## Monopsony Depressed Wages in Modern Moneyball

**ABSTRACT**

** **

From 2012 to 2016, baseball continues to value on-base percentage over slugging percentage, but in a way that only benefited teams as monopsony power is exploited to sign players with high on-base percentage under arbitration eligible status. This approach allowed teams to sign players below their marginal revenue of product while maximizing profits, which in turn created market inefficiency in the free agent labour market. Furthermore, 2016 witnessed a new era of baseball where teams invested more in homegrown talent via arbitration eligible players which further weakens the free agent labour market. Free agent data from 2012-2016 were collected with a revised version of Hakes & Sauer (2006)’s model confirming that both on-base and slugging percentage decreased in significance for 2016 free agent salaries as a result of teams enforcing monopsony power as shown by Brown, Link and Rubin (2015).

## 1 Introduction

Baseball has always been considered a sport with an enormous amount of data and statistics, but since the introduction of Moneyball in 2004, baseball executives have changed the way players’ productivities are being measured in the free agent labour market. As the market adjusted towards the market inefficiency during the post-Moneyball era, the central question now, is how will the market continue to behave? The goal of this literature is to determine the behaviour of the current free agent labour market between 2012-2016, and if on-base percentage continues to be heavily valued, given the higher contribution to winning. Previous literature by Hakes & Sauer (2006) will explain the mechanism behind the Moneyball model where on-base percentage contributes more to winning than slugging percentage, followed by additional literature during the post-Moneyball era by Brown, Link and Rubin (2015) where teams are enforcing monopsony power for arbitration eligible players, and pre-Moneyball era by Congdon-Hohman & Lanning (2017) where baseball’s transition from the ‘power’ era to the ‘getting on-base’ era. Free agent data will then be collected and computed into our revised version of Hakes & Sauer (2006)’s model with a focus on salary, on-base percentage and slugging percentage data between 2012 to 2016, along with criteria to filter the original free agent data pool from baseball-reference.com. The results show how the market continues to be inefficient once again, as teams are exploiting monopsony depressed-wages for players with less experience under arbitration eligible status. The remainder of the literature is as follows: In Section 2 we discuss the literature on Moneyball. In Section 3 we will discuss the data, the average of the data, and the comparison in salary data along with presenting the model. In Section 4 we analyze the results and tests for the significance of the estimates via t Test and F test along with the fixed effects method. The last section offers the final conclusion.

## 2 Literature Review

## 2.1 Moneyball

The sport of baseball has always provided the public with access to a wide array of statistic. These statistics were not always used in the most efficient manner to optimize Major League Baseball’s labour market, with decisions made by baseball executives in the past, and more specifically baseball’s free agency market at the beginning of the 2000s. “Michael Lewis (2003), cited in Hakes & Sauer (2006) made a striking claim: the valuation of skills in the market for baseball players was grossly inefficient.” In order to fully understand this claim, we will breakdown “Hakes & Sauer’s (2006)’s paper on An Economic Evaluation of the Moneyball Hypothesis” into two sections: Measuring offensive productivities in baseball, and the labour market’s valuation of skills.

The objective of a baseball game is to score the most runs in a 9-inning game with the home and away team taking turns between the top and the bottom of each inning. Also, each team is given 3 outs per inning. The most important skills for a position player that contributes to scoring a run is the ability to hit the ball, and the ability to avoid making an out. The ability to hit the ball is measured by batting average that accounts for total number of hits based on total number of at-bats, but this statistic ignores the additional productivity of any extra base hits, which is measured by slugging percentage that accounts for total number of bases, based on total number of at-bats. It is important to point out here that measurements of batting average and slugging percentage ignores sacrifices and walks, as these two statistics are important variables to determine the ability to avoid making an out. As a result, the ability to avoid making an out is measured by on-base percentage that accounts for total number of times a player reaches on base safely, based on total number of at-bats, which also include walks. Hakes & Sauer (2006) experimented with these measurements by setting winning percentage as the dependent variable, and setting slugging percentage and on-base percentage as independent variables. Based on the data for all 30 teams from 1999-2003 prior to the Moneyball era, there is a strong linear correlation between on-base percentage at of 82.5% and slugging percentage at of 78.7% on runs scored, which determines winning percentage. Furthermore, the coefficient for on-base percentage is twice the value of significance than the coefficient for slugging percentage. As a result, “Hakes & Sauer (2006) confirms Lewis’s claim that a one-point change in a team’s on-base percentage makes a significantly larger contribution to team winning percentage than a one-point change in team slugging percentage.” Rationally, on-base percentage not only showcases a player’s ability to hit, but also the ability to avoid an out. In comparison to slugging percentage, this statistic only measures a player’s ability to hit, but not the ability to avoid an out. Now that Hakes & Sauer (2006) determined on-base percentage creates more contribution to team’s winning percentage than slugging percentage, we now evaluate baseball’s labour market’s valuation of skills.

Baseball players are eligible to become free agents and enter the labour market after 6 years of service with their respective teams. Hakes & Sauer (2006) found that the average free agent salaries from 2000-2003 is between $2.56 million to $3.46 million, while power hitters who raked in at least 25 home runs or more during the previous season were compensated at least twice the amount of salary in comparison to the average free agent salaries. Based on this data, it is safe to point out that prior to the Moneyball era between 1999-2003, baseball executives across the league valued baseball players with power hitting skills and compensated these players generously. Also, since slugging percentage is a measurement of a player’s ability to hit for power, and on-base percentage contributes heavily to a team’s winning percentage as discussed above, then “Hakes & Sauer (2006) confirmed that an efficient labour market for baseball players would, all other factors held constant, reward on-base percentage and slugging percentage in the same proportions that those statistics contribute to winning.” In order to test the efficiency of baseball’s free agent labour market, data from 1999-2004 were gathered to determine the significance of how on-base percentage and slugging percentage affects the way baseball executives compensated free agent players. As a result, free agent players with high slugging percentage were compensated significantly more than free agent players with high on-base percentage during 1999-2003, meanwhile in 2004, free agent players with high slugging percentage were compensated significantly less than free agent players with high on-base percentage. This result showed how the valuation of skills in baseball were inefficient prior to the Moneyball era from 1999-2003 despite previously confirmed in the offensive productivity measurement, that on-base percentage contributes more to a team’s winning percentage than slugging percentage contributes. Consequentially in 2004, the free agent labour market adjusted itself by aligning the compensation in a player’s on-base percentage with the value of on-base percentage’s contribution to a team’s winning percentage, which is significantly higher than the compensation in a player’s slugging percentage and the value of slugging percentage’s contribution to a team’s winning percentage. One can surmise that Hakes & Sauer (2006)’s experiment confirmed Michael Lewis (2003)’s claim on the inefficiency of baseball’s valuation of skills during 1999-2003. In other words, on-base percentage’s contribution to winning was mispriced in baseball’s free agent labour market during 1999-2003.

The Oakland Athletics are an infamously prime example of how one team exploited the market inefficiency by maximizing their profits while winning games at a discounted rate. The ability to acquire players who contribute more to winning at a lower compensation was not the only factor to the team’s winning formula. The team also invested in coaches and player development personnel who also believed in the on-base percentage approach of winning games in an era where Major League Baseball favored slugging percentage heavily, due to contributions from baseball insiders who ignored quantitative analysis. Unfortunately, as shown from the result in 2004, the market adjusted itself while other teams also added this strategy as part of their baseball decision making process.

## 2.2 Modern Moneyball

The Moneyball approach was adopted league wide after the 2003 season when teams across baseball observed the success of the Oakland Athletics. Brown, Link and Rubin (2015) further contributed to Hakes & Sauer (2006)’s analysis in two ways. First, by examining when free agent baseball players’ contracts were signed and how long their contracts were signed for, and second, to examine whether or not Major League teams continued to value on-base percentage over slugging percentage 8 years after the league adjusted to the free agent labour market’s inefficiency starting at the beginning of the 2004 season. In order to determine when a player’s contract was signed and the length of the contract, data was collected in the range between 1996 to 2011 to fully interpret the results. Since 1996 makes a reasonable starting point, and 2011 makes a reasonable end point for contracts signed between 1999-2003 during the Moneyball era, this period can also determine if teams continued to value on-base percentage over slugging percentage after the Moneyball era. Also, Brown, Link and Rubin (2015) measured the data by separating baseball players into three groups: Reserve Clause players, Arbitration Eligible players, and Free Agent players. Reserve Clause players are players who are under team control for the first 6 years but only have less than 3 years of experience and salary is compensated at the league minimum. Arbitration Eligible players are players who are also under team control for the first 6 years but have at least 3 years of experience and salary is compensated based on performance in a manner of an arbitration process if necessary. Free Agent players are players who are no longer under team control after 6 years of experience and are eligible to sign with any team across the league. Essentially, Brown, Link and Rubin (2015)’s approach to measuring data between 1996-2011, and separating baseball players into three categories were able to extend Hakes & Sauer (2006)’s analysis to determine when the contracts were signed and the length of said contract, and if teams continued to value on-base percentage over slugging percentage simultaneously.

Brown, Link and Rubin (2015)’s approach to separate baseball players into three categories can determine when the contracts were signed based on a player’s experience measured in number of years. In order to determine the length of the contracts, the results are separated into pre-Moneyball era and post-Moneyball era. In the pre-Moneyball era between 1996-2003, players with more experience have longer contracts, played more and performed better. In the post-Moneyball era between 2004-2011, players with more experience continued to have longer contracts, played more and performed better, however, the length of contracts were lower for all three categories in comparison to the pre-Moneyball era. Also, performance was better off for Reserve Clause and Arbitration Eligible players, but worse for Free Agent players in comparison to the pre-Moneyball era. This can be explained as a result of cheaper players who were once overlooked that were now valued with higher on-base percentage in the post-Moneyball era, and teams were signing these players with no prior MLB experience, which gave them 6 full years of team control. As a result, salaries also increased significantly for Reserve Clause and Arbitration Eligible players, but did not change for Free Agent players in comparison to the pre-Moneyball era. Another interesting point in this analysis is that salaries are lower for Reserve Clause players and Arbitration Eligible players since monopsony power is greatest when these players are under team control, whereas salaries are higher for Free Agent players when monopsony power is lowest, and players are eligible to sign with any team across the league.

In order to extend Hakes & Sauer (2006)’s original model, Brown, Link and Rubin (2015)’s regression model added Major League service time as an additional variable to determine the specific category each player falls under. Furthermore, the model is then performed for all three categories separately to derive three sets of results which can better determine whether on-base percentage continues to be valued over slugging percentage in the post-Moneyball era between 2004-2011. Based on the results, on-base percentage was not a significant factor of wage during the pre-Moneyball era or the post-Moneyball era for both Reserve Clause players and Arbitration Eligible players, however, on-base percentage was a significant factor of wage for Free Agent players during the post-Moneyball era. The results for Reserve Clause players and Arbitration Eligible players can be explained by teams enforcing their monopsony power to prevent marginal revenue of product reaching the optimal wage, despite previous results above showing that Reserve Clause players and Arbitration Eligible players perform better than Free Agent players during the post-Moneyball era. For the free agent market, the results are consistent with Hakes & Sauer (2006)’s original results for on-base percentage since the market adjusted to the inefficiencies during the post-Moneyball era. It is important to distinguish that despite teams enforcing their monopsony power on Reserve Clause players and Arbitration Eligible players, with on-base percentage no longer being a significant factor of wage for both the pre-Moneyball era and post-Moneyball era, the actual wage did increase from the pre-Moneyball era to post-Moneyball era for Reserve Clause players and Arbitration Eligible players given that cheaper players who were once overlooked are now valued with higher on-base percentage, and signed with no prior MLB experience which gives the team 6 full years of team control. On the other hand, slugging percentage was less significant in the post-Moneyball era in comparison to the pre-Moneyball era. One can surmise that on-base percentage was valued in compensation for Free Agent players only, but not valued for Reserve Clause players and Arbitration Eligible players as teams enforce monopsony power to prevent marginal product of revenue from reaching optimal wage despite on-base percentage being a significant factor to winning percentage.

On-base percentage has become more important in determining salaries in the post-Moneyball era given the contribution to winning percentage. However, rewards from compensation only applies to the Free Agent market as teams exploit monopsony power for the non-Free Agent market in order to maximize profit and productivity simultaneously.

## 2.3 Moneyball In The Last Three Decades

The way Major League Baseball executives valued productivities that reflect the way players are compensated have changed over the last three decades. “Congdon-Hohman & Lanning (2017) looked to broaden Hakes & Sauer (2006)’s literature on Michael Lewis (2003)’s analysis by identifying which broad range of production indicators are rewarded in the free agency market in various time periods.” Congdon-Hohman & Lanning (2017) focused on three periods of the Free Agent market from 1988 to 1990, 1998 to 2000, and 2008 to 2010 along with one transitional period from 2002 to 2007 which specifically examines the changes in the Moneyball era. This approach allows the market to evolve over the period of a 10 year gap that will shift from one era of baseball to another. Also, aggregate statistics and single statistics were added to the analysis to further examine the consistency of the results during each decade. Single statistics are individual productivity such as Hits, and Base on Balls that add to aggregate statistics such as on-base percentage, as well as individual productivity such as Doubles, Triples, and Home Runs that add to aggregate statistics such as slugging percentage. Furthermore, a new aggregate statistic called on-base plus slugging percentage was introduced to better interpret the results in comparing different eras of baseball, as this statistic combines both on-base percentage and slugging percentage as an overall offensive productivity measurement.

Congdon-Hohman & Lanning (2017)’s analysis showed that under the aggregate statistics, on-base plus slugging percentage was increasingly more significant from the 1980s cohort to 1990s cohort, and less significant in the 2000s cohort. This can be explained since during the 1980s, baseball was undergoing a period that focused on hitting for high batting averages, which resulted in players focusing less on their slugging percentage. The 1990s was a period of baseball that focused on hitting for higher power numbers, which resulted in players focusing more on their slugging percentage. The 2000s was a period of baseball that focused on getting on-base, which resulted in players focusing less on their slugging percentage. These results are also consistent with on-base percentage and slugging percentage, as both on-base percentage and slugging percentage were less significant in 1980s as a result of baseball focusing on hitting for averages. On-base percentage was less significant and slugging percentage was more significant in 1990s as a result of baseball focusing on hitting for power. On-base percentage was more significant and slugging percentage was less significant in the 2000s as a result of baseball focusing on getting on-base. Suitably, we can see here that under the aggregate statistics analysis, baseball valued Free Agents who hit for average in the 1980s, Free Agents who hit for power in the 1990s, and Free Agents who got on-base in the 2000s.

The single statistics analysis showed that during the 1980s cohort, only Hits and Runs Batted-In were more significant. This result is consistent with baseball valuing Free Agents who hit for average in the 1980s under the aggregate statistics analysis, since the more Hits players produce, the more chances players can help drive runners home to score runs. During the 1990s cohort, Hits, Doubles and Home Runs were all more significant. This result is also consistent with baseball valuing Free Agents who hit for power in 1990s under the aggregate statistics analysis, since power is required to hit for Doubles and Home Runs. Lastly, during the 2000s cohort, Base On Balls and Runs Scored were more significant, while Hits and Home Runs were less significant. This result continues to be consistent with baseball valuing Free Agents who got on base in 2000s under the aggregate statistics analysis, since the more players got on base, the higher the chance of scoring a run. As a result, the single statistics are consistent with the same outcome as the aggregate statistics in determining the way baseball valued productivities in each of the three cohorts.

The transitional period between 2002-2007 showed that aggregate statistics of on-base percentage and slugging percentage are similar to the results in the 1990s cohort, while single statistics of Base on Balls are similar to the results in the 2000s. The results explained the Moneyball era as baseball was transitioning from hitting for power to getting on base, which is why on-base percentage and slugging percentage reflected the 1990s, and Base on Balls reflected the 2000s.

Baseball’s evolution in the way executives valued different productivities, determined that free agent salaries continue to shift towards productivity that contributes to the highest winning percentage. The shift from hitting for average in the 1980s, to hitting for power in the 1990s, and to getting on base in the 2000s were consistent in both aggregate statistics and single statistics, which further confirms the evolution of baseball over the last three decades.

## 2.4 Supporting Moneyball Inefficiency

The biggest question since Michael Lewis (2003)’s original paper is how the Free-Agent market’s inefficiency was only exploited by the Oakland Athletics, while the rest of the league remained stagnant until after Moneyball was revealed in the 2004 season. “Hakes (2012), cited in Berri & Schmidt (2010) asked a central question on how so many people paid so much to make good managerial choices can consistently and repeatedly make bad ones,” and continued that “the decision appeared predictably ill informed, even in a profession inundated by a veritable deluge of quantitative data.” This can be explained by the Principle-Agency problem where the analysts who are the agency, can misunderstand what motivates the decision-maker, by not interpreting information correctly, and the executives who are the principle, can incorrectly measure a player’s productivity, which affects the way compensation is rewarded in the free agent labour market. For example, on the Agency side, a baseball manager who values on-base percentage but was given incorrect information from the Analyst, caused a misunderstanding of the Analyst understanding what motivated the baseball manager in winning; on the Principle side, a baseball executive incorrectly valued slugging percentage in productivity measurement over on-base percentage that resulted in rewarding players with higher slugging percentage generously, despite that slugging percentage productivity contributes less to winning than on-base percentage productivity.

To further confirm this analysis, models were developed to explain the Principle-Agency problem. The reason behind the Agency problem with misunderstanding of what motivates the decision-maker is that teams across baseball have different business models in profit-maximization, winning-maximization, or winning-maximization subject to a budget or profitability constraint. This model explains why the Analyst misunderstood what motivates the baseball manager given the team’s business objective. The reason behind the Principle problem with incorrect player’s productivity measurement is a direct reflection of the Moneyball model that showed how players productivity contributing to winning, were mispriced in the free agent labour market. This model explains why Executives make incorrect decisions given the incorrect productivity measure. Furthermore, Financial and Risk Management models must also be accounted for, in an individual player’s performance, over a portfolio of players’ performances, as teams tend to invest heavily on one particular player instead of a portfolio of players in the free agent market. This approach can reduce the risk of team performance in the event if players are injured or underperform, which affects the overall winning percentage.

The Agency-Principle problem showed why Moneyball inefficiency occurred in the pre-Moneyball era from 1999-2003. Also, questions were answered on why baseball managers continued to make poor decisions despite vast amount of quantitative data available. With Analysts misunderstanding what motivates baseball managers, and executives incorrectly interpreting productivity measures that contributes to wining. By combining these models with Financial and Risk Management model of portfolio diversification, we now have a better understanding of Moneyball inefficiency.

## 2.5 Determining Free Agent Labour Market Efficiency

Bradbury (2013) analyzed two methods of determining marginal revenue of products in sports from Scully (1974)’s model based on revenue, and Krautmann (1999)’s model based on salary. Scully (1974) focused on team revenue to determine marginal revenue of product, but the results showed that marginal revenue of product were 5 to 6 times the wages in free agency, which is significantly larger, and the model must rely on unofficial team revenue data since official team revenue data is not shared to the public. Krautmann (1999) focused on free agent salaries to determine marginal revenue of product, but the results showed that salaries were significantly lower than marginal revenue of products as teams can always sign players with less than 6 years of experience with lower salaries as a form of monopsony-depressed wages, and players sometimes give teams hometown discounts or take longer contracts with lower annual salary. As a result, Scully (1974)’s model overvalues marginal revenue of product, and Krautmann (1999) model undervalues marginal revenue of product. Although both models have their flaws, both models have their own ways to determine free agent market efficiency. Scully (1974)’s model can reveal market inefficiencies since revenue is tied to performance, and if higher revenue and higher performance does not result in higher wages, as the case with the Oakland Athletics from 1999-2003, then market inefficiencies exists. Krautmann (1999)’s model can capture the way executives value free agents based on productivity, since free agent salaries reflect how much free agent players are valued to a team’s winning percentage which is the marginal revenue of product.

Krautmann (1999)’s approach has been widely adopted as Scully (1974)’s approach is limited to information not revealed by teams. However, Krautmann (1999)’s approach has also been modified and recalibrated to make up for the shortcomings of undervaluing free agents with variables such as experience, playing time, and positions played, to better determine to marginal revenue of product in the free agent labour market.

## 3 The Model

## 3.1 Data

In baseball, there are three groups of player status: Reserve Clause Players, Arbitration Eligible Players, and Free Agent Players. Reserve Clause Players are players that have less than 3 years of team service, which is also known as playing time, but these players are paid a salary of league minimum given their minimal to zero experience. Arbitration Eligible Players are players with at least 3 to 6 years of team service, and player salaries are determined by performance level via an arbitration process if necessary when players and their respective team do not agree to the salary offered at the end of the season, but the final salary level determined is still significantly lower than the player’s free agent market value. Free Agent Players are players with at least 6 years of service time, in which they can sign with any teams in the league. It is important to note here that only arbitration eligible players and free agent players shows up in the original data pool since salary for these players are yet to be determined for the following season. For the variables included in this literature, we will examine on-base percentage and slugging percentage more closely. On-base percentage is the number of times a player reaches on-base safely to the total number of times when a player is in the batter’s box. Players can also get on-base by drawing a walk, getting a hit, getting on-base via errors from the opposing team, and getting hit by pitch. Slugging percentage is the number of bases a player reaches to the total number of times when a player is in the batter’s box, in addition to single statistics like single, doubles, triples and home runs which are assigned to 1, 2, 3 and 4 bases respectively. From a contribution to winning standpoint, on-base percentage determines how effective a player is at the plate and their ability to avoid an out, while slugging percentage determines how much power a player can generate to help score runs. Also, at-bats measures the number of times a player is in the batter’s box. For the sample size, there are approximately 400 players available in the data pool each year, and 42-66 players are filtered out each year and considered for actual free agents used in the dataset, as the data pool includes arbitration eligible players and pitchers. Note that baseball has two leagues in the American League and the National League; and that in the National League, pitchers also take at bats in each game while in the American League, pitchers do not take at bats and are replaced by a Designated Hitter.

Free agent career data from each year between 2012 and 2016 were collected from baseball-reference.com. Our goal is to gather data that will fit the model and best determine the results of the free agent labour market efficiency during this period. In order to qualify, a player must have completed at least 6 years of service to be considered as free agent status, and as a result, arbitration eligible players are removed from the dataset as these players have less than 6 years of service. Since we are only considering career data for free agent players as baseball executives evaluate and compensate player performances based on their career track record, then players with less than 1000 career at-bats were not included in the dataset as data suggested that these players are still in the arbitration eligible status. Also, free agent players that were signed for a salary at league minimum, but did not make a major league appearance, as these players were only contributing for their team’s minor league affiliation teams were also removed from the dataset. On the contrary, one exception added to the dataset was for players that had less than 6 years of service, but were granted free agent status by their teams, and then signed by another team as a free agent. With these parameters in place, only relevant data were collected in the free agent labour market.

Table 1 displays career averages of free agents’ on-base and slugging percentage from 2012 to 2016. As evident by the data, both on-base and slugging percentage is decreasing during this period, which is a sign of a weak free agent pool. This can be explained by a team’s ability to enforce their monopsony power in signing arbitration eligible players into long term contract extensions that buys out their remaining arbitration eligible years, and additional free agent years at a discounted salary in exchange for long term financial security. Furthermore, career at-bats for free agents are also decreasing as a result of less experienced players entering the market given that teams have already signed their high productive players during their arbitration eligible years, which is another sign of a weak free agent pool. In addition, average salary level did not show any significant change, but with inflation in place, this result signals an indirect decrease in salary level which is yet another sign of a weak free agent pool. However, despite showing that salary did not change significantly, we can take a deeper look into how average salary has changed in each year in comparison to the 2016 average salary.

Figure 1 suggests that average salary has been increasing marginally from 2012 to 2015 which can be explained by inflation, but in 2016, average salary has decreased as a result of baseball’s transition into a new era where free agent players are no longer valued above their marginal revenue of product in favour of home grown talent; that will be discussed in more detail in the next section. However in comparison to the 2016 salary level, salaries in each year has been below the average salary in 2016 except for 2015, and despite that average salary in 2015 was higher than average salary in 2016, the total average salary from 2012-2016 was still below 2016 average salary, but only by a value of 0.1121 which is insignificant. As a result, this comparison displayed that average salary did not show any significant change, and with inflation, this result signals an indirect decrease in average salary, which is also evident in Figure 1 where the total average salary in 2012-2016 is below 2016 average salary.

By combining the analysis of average statistics in free agents during this period, the data suggests that the overall free agent market is less productive, because of teams exploiting monopsony-depressed wages for arbitration eligible players.

## 3.2 Empirical Methodology

This literature aims to determine if on-base percentage continues to be valued over slugging percentage as a measure of productivity when baseball executives compensate free agent players between 2012-2016 on the free agent labour market. More importantly, this literature tests to see if teams are still focusing on productivity such as getting on-base which contributes more to winning percentage, but is considered “boring baseball,” or if teams are reverting back to productivity such as hitting for power which contributes less to winning percentage, but is consider “exciting baseball.” The following model is a revised version of Hakes & Sauer (2006)’s original model, which will be used to run the regression:

This equation specifies productivity measurement in on-base percentage (OBP) and slugging percentage (SLG). At-bats (AB) determines how much a player contributed, which also measures player improvement with increase in experience, and At-bats squared (AB ) allows for diminishing rate of improvement with increased experience, while preventing performance decline when a player ages. It is important to note that the revised model focuses on career data where Hakes & Sauer (2006)’s model focused on data from previous seasons. The reason behind this revision is to align with baseball executives’ decision to compensate free agent players based on their career track record rather than their recent statistics, which reduces overall risk of underperformance once a player is signed. Also, arbitration eligible and free agent dummy variables were removed from the model since data collected only included free agent players with no arbitration eligible status. Lastly, only players with at least 1000 or more career at-bats will be included in the sample in order to consider their impact to the game.

It is important to note that this literature only tests for free agent players’ salary in aggregate statistics. The results can help us better understand how the market behaves from 2012-2016, whether there is any market inefficiencies, and if results reflect on teams exploiting monopsony-depressed wages for players with less experience.

## 4 Results

Since on-base percentage contributes more to a team’s winning percentage than slugging percentage contributes as a measure of productivity, then an efficient free agent labour market will also show that on-base percentage is a more significant factor in compensating a player’s value when rewarding free agent salaries, than the significance in slugging percentage.

Table 2 displays the results of the regression showing the significance in on-base percentage and slugging percentage to the dependent variable of salary between 2012 to 2016. During the 2012 free agent year, data suggests that on-base percentage is more significant in free agent salaries than slugging percentage, as this result is consistent with the post-Moneyball era analysis. However, between 2012 to 2015, slugging percentage’s significance increased in an upward trending direction, while on-base percentage’s significance decreased in a downward trending direction with the outlying exception of 2014. This result contradicts to the post-Moneyball era where slugging percentage is being valued more significantly than on-base percentage, despite that on-base percentage contributes more to winning. One indication from this analysis confirms Brown, Link and Rubin (2015)’s finding in which teams are enforcing their monopsony power to sign arbitration eligible players with high on-base percentage at a wage below their marginal revenue of product, and as a result, teams are no longer interested in compensating free agent players with high on-base percentage at a wage above or equal to their marginal revenue of product, which is why on-base percentage’s significance in salary compensation decreased in a downward trending direction. On the other hand, slugging percentage’s significance continues to increase as power hitters are compensated accordingly since teams are looking to maximize their profits given that power hitting attracts more fans and increases revenue with more tickets sold, despite less contribution to winning than on-base percentage. Based on the data from 2012 to 2015, on-base percentages are not being valued in the free agent labour market due to teams exploiting monopsony-depressed wages for players in arbitration eligible status with less experience , while slugging percentage continues to be valued as teams are trying to maximize profit by attracting fans with “exciting baseball”.

During the 2016 free agent year, Table 2 also suggests that there is a significant decrease in both on-base percentage and slugging percentage. This can be explained by baseball’s transition into a new era where free agent players are no longer valued above their marginal revenue of product since high productivity free agent players can leverage multiple contract offers to maximize their payoffs, but instead teams are focusing on developing homegrown talent which is significantly cheaper in terms of salary. The 2016 Chicago Cubs are a prime example where the team won the 2016 World Series with majority of their positional players developed from their minor league system. Furthermore, for the first time ever, the 2016 free agents witnessed players with high slugging percentage compensated below their marginal revenue of product while being punished for high strikeouts. Players such as Chris Carter and Edwin Encarnacion both hit over 40 home runs, but with their high strikeouts, they both received their contract near the end of the offseason below their marginal revenue of product. As a result, this also explains why salary did not change based on Table 1 over the last 5 years despite inflation. Essentially, baseball shifted into a new era in 2016 where the main focus was to develop homegrown talent at a lower salary, while signing free agents who produced high slugging percentage below their marginal revenue of product.

In combination of the two analysis above, teams are enforcing monopsony powers to depress wages for arbitration players, in addition to teams focusing on developing homegrown talent at a cheaper salary, as well as signing free agents with high slugging percentage at a salary below their marginal rate of product as a punishment of their high strikeouts statistics, shows why the average on-base percentage and slugging percentage were decreasing while salary did not change despite inflation as evident on Table 1. As a result, the overall free agent labour market becomes weaker while inefficiency is created. However, the inefficiency found here is different compared to the inefficiency found during the pre-Moneyball era, where the current labour market inefficiency benefits teams as talents are acquired internally, and proves to be disadvantageous to free agents, as teams no longer have an immediate need to acquire talent via the free agent labour market. It’s also important to point out that as a result of teams enforcing monopsony power where teams lock up arbitration eligible players to long term contracts which prevent these players from entering the free agent market, this approach further weakens the overall free agent labour market while creating market inefficiency.

In order to further confirm and validate the results and findings, we will test the significance of the estimates to strengthen our analysis.

Table 3 shows that at 95% Confidence Interval t-Test with a critical value of 1.67, on-base percentage is an insignificant estimate of the model from 2012 to 2016 except 2014, while slugging percentage is a significant estimate of the model from 2012 to 2016. However, with increased degrees of freedom and a critical value of 1.65, both on-base percentage and slugging percentage are significant estimates of the model between 2012-2016. As a result, we can conclude that overall, both on-base percentage and slugging percentage are significant estimates of salary. Furthermore, we will test the significance of the estimates again in F test.

Table 4 shows that at 95% Confidence Interval F-Test with a critical value of 2.53, on-base percentage is an insignificant estimate from 2012 to 2016 except 2014, while slugging percentage is a significant estimate of the model from 2012 to 2016. However, with increased degrees of freedom and a critical value of 2.37, both on-base percentage and slugging percentage are significant estimates of the model between 2012-2016. The results here are the same as the t-Test above, which confirms that both on-base percentage and slugging percentage are significant estimates of salary for both t-Test and F-Test. It is important to note here that despite both estimates showing significance between 2012-2016 as evident on Table 3 and Table 4, on-base percentage between 2012-2016 is marginally significant as a result of higher significance in 2014, while the remaining years in the dataset shows insignificance. This finding is consistent with results shown on Table 2, where despite on-base percentage having higher value to contributions in winning in comparison to slugging percentage, teams are not compensating free agent players to their marginal revenue of product level, and instead are enforcing their monopsony power on arbitration eligible players with high on-base percentage where salaries are compensated below the marginal revenue of product as shown by Brown, Link and Rubin (2015) in section 2.2 of this literature. As a result, free agent quality decreases for on-base percentage measurements, which causes on-base percentage an insignificant estimate of salary for 2012 to 2013 and 2015 to 2016 despite on-base percentage being a significant estimate of salary between 2012-2016.

Next we will use the fixed effects method to see if the estimates are significantly affecting salaries, since the fixed effects method focuses on within-person comparison to eliminate large sources of bias for non-experimental research given that the significance of the average difference between the estimates confirms the actual significance of the estimates to our dependent variable salary. Also, by using this method, we can also eliminate person-specific variables that may correlate with the dependent variable.

Table 5 shows significance of fixed effects for both on-base percentage and slugging percentage. For this method, if the significance is less than 0, then we cannot be sure that the measurements affect salaries. Based on the results, we can be certain that on-base percentage affects salary without bias, given that the fixed effects results show significance from 2012 to 2016 and between 2012-2016. However for slugging percentage, the fixed effects results show significance from 2012 to 2014 and 2016, but also shows insignificance in 2014 and between 2012-2016. This result is consistent with Hakes & Sauer (2006)’s finding on slugging percentage, in that it contributes less to winning percentage than on-base percentage, and as a result should affect salary less than on-base percentage. This was also the central finding in the post-Moneyball era where slugging percentage’s effect on salary was biased since power hitting was considered “exciting baseball” across baseball despite on-base percentage contributing more to winning but was considered “boring baseball.”

Essentially, from the free agent data, this literature was able to show that teams are still valuing on-base percentage over slugging percentage given the former’s higher contribution to winning in the past 5 years. However, this was not true in the free agent market, which signals that teams are enforcing their monopsony power in the arbitration eligible players pool who has high on-base percentage. We also confirmed that the estimates are significant for our revised version of Hakes & Sauer (2006)’s model. Lastly, we used the fixed effects method to confirm that on-base percentage estimate is not biased and affects salary more than slugging percentage, which is consistent with Hakes & Sauer (2006)’s findings.

## 5 Conclusion

This literature examined how baseball’s free agent labour market behaved in recent years between 2012 to 2016. From Hakes & Sauer (2006)’s original analysis, on-base percentage’s higher contribution to winning compared to slugging percentage continues to hold true, and based on the revised version of Hakes & Sauer (2006)’s model in this literature, the results showed that teams are exploiting this approach by signing arbitration eligible players at a wage below their marginal revenue of product, which in turn creates market inefficiency in the free agent labour market. Players in the free agent labour market were no longer being compensated accordingly, due to slugging percentage outweighing on-base percentage in productivity when baseball executives reward free agents. To make matters worse, 2016 witnessed a new era where teams are not valuing players with high slugging percentage as a result of higher strikeouts. In other words, teams are focusing more on homegrown talents by enforcing monopsony power, which only requires wages to be compensated below their marginal revenue of product, and as a result, this effect weakens the overall free agent labour market and creates market inefficiency.

## 6 Reference

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Congdon-Hohman, J., & Lanning, J. (2017). “Beyong Moneyball: Changing Compensation in MLB,” Journal of Sports Economics, doi:10.1177/1527002517704019.

Hakes, J. (2012). “Book Review on Stumbling on Wins,” Journal of Sports Economics, doi:10.1177/1527002511414508.

Bradbury, J. (2013). “What is Right With Scully Estimates of a Player’s Marginal Revenue Product,” Journal of Sports Economics, doi:10.1177/1527002511418981.

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Krautmann, A. (1999) “Whats Wrong With Scully-Estimates Of A Players Marginal Revenue Product,” Economic Inquiry, Volume 37, Number 2, 369-381.

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