered a free agent, where he exerts some form of monopoly power; he is the sole seller of his labor services, but he has potentially 30 teams that demand them, now that his services have entered the market.



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In this scenario, he is able to set a higher price than his competitive level, raising his salary by more than the relative worth of his output (Borjas, 2013) (Haupert, 2002). In order for a labor market to operate at optimal efficiency, neoclassical theory suggests that workers be compensated according to the value of their marginal revenue product (MRP) to the firm (Borjas, 2013) (Goolsebee and Levitt, 2016). In other words, workers ought to earn according to their output or what they produce. Therefore, for baseball to be efficient and for pay equity to be observed, players should be compensated according to the value of what they contribute to their teams in order for the neoclassical marginal productivity theory of wages to hold true. It is hypothesized that this theory fails to hold true in the professional baseball labor market given the current arbitration system if players are truly underpaid during their first 3 years of service, pay-efficient the following 3 years, and overpaid during the time thereafter comparable to the value of their output.

REVIEW OF PREVIOUS LITERATURE AND EMPIRICAL WORK: Since the 1970’s, empirical analysis has become a popular tool in evaluating the baseball industry; Gerald Scully started the revolution, calculating player MRP values and salary regressions in 1974, which led to Joseph Hunt and Kenneth Lewis conducting cost-benefit analysis of increasing dominance within the league in 1976. Eventually, this led to the popularity of Bill James’ late 1970’s writings on the use of sabermetrics in baseball, which uses objective data and evidence to make in-field decisions verses subjective coach and scout evaluations (Armour and Levitt, 2015). More recently, M.R. Yilmaz and Sangit Chaterjee developed logarithmic regression equations to assess the potential for a principle-agent problem in 2013, Michael Lewis used data-driven analysis to assess competitive balance in the MLB in 2008, and



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Mary Keener used ordinary least square (OLS) regression analysis to explain winning percentage in 2012 (Yilmaz and Chaterjee, 2013)(Lewis 2008)(Keener 2012). As the league continues to become more sabermetrics-heavy, empirical analysis will become more essential for evaluation of franchises, strategic decisions, and player evaluations, alike.

Scully (1974): A year before the abolishment of the Reserve Clause, Gerald Scully estimated the relationship between MLB player’s pay and performance to calculate the economic loss baseball was experiencing, finding that players were largely exploited. In many cases, player MRP was significantly greater than player salaries, proving the exercise of monopsony power on part of the owners. This was also the first instance in which the MRP for an occupation was estimated on a systematic basis (Scully, 1974). Scully measured player MRP based on the reasonable assumption that player performance effects team winning percentage, a measure of team on-the-field success, which directly and positively relates to team revenue, a measure of team financial success. Thus, it becomes possible to estimate an individual player’s worth to a team based on their measurable performance statistics. From there, he used previous research to determine the key performance indicators for hitters and pitchers, respectively, as their individual slugging averages (SA) and their individual strike-to-walk ratios (SW) in order to develop equations for the two position’s MRP. Using regression equations for estimating team winning percentage and team revenue, he was able to produce per-player MRP values using the coefficients for SA and SW’s impact on winning percentage and winning percentage’s impact on team revenue. Scully was also able to



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weight the players’ contributions to team performance, using lifetime at-bats (AB) and lifetime innings-pitched (IP) to value hitters’ and pitchers’ salaries, respectively (Scully, 1974). Continuing, he calculated per-player marginal cost (MC) using their salaries and the summation of a number of other costs ranging from aggregate nonplayer salaries, to average capital costs. The MC per player was netted against the MRP per player to obtain a value for net MRP, which Scully then compared to their actual compensation for the 1968-69 season. Scully then calculated the Lerner Index for players in order to address issues of pay equity and discrimination, categorizing them as either mediocre (comparable to today’s rookies and players in years 1-3 of arbitration), average (comparable to today’s players eligible for final offer arbitration), or superstar (comparable to today’s free agents). From there, he concluded that baseball players were largely exploited by owners. However, he found that superstar and average players were drastically underpaid compared to their net MRP, while mediocre players retained salaries greater than their relative contributions (Scully, 1974).

Lackritz 1990: A little over 15 years after Scully’s estimation of occupational MRP and after the abolishment of the Reserve Clause, James R. Lackritz reevaluated the salaries of professional baseball players on the basis of performance statistics. Focusing on replicating the first half of Scully’s methodology in regards to estimating winning percentage, he indicated key performance statistics for major league players, deriving a regression equation for both the American League and the National League. He then evaluated players’ relative contribution to their teams by using a utilization function based on league-wide averages. Multiplying their relative contributions by the team’s revenue for the respective year, he derived a predicted salary for a given player. That



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predicted salary was added to a base salary determined via Lackritz’s and Ross’ methodology from a 1985 study on predicting a baseball player’s true worth (Lackritz, 1990). While Lackritz’s foundation in player evaluation was sound, he failed to account for players’ costs to their organizations when comparing the calculated value of their contributions to their actual salaries, like Scully did. Neglecting administrative costs, travel costs, training costs, etc., fails to capture the true essence of a players’ net MRP, thus, leading to overstatement of players’ net worth to an organization.

Howard and Miller 1993: Furthermore, data envelopment analysis was conducted via Larry W. Howard and Janis L. Miller in the early 1990’s, this time, focusing on pay equity within the league, embodying the second half of Scully’s study that focused on player exploitation. In this instance, players were categorized as either underpaid, pay-efficient, or overpaid based on equity metrics. While the standards for underpaid and pay-efficient were defined as equity metrics less than one or equal to one, respectively, the standards for overpaid were much stricter. For a player to be classified as overpaid, their equity metrics had to exceed 2, causing a majority of observed players in their study to be either classified as underpaid or pay-efficient. A further shortcoming in this study was the fact that pitchers and rookies were omitted from this study (Howard and Miller, 1993). Today, pitchers, who take up a majority of a team’s roster and budget, are generally higher paid than position players. At the same time, rookies, who are typically a minority in team rosters, are generally paid substantially less. This suggests a larger pay equity spread than was observed in this restrictive study.



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ANALYTICAL FRAMEWORK: Comparative analysis of previous empirical work conducted before and after the Reserve Clause suggests that its abolishment has failed to achieve its primary goal; player exploitation may still persist, even in the presence of the prevailing $4.4 million average MLB player salary today and the financial stability of franchises may be threatened.7 During the height of the Reserve Clause, Scully concluded that players, especially experienced veterans, were not being compensated according to what they produced for their clubs (Scully, 1974). While abolishment of the Reserve Clause was aimed at decreasing player exploitation, empirical analysis thereafter from Lackritz, Howard, and Miller suggests otherwise (Lackritz, 1990) (Howard and Miller, 1993). With the minimum player salary sitting at over $500,000 and the highest paid player earning more than $30 million, it is baffling to suggest that this holds true.8 In fact, superficially, it would seem that the opposite prevails today and that players are largely overcompensated. Given the shortcomings in replications of Gerald Scully’s methodology in estimating player net MRP and exploitation in absence of the Reserve Clause, it becomes critical to address these issues today in order for baseball to find middle ground in regards to wages and financially stay afloat. Theoretically, if baseball is to operate at the minimal break-even point, whether in a perfectly competitive market or not, their marginal costs need to equate to their marginal revenues (Goolsebee and Levitt, 2016). In other words, their total expenses need to be constrained to their organizational income, not just player salaries. Player travel expenses, per diem allowances, and uniform costs, to name a few, must be allocated in the model in order to

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Average salary amounts extracted from https://www.baseball-reference.com

Minimum salary amounts extracted from https://www.baseball-reference.com and highest salary information extracted from http://sabr.org



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accurately calculate MRP valuations. Otherwise, if teams are annually paying out more than they are reaping, the business of baseball lacks financially soundness, causing the team to dip into debt or owners to eat the loss. In Lakritz’s study, players’ MC to clubs was not calculated for when calculating respective MRP values, artificially increasing players’ worth to clubs, and producing inflated player salaries (Lackritz 1990). At the same time, optimal conditions for the MLB labor market arise when each player earns according to the value of his output. According to the Neoclassical Marginal Productivity Theory of Wages, wages should equal net MRP to maximize utility and promote efficiency (Borjas, 2013). Although the conditions of the model assume perfect competition, homogeneous factors, and perfect mobility, it provides an objective framework to value player compensation versus productivity (Goolsebee and Levitt, 2016). If player salaries significantly deviate from the value of their individual contributions, it can be concluded that pay discrimination still exists in the league today. Any compensation value greater than respective MRP values suggest player monopoly over the owner, whereas any compensation value less than respective MRP values suggest that owners still exert some form of monopsony control over players. If the latter is primarily true, the goal of the abolishment of the Reserve Clause has not been achieved in its entirety. Seeing as three different market structures can be observed throughout the duration of a players’ career, arbitration status of the individual players is of particular interest when examining net MRP values and exploitation issues. If a player is in his rookie year or in a nonnegotiable year of arbitration, his net MRP value is likely to be greater than his salary due to the monopsony power the owners have over their labor services. Since the team dictates player salaries during the first three years, they have little incentive to pay these players above the



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minimum amount: $535,000. Once a player enters his negotiable arbitration years, a bilateral or dual monopoly market prevails, and his salary is more likely to be equated to his net MRP value, seeing as players and teams are now allowed to negotiate a fair market value contract. In the event that a deal fails to be agreed upon, an independent agent will choose the offer that best matches the players’ worth in a final offer arbitration hearing, allowing for a more competitive labor market structure. On the other hand, once a player is vetted into free agency after his 6th year of play in the major leagues, his salary is hypothesized to be greater than his net MRP value. Although they technically enter a free market, which should lead to expected outcomes close to perfectly competitive, they exert monopoly power over owners for their respective services, given that players are imperfect substitutes for one another. In order to address these issues at hand, I will observe a single MLB team and its 40-man roster. Rather than looking at this from a league-wide basis, approaching this at the micro level allows me to conduct a more tailored and accurate study, as well as obtain more precise, teamspecific results. Furthermore, if a single team is an accurate sample of the MLB as a whole, conclusions made about a single organization can translate into conclusions about the entire league. However, a shortcoming of this methodology lies in the fact that using a singular season’s statistics to calculate net MRP values for that same year makes this model static in nature. The professional baseball market is one characterized by its dynamic structure, which this fails to embody. Current compensation contracts are tied to expected future performance based on previous performance and team-specific predictive models, not present-day performance. Nevertheless, this provides a sound foundation to evaluate player pay and performance, as well as provide means for deriving future compensation contracts. Furthermore, the robust features of



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this methodology allows for the analysis of both financial stability and pay equity in the presence of variability.

Issue #1: Franchise Financial Stability Focusing on the first issue of financial stability and baseball’s ability to operate at the minimal break-even point, I will objectively value this singular team under the constraints of the organization’s reported revenues for a given season. Given a budget constraint based on annual revenue, I will allocate it according to players’ specific contributions to team revenues by monetizing their output. Concluded by Yilmaz and Chaterjee (2013), wins translate to a measure of both on-the-field performance and financial performance (Yilmaz and Chaterjee, 2013). Thus, each players’ proportional contribution to wins will translate into their compensation for such. However, this contribution will be evaluated, first, by separating pitchers and position players, just as both Scully and Howard and Miller did (Scully, 1974) (Howard and Miller, 1993). It is assumed that pitchers and position players ought to be evaluated on different grounds, seeing as the former is primarily a defensive position and the latter is primarily an offensive position; thus, each compile a unique set of statistics that aid in explaining their contributions to their organizations. To evaluate their respective contributions, ordinary least square (OLS) regression analysis will be used, with WPA (win probability added) for pitchers and hitters as the independent variables of interest on wins, the dependent dummy variable, and is demonstrated in Equation 1. By definition, the WPA measures the increase or decrease in win expectancy, a quantification of the percentage change in terms of the chance of winning from one event to the



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next, on a player-to-player basis9. By measuring and comparing compiled hitters’ and compiled pitchers’ impacts on wins for each of the 162 games that constitute a regular season, it will allow me to allocate the teams’ revenue accordingly, assigning a specific budget for position players pitchers separately.

EQUATION 1: Y= 𝛽o + 𝛽1WPApitch + 𝛽2WPAhit+ e

From there, it is necessary to conduct two further OLS regression models: one to explain runs scored on part of the hitters and another to explain runs allowed on part of the pitchers. In baseball, runs are the sole determinant of wins; again, referring to Yilmaz and Chaterjee’s (2013) conclusions, if runs translate to wins and wins translates to financial performance, runs, therefore, can be tied to revenues (Yilmaz and Chaterjee, 2013). Thus, their place in establishing player MRP valuations is justified.

Evaluating Hitters’ MRP To explain runs scored on behalf of hitters, and to further tie these values to player compensation, it is necessary to, first, value runs scored in terms of the budget designated for position players. In order to do this, I will take the hitters’ budget and divide it by the aggregate number of runs the team scored in a given season to derive a value for the maximum amount the organization can afford to spend on runs.

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Refer to the MLB’s definition of WPA http://m.mlb.com/glossary/advanced-stats/win-probability-added

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Then, I will explain runs scored with data compiled on a per player basis using OLS regression techniques using the variables found in Table 1a10 and Equation 2. Variables were chosen with the help of Howard and Miller’s Fair Pay for Fair Play (1993) and what they defined as significant performance indicators (Howard and Miller, 1993). Careful attention was paid not to include any variables that are used in deriving another variable in the model and to leave out statistics that can’t be held constant while increasing another. For example, batting averages (BA) cannot be included in the model, seeing as it cannot be held constant if strikeouts (SO) or homeruns (HR) were to increase. On the other hand, on base percentage (OBP), a recently stressed statistic in recent baseball literature, cannot be included, either, seeing as the variable for walks (BB), doubles (twoB), triples (threeB), and homeruns (HR) are used when deriving this one performance indicator (Lewis, 2003).

EQUATION 2: Y= 𝛽o + 𝛽1BB- 𝛽2SO + 𝛽3twoB + 𝛽4threeB + 𝛽5HR – 𝛽6GDP + e

The OLS regression estimate derived from these variables will create a model to objectively measure an individual position players’ impact on team success in terms of runs scored. The predicted value to contribution to runs scored will then be multiplied by the price per run given the budget constraint to derive a player’s individual MRP according to his output. It is necessary to then calculate the individual players’ MC values in order to generate net MRP values; values for player per diem, transportation costs, hotel expenses, and player development will be aggregated and allocated amongst a 40-man MLB roster. Once a MC figure

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Refer to Appendix A

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is obtained, it will be deducted from each MRP value to generate net MRP values; these will represent the amount of additional compensation players ought to receive in form of salary if players are to receive pay comparable to their output and if optimal conditions are to be observed in the labor market. These values will be compared alongside actual 2017 compensation amounts, as well.

Evaluating Pitchers’ MRP Before explaining runs allowed via pitchers, it is important to note that most significant pitching statistics have a strong inverse relationship to performance; in other words, the higher the value of these pitching statistics, the more they negatively affect their respective teams’ position. For these reasons, I will start by calculating base salaries for all pitchers. If this system is not used and pitcher compensation starts out at $0, as hitters’ do, the model will show that each pitcher would theoretically owe the organization money. On the basis of a time-rate system of compensation, each pitcher will be given a salary based on their aggregate innings pitched for the regular season. An inning pitched will be worth the value of the pitching budget divided by the cumulative amount of innings pitched for the team. From there, I will explain runs allowed using OLS regression techniques using the following variables found in Table 2a11 and Equation 3. Again, variable choice was influenced from Howard and Miller’s Fair Pay for Fair Play (1993). Statistics such as homeruns (HR) and wins (W), which are thought of as significant when referring to recent baseball literature, were not included in the model for the reason that it is impossible to increase one while holding all

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Refer to Appendix A

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other variables constant in the model. To avoid violating this essential assumption of OLS regression analysis, they will be omitted for this case study.

EQUATION 3: Y= 𝛽o + 𝛽1BB – 𝛽2SO + 𝛽3H + e

While individual position players’ aggregate performance statistics will be used when predicted runs scored, individual pitchers’ aggregate performance statistics as deviations from team averages will be used when predicting runs allowed. If player statistics were imputed simply based on their aggregates, each player would automatically have a salary cut, regardless of whether his performance positively or negatively impacted his team. By comparing relevant performance measures to the average, relatively ‘good’ pitchers will be awarded additional compensation, while relatively ‘poor’ pitchers will be given a decrease in compensation. This way, the entirety of the revenue remains and the principles by which the marginal productivity theory of wages is established is conserved. Additionally, starting pitchers and relief pitchers will be separated when computing averages; otherwise, starting pitchers will seemingly outperform their relieving counterparts simply due to the substantial increase in plate apperances. This separation addresses this issue and allows each individual pitcher to be evaluated against his equals. The OLS regression estimate derived from these variables will create a model to objectively measure an individual pitcher’s impact on team success in terms of contribution to runs allowed. The predicted contribution to runs allowed will then be multiplied by the price per run scored that was previously derived in hitters’ valuations; this value will either be added or



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subtracted from pitchers’ base salaries depending on if they allowed more or less runs than the team average. The same MC figures obtained for offensive players will be used when arriving at pitchers’ net MRP values. Again, these will represent the salaries players ought to receive if players are to be compensated per their output and if neoclassical theory is to prevail.

Issue #2: Pay Equity To address the second issue of potential pay inequality and discrimination, foundations in demand elasticity will be utilized by calculating the Lerner Index, like Scully, except for each individual player, instead of only combined at the aggregate level. Upon calculating each players’ net MRP values from the above methodology and by obtaining players’ actual salaries, I will be able measure the deviation between the two. This way, I will be able to statistically observe the level of the teams’ (or the players’) market power; if the value is closer to 0, then near perfectly competitive conditions exist, implying pay equity. On the other hand, if the value is closer to 1, then a more monopolistic or monopsonistic structure exists, depending on if it is in favor of the club or the player. The arbitration status of the player will also be a key component when addressing this issue at hand; whether the player is in a nonnegotiable year of arbitration, a negotiable year of arbitration, or in free agency will affect the level of competition in the labor market. Upon examining these values on the individual and arbitration-level basis, I will be able to quantify market power within a team. If a single team is an accurate representation of the league as whole, whether or not the Reserve Clause eliminated exploitation in the MLB will be revealed.



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Data Description For this particular study, I have chosen to analyze the 40-man roster for the St. Louis Cardinals for the 2017 regular season. Per-game statistics for all 162 games have been taken from thebaseballcube.com in order to find the relative contributions of position players and pitchers, respectively12. To explain both runs scored and runs allowed, data from baseballreference.com has been extracted, providing aggregate season statistics on a per-player level for the entire 40-man roster13. Additionally, actual salary data has been provided via spotrac.com in order to calculate the Lerner Index on a per-player, per-position, team-wide, and arbitrationstatus basis14.

EMPIRICAL RESULTS: Addressing Issue #1 Measuring Hitting and Pitching Contributions To calculate position players’ and pitchers’ relative contribution to team wins, 162 observations for both hitter WPA and pitcher WPA were collected and used in OLS regression analysis to explain wins, a dummy variable that equals 1. Output figures and the resulting equation is given in Table 1b15 and Equation 4.

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Per game statistics for the 2017 St. Louis Cardinal’s regular season provided by http://www.thebaseballcube.com Individual performance statistics for the 2017 St. Louis Cardinals provided by http://baseball-reference.com 14 2017 salary amounts for the St. Louis Cardinals provided by http://www.spotrac.com 15 Refer to Appendix B 13



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EQUATION 4: Y= 𝟎. 𝟓𝟎𝟎 + 1.008WPApitch + 0.991WPAhit (0.004) (0.013) (0.013) Weighting the impact of each individual coefficient against the sum, hitters and pitchers are calculated to contribute 49.6% and 50.4% to wins, respectively. The adjusted r-squared value of 0.987 indicates that this model explains 98.7% of the variability in wins, validating the use of WPA to value different positions’ effects on on-the-field, and therefore, financial performance. To allocate the revenue accordingly, the St. Louis Cardinal’s 2017 revenue figure of $310 million was obtained via forbes.com, embodying ticket sales, food and merchandise, and their current contract with Fox Midwest Sports Live16. However, three factors that need to be deducted from total revenue in order to estimate revenue available for player salaries for St. Louis, specifically, are their city/state taxes, their bonds payable, and their miscellaneous other non-player expenses (i.e. coaches’ compensation, front office salaries, equipment, etc.). These costs represent fixed costs that are incurred whether players are signed or not. City/state tax expenses were obtained directly from the St. Louis Cardinal’s website, values for outstanding bonds payable on Busch Stadium for 2017 were extracted via ballparks.com, and other nonplayer expenses were found from baseballprospectus.com17. However, the most recent nonplayer expense figure for St. Louis was from 2002; this value has been adjusted for inflation to estimate the 2017 non-player expenses18. Furthermore, neither exact or estimated values for

St. Louis Cardinal’s 2017 revenue amount collected from https://www.forbes.com/teams/st-louis-cardinals Information on bonds payable provided by http://www.ballparks.com, amounts for city/state taxes extracted from http://stlouis.cardinals.mlb.com and non-player expense information provided by https://www.baseballprospectus.com 18 Non-player expense amounts from https://www.baseballprospectus.com adjusted via https://www.bls.gov 16

17



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team contributions to player pension funds (amounts which are specified in the most recent Collective Bargaining Agreement), could be obtained for the sake of this study, and as a result, have not been imputed into these costs. In any case, a summary of the estimated values is found in the Table 1c19, below, leaving $193,743,085.48 worth of distributable revenue for player compensation. Building on the fact that position players contribute 49.6% to team wins, they ought to receive 49.6% of this revenue amount, or $96,096,570.40. By those same accounts, given that pitchers contribute 50.4% to team wins, they ought to receive $97,646,515.08 according to my methodology.

Measuring Hitters’ MRP Using the position player budget constraints calculated above, it is possible to derive a value for each player’s contribution to runs scored. By dividing the $96,096,570.40 allocated to hitters by the aggregate amount of team runs for the 2017 season, 753, it is estimated that the maximum amount the Cardinals can afford to spend on each one contribution to runs scored is $127,618.29, shown in Equation 5. Furthermore, by conducting OLS regression analysis to derive each player’s relative contribution to runs scored, it will be possible to multiply that value by the dollar amount associated with each run, in order to obtain individual MRP values.

EQUATION 5: $96,096,570.40 / 753 Aggregate Team Runs = $127,618.29 per Run Scored

19



Refer to Appendix C

26

To calculate values for contribution to runs scored, 25 observations, the number of strictly position players plus the number of pitchers who hit, were collected from the Cardinal’s 40-man roster and used in OLS regression analysis to explain runs scored, the independent variable.

EQUATION 6: Y= 3.085 + 0.022BB – 0.170SO + 2.476twoB + 2.998threeB + 1.254HR (2.001) (0.124) (0.149) (0.435) (1.363) (0.620) 2.44GDP (0.640) Table 1b20 and Equation 6 reveal exactly how different aspects of player performance impacts the aggregate Cardinal runs, and therefore, their chances of winning. It is interesting to note that walks (BB), the key component to Billy Beane and the Oakland Athletics’ sabermetrics-heavy methodology that was highlighted in the recent novel and motion picture, Moneyball, show to be less impactful on wins than suggested (Lewis 2003). For every walk generated, a player will contribute just over one one-hundredth to aggregate team runs, all other variables constant. Another popular statistic, homeruns (HR), also shows to have less of an impact on a team’s chances of winning relative to other performance indicators. Each homerun a player generates, holding all other variables constant, contributes just over one to total team runs, which is less than both double’s (twoB) and triple’s (threeB) impact. As a result, there is a reduced need for at least the Cardinals organization to enter the market for expensive home runs hitters; homeruns fail to have the impact on runs to the degree that other performance indicators do.

20



Refer to Appendix B

27

Perhaps the most impactful performance statistics for the Cardinals organization are triples (threeB) and grounded double plays (GDP): for every triple a hitter earns, they are predicted to contribute almost 3 runs to the team and for every grounded double play, they are expected to cost the team over 2 runs, all other variables constant. Strikeouts (SO) also threaten Cardinal run production, seeing as a mere 6 additional strikeouts that a player allows will decrease aggregate team runs by a factor of 1, all other performance variables in the model constant. The adjusted r-squared value of 0.859 indicates that this model explains 85.9% of the variability in runs scored and has high explanatory power. If the Cardinals are a representative sample of the MLB population, parallel conclusions can be inferred for other franchises.

Deriving Marginal Costs Extracting these values for individual players and plugging them into the above model, I derived a value for each player’s contribution to runs scored, and therefore, to the organization’s financial success. Multiplying these predicted y values by the monetary value for contribution to runs scored, $127,618.29, each player’s predicted compensation has been found. Before deeming these values as justified hitters’ salaries, however, it is necessary to subtract the marginal cost of each player to the organization. These marginal costs in the form of player per diem, transportation expenses, lodging expenses, uniform costs, and player development also represent forms of compensation the players are already receiving. Player per diem refers to cash amounts given to each player per away game to spend on food, toiletries, and other miscellaneous personal travel expenses. Obtained from usatoday.com, the MLBPA revealed that their contract demands that each player receive $100.50 per day to



28

cover these amounts21. To calculate total per diem costs for the 2017 season, the $100.50 per day amount was multiplied by the 25-man roster that typically travels to away games, and then again by the 81 total away games for the 2017 season. This resulted in total per diem amounts of $203,512.50, shown in Equation 7.

EQUATION 7: $100.50 per day x 25-man roster x 81 away games = $203,512.50 Total Per Diem Expense 2017

Player transportation costs embody both air travel expenses, as well as charter bussing to and from the various stadiums. While information availability on specific travel arrangements, expenses, etc. was limited, it is estimated via forbes.com that it costs approximately $15,000 per hour of travel to transport a professional baseball team; from there, the Cardinal’s total travel time was compiled by referring to their 2017 schedule and sequentially calculating travel time from one destination to the next, using travelmath.com22. Upon arriving at 55.5 hours of total travel time for the 2017 season, shown in Table 2c23, it was multiplied by the hourly approximated cost to arrive at a rough estimate of $631,050.00 for transportation expenses, shown in Equation 8.

EQUATION 8: 55.5 hours x $15,000 per hour = $631,050.00 Total Transportation Expense 2017

21

Player per diem amounts provided by http://ftw.usatoday.com/2015/04/major-league-baseball-average-salarymeal-money-2015-mlb 22 Transportation expenses estimated via https://www.forbes.com/2008/05/16/professional-sports-travel-biz-sportscx_tvr_0516teamtravel.html#2f0e91d8c97b, travel times calculated from https://www.travelmath.com and the Cardinal’s 2017 schedule extracted from https://www.mlb.com/cardinals/schedule/2017 23 Refer to Appendix C



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Again, total lodging expenses were calculated using rough estimates due to the lack of information available about its specific amount for the Cardinals organization, or any MLB franchise for that matter. To overcome this, a list of every single hotel the Cardinals stay at while on the road was found on fromthisseat.com and used to obtain average rates for single suites for the respective resorts for the dates in which the players stayed there during the 2017 season24. To roughly account for Marriott’s partnership with the St. Louis Cardinals, I subtracted 25% off of the average single room suite price, seeing as it remains the average group rate discount provided, according to grouptravel.org25. Compiling the individual hotels with their respective rates, the duration of the stay, and assuming a 25-man travel roster, I found the total lodging expenses for 2017 to amount to approximately $932,500. All relevant figures are condensed into Table 3c26. Baseball uniform components and their respective prices were found on sportsstudio.net, which totaled out to $567 per player and are summarized in Table 4c2728. This amount was multiplied by the 40-man roster to get a total amount of $22,680 in uniform expenses and is shown in Equation 9. Note that this accounts for the standard Cardinal uniform, and does not include amounts for specialty jerseys that are occasionally implemented at various points throughout the season.

24

Information regarding the Cardinal’s lodging choices were provided by http://www.fromthisseat.com and each hotel’s specific rates from their respective websites were used in the calculations. The Cardinal’s 2017 schedule extracted from https://www.mlb.com/cardinals/schedule/2017-11 25 Group travel rate estimates given from http://grouptravel.org 26 Refer to Appendix C 27 Uniform costs broken down via http://sportsstudio.net 28 Refer to Appendix C



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EQUATION 9: $567 Uniform Cost per Player x 40-man Roster = $22,680 Total Uniform Expense 2017

Finally, player development remains the fifth and last marginal cost component calculated and embodies the club’s cumulative investment in the players starting from the day they were drafted. These costs include those incurred in their times in the minor leagues, athletic performance training in and out of season, and a variety of other costs that contribute to individual player performance. While precise amounts cannot be obtained on a per-player basis, USA Today generated a rough estimate of $4.25 million in regards to the average amount an MLB franchise spends on each player29. By dividing this total amount by the average career duration of an MLB player, which is 5.6 years according to a recent study published by Science Daily, the average amount the Cardinals likely spend on player development per player per year is revealed in Equation 1030. Multiplying this per-player expense by the 40-man roster leads to $758,928 in the teams’ total investment in player development for the 2017 season, approximately, and is shown in Equation 11. A summary of total marginal costs incurred by the Cardinals organization for the 2017 season is found in Table 5c31.

EQUATION 10: $4.25 million Total Expense / 5.6 year career length = $758,928 per player per year

29

Player development costs estimated via http://ftw.usatoday.com/2015/04/major-league-baseball-average-salarymeal-money-2015-mlb 30 Average player career lengths estimated via https://www.sciencedaily.com/releases/2007/07/070709131254.htm 31 Refer to Appendix C



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EQUATION 11: $758,928 x 40-man roster = $30,357,120 Total Player Development Expense 2017

For allocation purposes and simplicity, homogeneous marginal cost figures will be given to every single player for the Cardinals organization, regardless of position. Unfortunately, this fails to produce exact marginal cost amounts individually. For example, each player spends a unique amount of time in the minor leagues and certain players stipulate nonmonetary benefits in their contracts; they are able to get room upgrades or family ticket packages free of charge, to illustrate a few. However, deducting these MC values from their output-driven MRP values will produce estimates for the true net MRP values for each player; these represent the salaries the hitters should be receiving according to my models and methodology. However, these amounts remain approximately accurate on a team level and give a robust foundation. These results are shown in Table 1d32, along with actual salaries for the 2017 season and arbitration status. Additionally, Table 2d33 breaks down net MRP values, average net MRP values, and actual 2017 salaries on the aggregate level by arbitration status category for position players. However, it should be noted that hitters who are also pitchers will refrain from having their marginal costs deducted in this step; their offensive contributions will be calculated and carried over to the pitching models to avoid double deducting marginal costs. Looking at the aggregate difference between calculated net MRP values for hitters and real 2017 salaries, only a 1% discrepancy exists, in favor of the players. While there are clearly larger amounts of deviations for specific individual players, the general picture suggests that the Cardinals organization can financially afford their position players given their budget constraints. 32 33



Refer to Appendix D Refer to Appendix D

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The results suggest that production is nearly equivalent to amounts being paid for it, although the franchise is slightly overpaying for production by a little over $400,000. However, analyzing these values according to arbitration status allows for a micro analysis of offensive spending versus production and offers a different depiction of the whole picture. Any player in a nonnegotiable arbitration standing, for example, experiences great disparity, and receives just over half of what their net MRP values suggest they should be. This salary discrepancy significantly drops from 44% to 15% for players in their last 3 years of negotiable arbitration, at the same time average net MRP is shown to be at its height. Free agents seem to account for these disparities, receiving over double the value of their output. This, in turn, skews the data to make it seem as if pay and production are near equal on the aggregate level. Although free agents have a relatively high average net MRP value, it is not as high as their 2017 salaries suggest. Issues of pay equality regarding the figures shown in Table 11 will be discussed further in the proceeding sections.

Measuring Pitchers’ MRP Using the pitching budget constraints previously calculated above, a base salary has been awarded to each pitcher. The $97,646,515.08 allocated to pitchers has been divided by the aggregate amount of innings pitched for the 2017 season, 1229.1. It is estimated that the maximum amount the Cardinals can afford to spend on each inning pitched, then, is $79,445.54, shown in Equation 12. Multiplying this figure by individual players’ cumulative innings pitched for the 2017 season will produce base salaries for each pitcher.



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EQUATION 12: $97,646,515.08 / 1229.1 Aggregate Innings Pitched= $79,445.54 per Inning Pitched

As was done for position players, OLS regression analysis has been conducted in order to explain runs allowed by pitchers. 20 observations, the total number of pitchers on the Cardinals, were taken from the Cardinal’s 40-man roster and the results are shown in Table 3b34 and Equation 13.

EQUATION 13: Y= -0.164 + 0.269BB – 0.05SO + 0.456H (0.8) (0.087) (0.028) (0.037) Equation 13 is the regression that shows how pitching performance directly impacts runs allowed and negatively effects St. Louis’ chances of winning. Interestingly enough, strikeouts (SO) simply do not have the significant impact that previous studies have found when looking at the Cardinals organization; a pitcher would have to generate 20 cumulative strikeouts before he would save the team from an additional allowed run, all other variables constant (Howard and Miller, 1993). However, allowing a mere 2 hits is predicted to contribute an additional run to the opponent’s score, holding all other statistics in the model constant. This reveals the detrimental impact hits have on the organization’s performance and discredits pitchers who are known for their ability to strikeout the opponent. Moreover, the adjusted r-squared value of 0.993 indicates that this model explains 99.3% of the variability in runs allowed and shows the robust foundation

34



Refer to Appendix B

34

in this testing method. Therefore, assuming the St. Louis Cardinals are an accurate representation of the league as a whole, similar conclusions can be made for the aggregate MLB. Pitchers’ statistics as they deviate from team averages have been extracted and implemented into this model to derive predicted y values. Average values have been calculated separately for starting and relief pitchers. On these premises, each pitchers’ contribution to runs allowed, on a monetary basis, is found by multiplying these predicted y values by the value for price per run scored that was previously calculated for hitters, $127,618.29. This value has either been added to or subtracted from each player’s base salary, in addition to any calculated offensive contribution, to arrive at predicted compensation for pitchers. Again, marginal costs must be factored in to arrive at a true net MRP value for pitchers. Using the same figures as position players (refer to Table 935), seeing as every man on the 40man roster is given the same marginal cost value in my model, pitcher MRP values have been derived. These represent the salaries they ought to be receiving according to my models and methodology in order for pay to equate to output and are shown in Table 3d36, alongside actual 2017 salaries and arbitration status. Additionally, Tables 4d, 5d, and 6d summarize net MRP values, average net MRP values, and actual 2017 salaries according to arbitration status37. These values have been separately calculated for relief pitchers and starting pitchers, as well as combined to depict the aggregate picture. Similar to position players, relief pitchers only see a 4% deviation in their net MRP values compared to their 2017 salaries, in total. However, unlike the $400,000 the Cardinals are overpaying for position players, the results suggest they are underpaying their bullpen by over $1

35

Refer to Appendix C Refer to Appendix D 37 Refer to Appendix D 36



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million. Although both deviations are not significant, analyzing them on an arbitration status basis allows for a further breakdown of pay and production. Looking at rookies, specifically, it is apparent that only receive half of the value of their output. Compiling all relief pitchers in arbitration (years 1 through 6), it is apparent that this situation does not improve and players still receive salary amounts less than half of their net MRP valuation. At the same time, free agents are receiving almost triple their calculated net MRP value, alleviating the latter’s impact on aggregate relief pitching compensating differentials. Starting pitchers have drastically different outcomes than their relief counterparts and position players in this framework; there is a 36% deviation in their aggregate net MRP values compared to their 2017 salaries, causing them to be underpaid, according to their performance, by over $20 million according to these findings. This significant amount of economic rent earned demonstrates that the Cardinals can more than afford their starting pitching lineup given their seasonal performance. Further analyzing this on an arbitration status basis, it is clear that a similar structure to what is observed at both the position player and relief pitching level exists, but to a larger extent. Here, rookies fail to make even one tenth of their net MRP, and represent the biggest deviation status-wise at 92%. Matters do not get much better, even when starting pitchers enter into their negotiable years of arbitration, seeing as there is still a 62% deviation from net MRP values to salaries. However, once players establish free agency as a starting pitcher, they earn about 50% more than their net MRP value. Further issues on pay equality and exploitation regarding these figures will be discussed in the following sections.



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Evaluating the Team’s Financial Stability Shifting focus to the whole picture, the results show that the Cardinals can, in fact, afford their 2017 payroll based on this year’s performance and this year’s revenue according to my methodology and calculations. While their players are contributing $137.2 million to team wins, and therefore, to team financial success, the organization is only compensating labor efforts for $116 million worth of production, shown in Tables 7d and 8d38. The over $20 million in economic rent earned by the owners shows that players are producing output in the form of onthe-field performance beyond their compensation; although on a league-wide basis, salary increases have been accompanied by decreased attendance rates and ticket prices, they are sustainable and justifiable for the Cardinals organization. In fact, this suggests that the club can afford to allocate more resources towards labor relations and the payroll given 2017 figures if the goal is to break even at minimal. While the summarized picture looks optimal for St. Louis, breaking these values down by arbitration standing, shown in Table 9d39, reveals otherwise. Areas of significant deviation exist, that if addressed, could help to maximize the organization’s and players’ financial position, production abilities, and total utility. While rookies receive only about a third of their net MRP values, free agents are earning over double their calculated value to the organization. At the same time, players in their negotiable years of arbitration are still only earning two thirds of the value they contribute to the team, in spite of the fact that their average net MRP value is the greatest during these years. This suggests that if payroll resources were reallocated, smaller deviations would be observed, players’ pay would be more closely tied to their performance, and the team would theoretically be operating in a more productive fashion. Extending this to a 38 39



Refer to Appendix D Refer to Appendix D

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league-wide analysis, teams could potentially increase efficiency and could directly impact regular season winning records by compensating according to on-the-field output.

Addressing Issue #2 Calculating the Lerner Index After fulfilling the first objective of producing net MRP values for professional baseball players given the financial constraints of the Cardinals organization and validating its capabilities, it is necessary to focus on the second issue at hand: pay equity. To measure this crucial labor market characteristic, the Lerner Index has been calculated on a per-player, perposition, aggregate-team, and arbitration-status level. This will indicate the degree to which there are still lasting effects from the Reserve Clause (suggested via Howard and Miller (1993) and the vast spread of player salaries), the degree to which players exert monopoly power over owners (suggested via the exponentially increasing player salaries), or some combination of the two. The variable P in the Lerner Index equation (Equation 14) represents the net MRP value derived from my methodology and regression analyses, or the salaries my models predict the players should earn. The variable MC embodies what player salaries actually were for the 2017 season and is shown in Equation 15.

EQUATION 14: Original Lerner Index Equation: (P – MC) / P EQUATION 15: Lerner Index Equation in the Context of the Model: (Net MRP – Salary) / Net MRP



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A value close to 0 indicates pay equity either for that particular player, that position, on a team basis, or on an arbitration-status basis. I have identified any instance where the Lerner Index is less than or equal to 0.25 as a nearly perfectly competitive outcome for the purpose of this study. On the other hand, a value closer to 1 suggests that either monopoly power is exerted on the owner via the player(s) or that monopsony power is exerted on the player(s) via the owner, depending on if relative over or under compensation is observed. For this study, I have identified any index value greater than or equal to 0.75 as a nearly uncompetitive outcome. However, two exceptions occur: players that have a calculated negative net MRP will produce an index value greater than 1 and players that are being paid more than their calculated net MRP will produce an index value less than 0. Largely, these negative net MRP values are due to rookies’ limited time in the major leagues. It is possible that these players failed to be brought up until late in the season, were sent back down to the minors at some point, or simply did not get significant playing time. Either scenario fails to result in performance statistics that would produce contributions greater than their marginal cost to the club. Unfortunately, these results tend to skew the data due to the small number of observations. For example, rookie hitter Breyvic Valera, given his limited major league appearances, has an index value of 4.79 because of the net negative value of his calculated MRP, which will bias the data upwards. Results are presented in Table 1e and Table 2e40.

Evaluating Pay Equity On the team level, the St. Louis Cardinals have a Lerner Index value of 0.32; while it does not quite meet this study’s standards for a nearly perfectly competitive market, it does fall

40



Refer to Appendix E

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more towards competitive and pay equitable than not. However, this value deviates significantly when broken down by position. Although relief and starting pitchers’ calculated indexes, 0.10 and 0.36, respectively, fall in the bottom half in terms of value at both the separated and combined level, the hitters’ value remains higher at 0.50. This implies that pay equity differs by position, leading hitters to enter a less competitive market than pitchers, generally speaking, even though owners earn economic rent from pitchers and are overpaying hitters relative to output. In the Cardinal’s instance, hitters tend to be either significantly over or undercompensated compared to their 2017 season production, with only three observations of near perfect competition seen with Stephen Piscotty, Matt Carpenter, and Aledmys Diaz. Free agents Yadier Molina and Dexter Fowler, exert the most market power in terms of position players, earning over double their calculated net MRP value and producing a negative index value of -1.35. On the other hand, Paul DeJong, who represents the hitter owners are able to extract the most surplus from, is only receiving about 8% of his calculated net MRP value, producing an index value of .92. This causes a bigger disparity between the value of their added contribution relative to their compensation, a less than optimal outcome. Not only is pay equity an issue at the position level, but it is increased in magnitude at the arbitration-status level. Looking at Table 22, rookies have a calculated index of 0.93, indicating nearly perfectly imperfect competition and the existence of market power. Even the aggregated index for all players in nonnegotiable arbitration is 0.77, further revealing the uncompetitive nature of the market. Given that the majority of St. Louis Cardinals’ rookies and nonnegotiable arbitration players are receiving salaries less than the value of their output, this 0.77 index shows that owners still exert monopsony power over players to some extent, and suggests the existence



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of a monopsony market during the first stage of a player’s career; as a result, owners are able to extract rents from these players and perpetuate pay inequality within the league. These rents help offset the high costs of the free agents they employ, who have an aggregate Lerner Index equal to -1.38. This negative value is evidence that these players are receiving substantially more in the form of salaries than they contribute in output to the team, forcing club owners to take a loss on their behalf. Unfortunately for rookies, this cost is passed on to them in the form of compensation less than the value of their contribution, seeing as owners’ elasticity of demand for free agents is relatively inelastic compared to that for rookies. Either way, this value is an indication of the market power that players obtain once they establish free agency and demonstrates how the labor market structure completely changes for players throughout the duration of their career. While this study supports the definition of a monopsony and monopoly market during the first and last stages of a player’s career, respectively, the second stage of bilateral monopoly fails to show as strong of evidence. It is hypothesized that this stage is the most near perfectly competitive given the negotiation power allotted to both parties and the eligibility of final offer arbitration to establish fair market value contracts. While this value is expected to be near zero, its value stands at 0.39. Although a low value, it fails to meet the standards previously set for this study to suggest it is nearly perfectly competitive. At the same time, it remains the most competitive market relative to the other two stages of a player’s career.

Comparative Analysis Using Scully’s 1974 Index Values These same calculations were done by Gerald W. Scully in 1974, the year before the Reserve Clause was abolished, where he calculated exploitation on a league-wide basis and



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categorized hitters and pitchers based on the criteria of mediocre, average, and superstar, seeing as the arbitration system observed today was nonexistent then. Through this methodology, he showed how this oppressive labor regulation was largely exploiting players (Scully, 1974). It was for these reasons that the Reserve Clause was struck down by the courts in 1975 and player exploitation was deemed solved. Since then, a similar replication of Scully’s work has yet to be done, resulting in no current or concrete proof that the objective of removing the Reserve Clause was successful. Although this study focuses on a single team and categorizes hitters and pitchers based on their arbitrations standings, it provides objective grounds to compare outcomes. Tables 3e, 4e, and 5e shows a direct comparison between Scully’s index values from 1974 and this study’s values from the 2017 season on a total position basis and by isolating both hitters and pitchers, respectively41. His mediocre players have been compared to rookies and players in nonnegotiable arbitration, his average players have been compared to players in negotiable arbitration, and his superstars have been compared to free agents. The most notable observation, looking at hitters and pitchers combined in Table 3e, is the fact that the reverse outcome prevails in the present day; while mediocre players were receiving salaries greater than their output during the Reserve Clause, demonstrated with an index level of 1.75, these same types of players are now the most significantly undercompensated relative to production, demonstrated with a current index of 0.77. On the other hand, superstars were inherently receiving salaries less than their calculated output under these same market characteristics and are now experiencing the opposite effect. Their index value has gone from 0.85 in 1974 to -1.38 in 2017. Now, the index values for superstars under the Reserve Clause are comparable to those for present day rookies and the extreme values of today’s free agents can be

41



Refer to Appendix E

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compared to those of mediocre players before the arbitration system existed, although to a lesser degree in 1974. However, it should be noted that market power has become significantly less concentrated for players in their negotiable years of arbitration; their index value has gone from 0.8 in 1974, to 0.39 today, representative of the improved market conditions during the final 3 years of arbitrations status. Examining these comparisons by position yields similar conclusions that can be translated to the entire league, using the St. Louis Cardinals as a representative sample of it. By these accounts, it is apparent that pay inequity still persists in the MLB and that owners still exert monopsony power over players to some degree. Although it is primarily concentrated in today’s rookies and nonnegotiable arbitration-status players verses average players and superstars, pay discrimination is clearly observed. Alternatively, the results indicate that today’s free agents, the superstars of Scully’s era, have obtained market power, an issue that did not exist during the Reserve Clause’s rule. This reveals an even more inefficient structure than what prevailed during the Reserve Clause; not only are a large group of players continuing to receive pay less than the value of their output, but an equally large group of players are receiving pay well above the value of their output. These extremities characterize a market of inefficiencies, failing to operate at maximum productive capacity, and resulting in decreased total utility and output. As a result, baseball would greatly benefit from eliminating market discrimination and adopting a more objective pay structure. However, this model fails to account for past discrepancies in player pay and performance, seeing as it is static in nature, compared to the dynamic professional baseball market. It is possible that the pay discrepancies rookies experience is due to their performance being the least tested, and theoretically, a player could have been over or underpaid in previous



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seasons, netting out the 2017 effects to suggest pay equity in regards to salaries reflecting on-thefield performance. At the same time, the tendency for rookies to experience monopsony control from owners could be offset by the monopoly power they are observed to have as free agents, leading to a perfectly competitive outcome in the long run. However, the 5.6 average career length in the MLB suggests a majority of players never make it to free agency, which does not allow players to reap their returns on investing their time in the arbitration process. Furthermore, this model fails to account for long term contracts (LTCs) and their place in the professional baseball labor market; LTCs are tied to expected future performance and computed using team-specific forecasting models by imputing past production. These models could not be accessed for the purpose of this study and the ability to predict expected future performance is limited in this study. An additional complication that lies within LTCs is the payout structure, which typically awards recipients’ larger sums of money towards the end of the contract, causing pay and performance to be relatively unrelated when looking at a single year. As a result, player contracts do not reflect current MRP valuations. Nevertheless, this study reveals the various inefficiencies that exists in the league and the lack of pay equity that plagues the MLB today.

POLICY SUGGESTIONS AND AREAS FOR FURTHER RESEARCH: Comparing this study to Scully’s 1974 model highlights the imperative nature of testing policy effectiveness; while exploitation issues were thought of as being addressed upon the end of the Reserve Clause, they have only increased in magnitude. Although superstars are no longer exploited, their rookie and arbitration-status counterparts are and to a larger degree. While the



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source of the exploitation differs, the outcome is parallel; pay discrimination continues to persist in the MLB and will only perpetuate unless addressed in its entirety. A possible remedy, although a radical one, could involve a complete overthrow of the arbitration system. Instead of a player being bound to a team for 6 years, unless released or traded, they would be able to enter the market as a free agent after simply completing one year in the majors with their original draft team. This way, teams are able to reap at least a fraction of their investment in that player guaranteed, at minimum, and that player has at least a season’s worth of statistics to either prove his worth to that organization or increase his value to other teams. The ease of information availability in today’s technology-driven markets would allow each player to be offered what he is expected to contribute based on the previous year’s standings. This way, resource allocation is at its optimal level, players will earn according to output, and their talents will be distributed to teams where they will be the most productive. Another proposal would be to eliminate LTCs, allowing for year-to-year contract renewals. Similar to if the arbitration system were restructured, as suggested above, each player would sign a contract based on his performance from the previous season, possible with the perfect information availability that exists. This eliminates forecasting needs and ties players to what they have proved they can produce, not what a model predicts they can produce in theory. Although this sets up a delayed compensation structure of sorts, it abandons the income variability over the many stages of a player’s career that the arbitration system creates. It also alleviates pay discrepancies, allowing players that end up contributing more than their contract was previously worth to receive increased compensation in the future and vice versa. Furthermore, it ensures that pay is tied to performance and pay equity is observed in the league.



45

There are many ways in which further research could enrich the conclusions made from this study. Compiling data from multiple seasons on expected versus actual performance on an individual player basis through his time from rookie to free agent status would allow for comparisons to indicate whether or not pay discrepancies continue or even out over time. Extending this to a league-wide analysis would also verify if this issue is apparent across all franchises or simply an issue for the Cardinals organization.

CONCLUSION: Although this study has validated general financial stability in MLB franchises, it has shed light on the underlying issue of exploitation that has lingered within the league. While the Reserve Clause of the pre-1975 era proved to exploit professional baseball players, especially superstar-status players, its removal has not remained effective. Although superstar-caliber players are no longer experiencing pay discrimination with the implementation of free agency, players in the arbitration-status years that precede free agent standing are. In fact, comparing exploitation with that during the Reserve Clause that Scully calculated, today’s levels show to be greater in value (Scully 1974). Moreover, the labor market of the MLB, as it stands today, shows that this monopsony power that owners are exerting over rookies and arbitration-status players is being matched with free agents exerting monopoly power over owners. While these two effects cancel each other out when combined at the aggregate and suggest a competitive labor market, a micro-level analysis shows otherwise; pay equity does not exist in the MLB. The inefficiencies that lie beneath the surface create less than optimal conditions to maximize productivity, profits, and labor relations.



46

Unless the pay discrimination that the current arbitration and free agent system perpetuate is reconstructed, exploitation will continue to plague the MLB.



47



48

APPENDIX A: Variable Tables Table 1a: Variables to Derive Hitters’ MRP Variable Rscore BB SO 2B 3B HR GDP

Defined Notes Runs Scored Base-on-Balls (Walks) Strikeouts Doubles Triples Home Runs Grounded Double Plays Results in 2 Outs

Expected Sign na + + + + -

Table 2a: Variables to Derive Pitchers’ MRP Variable Rallow BB SO H



Defined Notes Runs Allowed Base-on-Balls (Walks) Both Intentional and Unintentional Strikeouts Hits

49

Expected Sign na + +



50

APPENDIX B: Output Tables Table 1b: Output for Evaluating Hitters’ versus Pitchers’ Contributions

Constant WPApitch WPAhit

Unstandardized B Coefficients Standard Error 0.500*** 0.004 1.008*** 0.013 0.991*** 0.013 r-squared 0.910 adjusted r-squared 0.885

Table 2b: Output Table for Hitters’ MRP

Constant BB SO 2B 3B HR GDP

Unstandardized B Coefficients Standard Error 3.085 2.001 0.022 0.124 -0.170 0.149 2.476*** 0.435 2.998** 1.363 1.254** 0.620 -2.44*** 0.640 r-squared adjusted r-squared

0.882 0.859

Table 3b: Output Table for Pitchers’ MRP

Constant BB SO H

Unstandardized B Coefficients Standard Error -0.164 0.8 0.269*** 0.087 -0.05* 0.028 0.456*** 0.037 r-squared adjusted r-squared



0.994 0.993

51



52

APPENDIX C: Revenue and Expense Tables Table 1c: St. Louis Cardinal’s 2017 Revenue and Expenses Source

Amount

2017 Reported Revenue City/State Taxes Bonds Payable Other Nonplayer Expenses Amount Left for Player Compensation

Notes

$310,000,000.00 $31,151,556.00 from construction of Busch $15,900,000.00 Stadium $69,205,358.52 coaches, trainers, equipment, etc. $193,743,085.48

Table 2c: St. Louis Cardinal’s 2017 Transportation Expense Place of Origin Destination Hours in Air Place of Origin Destination Hrs in Air STL DC NYC STL MKE STL ATL Miami STL LA Colorado STL CHI Cincinnati STL Baltimore Philly STL AZ STL



DC NYC STL MKE STL ATL Miami STL LA Colorado STL CHI Cincinnati STL Baltimore Philly STL AZ STL Pittsburgh

1.5h 45m 2h 1h 1h 1h 1h 30m 2h 15m 3h 1h 45m 2h 45m 45m 1h 1.5h 30m 2h 2h30m 2h 30m 1h 30m

Pittsburgh NYC CHI STL MKE Cincinnati KC STL Boston Pittsburgh STL MKE SF SD STL CHI Cincinnati Pittsburgh TOTAL

53

NYC CHI STL MKE Cincinnati KC STL Boston Pittsburgh STL MKE SF SD STL CHI Cincinnati Pittsburgh STL

1h 1h 45m 45m 1h 45m 1h 30m 45m 2h 15m 1h 15m 1h 30m 1h 4h 1h 15m 3h 30m 45m 45m 45m 1h 30m 55h 30m

Table 3c: St. Louis Cardinal’s 2017 Lodging Expense Hotel (via fromthisseat. City com) Washingt Ritz-Carlton on DC Pentagon City New York Westin at (Yankees/ New York Mets) Times Square The Pfister MKE Hotel Ritz-Carlton ATL Buckhead JW Marriott Miami Marquis Langham LA Huntington Westin Colorado Downtown Ritz-Carlton CHI Chicago Westin Cincinnati Cincinnati Renaissance Baltimore Baltimore Hotel Four Seasons Philly Philadelphia The Camby AZ Hotel The Westin Pittsburgh Pittsburgh Intercontinent KC al at the Plaza Sheraton Boston Boston Hotel Westin St. Francis on SF Union Square Omni San SD Diego

Avg. Suite Rate

X 25Man Travel Roster=Cost per Night

$529

$13,225

$484

$12,100

7

$259

$6,475

10

$539

$13,475

3

$309

$7,725

4

$499

$12,475

3

$241

$6,025

3

$619

$15,475

9

$269

$6,725

10

$289

$7,225

3

$775

$19,375

3

$339

$8,475

3

$351

$8,775

10

$392

$9,800

2

$619

$15,475

2

$404

$10,100

4

$350

$8,750

4

TOTAL



# Ni X# 25% MINUS 25% ght Nights Disco Discount = s Stayed unt TOTAL $39,67 $9,91 3 5 9 $29,756.25 $84,70 0 $64,75 0 $40,42 5 $30,90 0 $37,42 5 $18,07 5 $139,2 75 $67,25 0

$21,1 75 $16,1 88 $10,1 06 $7,72 5 $9,35 6 $4,51 9 $34,8 19 $16,8 13

$21,67 5 $58,12 5 $25,42 5 $87,75 0 $19,60 0 $30,95 0

$5,41 9 $14,5 31 $6,35 6 $21,9 38 $4,90 0 $7,73 8

$40,40 0 $35,00 0

$10,1 00 $8,75 0

$63,525.00 $48,562.50 $30,318.75 $23,175.00 $28,068.75 $13,556.25 $104,456.25 $50,437.50 $16,256.25 $43,593.75 $19,068.75 $65,812.50 $14,700.00 $23,212.50 $30,300.00 $26,250.00 $631,050.00

54

Table 4c: St. Louis Cardinal’s 2017 Uniform Expense Item Helmet Gloves Cap Jersey Shorts Pants Belt Cleats Socks Gloves

Cost $55.00 $60.00 $20.00 $65.00 $70.00 $30.00 $7.00 $100.00 $10.00 $150.00

TOTAL

$567.00

Table 5c: St. Louis Cardinal’s 2017 Total Per Player Expense Source Player Compensation Budget Pere Diem Allowance Transportation Expenses Lodging Expenses Player Development Costs Uniform Costs Total Player Expense Amount Left for Player Salaries



Total Amount $193,743,085.48 $203,512.50 $631,050.00 $932,500.00 $30,357,120.00 $22,680.00 $32,346,862.40 $161,596,222.98

55

Amount Per Player (assuming 40man roster) $5,087.81 $15,776.25 $23,312.50 $758,928.00 $567.00 $808,671.56



56

APPENDIX D: MRP Results Tables Table 1d: Hitter MRP Valuations for the 2017 St. Louis Cardinals Individually Strictly Position Players Name

Status

net MRP

2017 Salaries

MRP

MC $808,6 71.56

$(748,14 $535,00 2.87) 0

Alberto Rosario

Rookie

0.475

$60,618. 69

Magneuris Sierra

Rookie

0.793

$101,20 1.30

$808,6 71.56

$(707,56 $535,00 0.26) 0

$808,6 71.56

$1,170,4 $535,00 70.50 0

Luke Voit

Rookie

15.509

$1,979,2 32.06

Stephen Piscotty

Arbitration nonnegotiable

16.499

$2,105,5 74.17

$808,6 71.56

$1,296,8 $1,333,3 12.61 33

30.147

$3,847,3 08.59

$808,6 71.56

$3,038,5 $535,00 47.03 0

3.107

$396,51 0.03

$808,6 71.56

$(412,25 $535,00 1.53) 0

49.383

$6,302,1 74.02

$808,6 71.56

$5,493,4 $14,200, 12.46 000

7.865

$1,003,7 17.85

$808,6 $194,956 $535,00 71.56 .29 0 $808,6 71.56

$9,863,5 $10,000, 73.18 000

Tommy Pham Rookie Breyvic Valera

Rookie

Yadier Molina

Free Agent

Harrison Bader

Rookie

Matt Carpenter

Arbitration negotiable

83.627

$10,672, 334.74

Paul DeJong

Rookie

61.671

$7,870,3 47.56

$808,6 71.56

$7,061,5 $535,00 86.00 0

25.141

$3,208,4 51.43

$808,6 71.56

$2,399,6 $2,500,0 89.87 00

66.927

$8,541,1 09.29

$808,6 71.56

$7,732,3 $16,500, 47.73 000

Arbitration Aledmys Diaz nonnegotiable Dexter Fowler



Predicted Runs Contributed

Free Agent

57

Greg Garcia

Arbitration nonnegotiable

9.167

$1,169,8 76.86

$808,6 $361,115 $547,90 71.56 .30 0

Randal Grichuk

Arbitration nonnegotiable

57.569

$7,346,8 57.34

$808,6 71.56

$6,538,0 $557,20 95.78 0

Jedd Gyorko

Arbitration negotiable

40.061

$5,112,5 16.32

$808,6 71.56

$4,303,7 $6,000,0 54.76 00

Carson Kelly

Rookie

$(765,07 -5.995 1.65)

$808,6 71.56

$(1,573, $535,00 833.21) 0

Jose Martinez

Rookie

24.371

$3,110,1 85.35

$808,6 71.56

$2,301,4 $535,00 23.79 0

Alex Mejia

Rookie

$(351,07 -2.751 7.92)

$808,6 71.56

$(1,159, $535,00 839.48) 0

Kolten Wong

Arbitration negotiable

64.889

$8,281,0 23.22

$808,6 71.56

$7,472,2 $2,500,0 61.66 00

3.085

$393,70 2.42

$808,6 71.56

$(415,05 $535,00 9.14) 0

Edmundo Sosa

Rookie

$54,211, $54,623, 360.47 433.00

TOTAL Pitchers Name

Predicted Runs Contributed

MRP

Carlos Martinez

Arbitration negotiable

4.865

$620,86 2.98

Lance Lynn

Free Agent

4.769

$608,61 1.63

Michael Wacha

Arbitration negotiable

Adam Wainwright

Free Agent

Luke Weaver

Status

Rookie

$(703,55 -5.513 9.63) 3.137

$400,33 8.58

1.577

$201,25 4.04

58

MC

net MRP

Table 2d: Hitter MRP Valuations for the 2017 St. Louis Cardinals by Arbitration Status



% Deviatio n

Net MRP

Avg. Net MRP

Real 2017 Salaries

Rookies

$8,750,29 7.13

$795,481. 56

$5,885,000. 00

33%

67%

Other Nonnegotiable Arbitration

$10,595,7 13.56

$2,648,92 8.39

$4,938,433. 00

53%

47%

ALL Nonnegotiable Arbitration

$19,346,0 10.69

$1,289,73 4.05

$10,823,433 .00

44%

56%

Negotiable Arbitration

$21,639,5 89.59

$7,213,19 6.53

$18,500,000 .00

15%

85%

ALL Arbitration

$40,985,6 00.28

$2,276,97 7.79

$29,323,433 .00

28%

72%

Free Agents

$13,225,7 60.19

$6,612,88 0.10

$30,700,000 .00

-132%

232%

59

Salary as % of Net MRP

Table 3d: Pitcher MRP Valuations for the 2017 St. Louis Cardinals Individually Relief Pitche rs Predicte d Runs +/- Avg.

Value of Runs Allowed

-9.30975

$(1,188, 094.38)

17.81525

$2,273,5 51.74

$4,29 0,059 .16

5.23625

$668,24 1.27

Rookie

$564, 063.3 3

10.60975

$(1,353, 998.15)

Ryan Sherrif f Rookie

$1,12 0,182 .11

-8.27375

$(1,055, 881.83)

Sam Tuivai lala

$3,34 4,657 .23

Name Sandy Alcant ara

Status

Rookie

Seunghwan Free Oh Agent Arbitratio nTyler nonnegoti Lyons able Josh Lucas

Rookie Arbitratio nnonnegoti able

Juan Nicasi o Matthe w Bowm an Rookie Arbitratio John nBrebbi nonnegoti a able



Base Salar y $643, 508.8 7 $4,69 5,231 .41

$5,72 8,023 .43 $4,62 3,730 .43 $4,06 7,611 .65

2.69125 13.48575

11.72625

2.75325

$343,45 2.72 $(1,721, 028.35) $1,496,4 83.97 $351,36 5.06

60

Value of Runs Scored

MRP

MC

net MRP

2017 Salar ies

$-

$1,83 1,603 .25

$80 3,67 1.56

$1,02 2,931 $535, .69 000

$-

$2,42 1,679 .67

$80 3,67 1.56

$1,61 $2,75 3,008 0,000 .11

$-

$3,62 1,817 .89

$80 3,67 1.56

$2,81 3,146 $549, .33 800

$-

$1,91 8,061 .49

$80 3,67 1.56

$1,10 9,389 $535, .93 000

$-

$2,17 6,063 .94

$80 3,67 1.56

$1,36 7,392 $535, .38 000

$-

$3,00 1,204 .51

$80 3,67 1.56

$2,19 2,532 $536, .95 500

$-

$7,44 9,051 .79

$80 3,67 1.56

$6,64 $3,65 0,380 0,000 .23

$-

$3,12 7,246 .45

$80 3,67 1.56

$2,31 8,574 $546, .89 600

$-

$3,71 6,246 .59

$80 3,67 1.56

$2,90 7,575 $535, .03 000

Brett Cecil

Free Agent

$5,33 0,795 .73

Zach Duke

Free Agent

$1,43 7,964 .27

Rookie

$15,8 89.11

Mike Mayer s

Rowan Wick Rookie

$-

17.02825

$2,173,1 16.15

-7.58575

$(968,08 0.44)

-9.95375

$(1,270, 280.55)

0

0

$-

$3,15 7,679 .59

$80 3,67 1.56

$2,34 $7,75 9,008 0,000 .03

$-

$2,40 6,044 .72

$80 3,67 1.56

$1,59 $5,50 7,373 0,000 .16

$-

$1,28 6,169 .66

$80 3,67 1.56

$477, 498.1 $535, 0 000

$-

$80 3,67 1.56

$(808 ,671. $535, 56) 000

$-

TOTA L Relief

$25,6 00,13 9.27

$24,4 92,90 0.00

2017 Salar ies

Starti ng Pitche rs Name

Predicte d Runs +/- Avg.

Value of Runs Allowed

Value of Runs Scored

MRP

MC

net MRP

$16,2 86,33 5.70

35.77074 492

$4,565,0 01.30

$620,86 2.98

$12,3 42,19 7.38

$80 3,67 1.56

$11,5 $4,50 33,52 0,000 5.82

$608,61 1.63

$11,8 09,17 1.88

$80 3,67 1.56

$11,0 $8,50 00,50 0,000 0.32

$-

$7,00 0,555 .89

$80 3,67 1.56

$6,19 1,884 $536, .33 600

$-

$7,02 6,602 .64

$80 3,67 1.56

$6,21 7,931 $535, .08 000

Carlos Martin ez

Status Arbitratio nnegotiabl e

Lance Lynn

Free Agent

$14,7 84,81 4.99

28.08574 492

$3,584,2 54.74

Rookie

$1,35 8,518 .73

44.21025 508

$(5,642, 037.15)

Jack Flahert y Rookie

$1,67 6,300 .89

41.92425 508

$(5,350, 301.74)

John Gant



Base Salar y

61

Luke Weave r Rookie

$4,77 4,676 .95

26.22525 508

$(3,346, 822.21)

$201,25 4.04

$8,32 2,753 .21

$80 3,67 1.56

$7,51 4,081 $535, .65 000

Adam Wain wright

$9,77 9,745 .97

17.04274 492

$2,174,9 65.96

$400,33 8.58

$8,00 5,118 .59

$80 3,67 1.56

$7,19 $19,5 6,447 00,00 .03 0

$13,1 24,40 3.21

30.31274 492

$3,868,4 60.67

$(703,5 59.63)

$8,55 2,382 .90

$80 3,67 1.56

$7,74 $2,77 3,711 5,000 .34

Free Agent Arbitratio Micha n el negotiabl Wacha e TOTA L Starti ng

TOTA L All



62

$57,3 98,08 1.56

$36,8 81,60 0.00

$82,9 98,22 0.83

$61,3 74,50 0.00

Table 4d: Relief Pitcher MRP Valuations for the 2017 St. Louis Cardinals by Arbitration Status

Net MRP

Avg. Net MRP

$7,679,648. 38

$1,097,092. 63

$3,758,100.00

51%

49%

$5,720,721. 36

$2,860,360. 68

$1,084,800.00

81%

19%

ALL Nonnegotiable Arbitration

$13,400,369 .74

$1,488,929. 97

$4,842,900.00

64%

36%

Negotiable Arbitration

$6,640,380. 23

$6,640,380. 23

45%

55%

ALL Arbitration

$20,040,749 .97

$2,004,075. 00

$8,492,900.00

58%

42%

Free Agents

$5,559,389. 30

$1,853,129. 77

$16,000,000.00

-188%

288%

Rookies Other Nonnegotiable Arbitration



Real 2017 Salaries

$3,650,000.00

63

% Deviation

Salary as % of Net MRP

Table 5d: Starting Pitcher MRP Valuations for the 2017 St. Louis Cardinals by Arbitration Status

Rookies Other Nonnegotiable Arbitration



Net MRP

Avg. Net MRP

Real 2017 Salaries

% Deviati on

$19,923,8 97.05

$6,641,29 $1,606,600.0 9.02 0

92%

NA

NA

NA

NA

Salary as % of Net MRP 8% NA

ALL Nonnegotiable Arbitration

$19,923,8 97.05

$6,641,29 $1,606,600.0 9.02 0

92%

8%

Negotiable Arbitration

$19,277,2 37.17

$9,638,61 $7,275,000.0 8.59 0

62%

38%

ALL Arbitration

$39,201,1 34.22

$7,840,22 $8,881,600.0 6.84 0

77%

23%

Free Agents

$18,196,9 47.35

$9,098,47 $28,000,000. 3.68 00

-54%

154%

64

Table 6d: Combined Starting and Relief Pitcher MRP Valuations for the 2017 St. Louis Cardinals by Arbitration Status

% Deviatio n

Net MRP

Avg. Net MRP

Real 2017 Salaries

Salary as % of Net MRP

Rookies

$27,603,5 45.43

$2,760,35 4.54

$5,364,700. 00

81%

19%

Other Nonnegotiable Arbitration

$11,850,9 80.30

$5,925,49 0.15

$4,734,800. 00

60%

40%

ALL Nonnegotiable Arbitration

$33,324,2 66.79

$2,777,02 2.23

$6,449,500. 00

81%

19%

Negotiable Arbitration

$19,166,0 35.03

$6,388,67 8.34

$7,275,000. 00

62%

38%

ALL Arbitration

$59,241,8 84.19

$3,949,45 8.95

$17,374,500 .00

71%

29%

Free Agents

$23,756,3 36.65

$4,751,26 7.33

$44,000,000 .00

-85%

185%

Table 7d: Summary of MRP Valuations for the 2017 St. Louis Cardinals by Position



% Deviatio n

Net MRP

Real 2017 Salaries

Hitters

$54,211,36 0.47

$54,623,433. 00

-1%

101%

$(412,072.53)

Starting Pitchers

$57,398,08 1.56

$36,881,600. 00

36%

64%

$20,516,481.56

Relief Pitchers

$25,600,13 9.27

$24,492,900. 00

4%

96%

$1,107,239.27

TOTAL

$137,209,5 $115,997,933 81.30 .00

15%

85%

$21,211,648.30

65

Salary as % of Net MRP

Net Gain/Loss to Club

Table 8d: Deviation of MRP Valuation and 2017 Payroll for the St. Louis Cardinals

Total Player net MRP Cardinals 2017 Payroll Difference

$137,209,581.30 $115,997,933.00 $21,211,648.30

Table 9d: Summary of MRP Valuations for the 2017 St. Louis Cardinals by Arbitration Status



% Deviati on

Net MRP

Avg. Net MRP

Real 2017 Salaries

Rookies

$36,353,84 2.56

$1,731,13 5.36

$11,249,700 .00

69%

31%

Other Nonnegotiable Arbitration

$16,316,43 4.92

$2,719,40 5.82

$6,023,233. 00

63%

37%

ALL Nonnegotiable Arbitration

$52,670,27 7.48

$1,950,75 1.02

$17,272,933 .00

67%

33%

Negotiable Arbitration

$47,557,20 6.99

$7,926,20 1.17

$29,425,000 .00

38%

62%

ALL Arbitration

$100,227,4 84.47

$2,947,86 7.19

$46,697,933 .00

53%

47%

Free Agents

$36,982,09 6.84

$5,283,15 6.69

$74,700,000 .00

-102%

202%

66

Salary as % of Net MRP

APPENDIX E: Lerner Index Results Tables Table 1e: Lerner Index Values for the 2017 St. Louis Cardinals Individually Position Players Name Alberto Rosario Magneuris Sierra Luke Voit Stephen Piscotty Tommy Pham Breyvic Valera Yadier Molina Harrison Bader Matt Carpenter Paul DeJong Aledmys Diaz Dexter Fowler Greg Garcia Randal Grichuk Jedd Gyorko Carson Kelly Jose Martinez

Rookie Rookie

Alex Mejia

Rookie Arbitration negotiable Rookie

Kolten Wong Edmundo Sosa TOTAL Position Players



Status Rookie Rookie Rookie Arbitration nonnegotiable Rookie Rookie Free Agent Rookie Arbitration negotiable Rookie Arbitration nonnegotiable Free Agent Arbitration nonnegotiable Arbitration nonnegotiable Arbitration negotiable

net MRP Real Salaries $(748,142.87) $535,000 $(707,560.26) $535,000 $1,170,470.50 $535,000 $1,296,812.61 $3,038,547.03 $(412,251.53) $5,493,412.46 $194,956.29

Lerner Index 1.72 1.76 0.54

$1,333,333 $535,000 $535,000 $14,200,000 $535,000

-0.03 0.82 2.30 -1.58 -1.74

$9,863,573.18 $10,000,000 $7,061,586.00 $535,000

-0.01 0.92

$2,399,689.87 $2,500,000 $7,732,347.73 $16,500,000

-0.04 -1.13

$361,115.30 $547,900

-0.52

$6,538,095.78 $557,200

0.91

$4,303,754.76 $6,000,000

-0.39

$(1,573,833.2 1) $535,000 $2,301,423.79 $535,000

1.34 0.77

$(1,159,839.4 8) $535,000

1.46

$7,472,261.66 $2,500,000 $(415,059.14) $535,000

0.67 2.29

$56,875,581.8 6

67

$54,623,433.0 0

-0.01

Relief Pitchers Name Sandy Alcantara Seung-hwan Oh Tyler Lyons Josh Lucas Ryan Sherriff Sam Tuivailala Juan Nicasio Matthew Bowman John Brebbia Brett Cecil Zach Duke Mike Mayers Rowan Wick

Status Rookie Free Agent Arbitration nonnegotiable Rookie Rookie Rookie Arbitration nonnegotiable Rookie Arbitration nonnegotiable Free Agent Free Agent Rookie Rookie

TOTAL Relief

net MRP Real Salaries $1,022,931.69 $535,000 $1,613,008.11 $2,750,000 $2,813,146.33 $1,109,389.93 $1,367,392.38 $2,192,532.95

$549,800 $535,000 $535,000 $536,500

$6,640,380.23 $3,650,000 $2,318,574.89 $546,600 $2,907,575.03 $2,349,008.03 $1,597,373.16 $477,498.10 $(808,671.56)

$535,000 $7,750,000 $5,500,000 $535,000 $535,000

$22,958,850.0 9

$24,492,900.0 0

net MRP

Real Salaries

Lerner Index 0.48 -0.70 0.80 0.52 0.61 0.76 0.45 0.76 0.82 -2.30 -2.44 -0.12 1.66 0.04

Starting Pitchers Name Carlos Martinez Lance Lynn John Gant Jack Flaherty Luke Weaver Adam Wainwright Michael Wacha TOTAL Starters



Status Arbitration negotiable Free Agent Rookie Rookie Rookie Free Agent Arbitration negotiable

$11,533,525.8 2 $4,500,000 $11,000,500.3 2 $6,191,884.33 $6,217,931.08 $7,514,081.65 $7,196,447.03

$8,500,000 $536,600 $535,000 $535,000 $19,500,000

Lerner Index 0.61 0.23 0.91 0.91 0.93 -1.71

$7,743,711.34 $2,775,000

0.64

$58,581,905.3 0

0.36

68

$36,881,600.0 0

TOTAL Pitching

$81,540,755.3 9

$36,881,600.0 0

0.55

TOTAL All

$135,752,115. 86

$115,997,933. 00

0.15

x1

indication of net MRP < salary perfectly competitive near perfectly competitive strong monopoly or monopsony power exerted indication of negative net MRP value

Table 2e: Lerner Index Values for the 2017 St. Louis Cardinals by Arbitration Status Avg. Lerner Index Rookies 1 Other Nonnegotiable Arbitration 0.17 ALL Nonnegotiable Arbitration 0.8 Negotiable Arbitration 0.312 ALL Arbitration 0.73 Free Agents -1.18 Table 3e: Comparing Scully’s 1974 Lerner Index Values to the St. Louis Cardinal’s 2017 Values – Combined Hitters and Pitchers Scully's Index 2017 Cardinals Index Nonnegotiable Arbitration/Mediocre Players 1.75 0.77 Negotiable Arbitration/Average Players 0.8 0.39 Free Agents/Superstars 0.85 -1.38



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Table 4e: Comparing Scully’s 1974 Lerner Index Values to the St. Louis Cardinal’s 2017 Values – Hitters Scully's Index 2017 Cardinals Index Nonnegotiable Arbitration/Mediocre Players 1.47 0.83 Negotiable Arbitration/Average Players 0.79 0.09 Free Agents/Superstars 0.85 -1.36 Table 5e: Comparing Scully’s 1974 Lerner Index Values to the St. Louis Cardinal’s 2017 Values –Pitchers Scully's Index 2017 Cardinals Index Nonnegotiable Arbitration/Mediocre Players 2.02 0.75 Negotiable Arbitration/Average Players 0.8 0.57 Free Agents/Superstars 0.85 -1.38



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