THE ROCKIES AND MARKET INEFFICIENCY

IN MAJOR LEAGUE

A THESIS

Presented to

The Faculty of the Department of Economics and Business

The Colorado College

In Partial Fulfillment of the Requirements for the Degree

Bachelor of Arts

By

Andrew J. Grosenbaugh

May 2015

THE AND MARKET INEFFICIENCY

IN

Andrew J. Grosenbaugh

May 2015

Mathematical Economics

Abstract

The Colorado Rockies play their home games in an environment unlike any other team in Major League Baseball. The altitude effect present in , CO potentially plays a role in why hitters thrive for the Rockies and struggle. Player’s statistics are altered by playing in Denver, and these performance indicators’ significance diminishes, especially for Rockies players. Statistics are influential in determining player compensation in professional baseball. The statistics of Rockies players, however, are biased because they play 81 home games at high altitude each season. The results of this paper support the notion that the Rockies capitalize on their unique effect by paying players differently than the rest of the league.

Keywords: (Baseball, Market Efficiency, Altitude) JEL Codes: (Z22, L83)

ON MY HONOR, I HAVE NIETHER GIVEN NOR RECEIVED

UNAUTHORIZED AID ON THIS THESIS

Signature

LIST OF ABREVIATIONS

BA Batting Average ER ERA HBP By Pitch IBB Intentional Walk IP Inning Pitched IPouts_starter Outs Recorded as a Starter IPouts_reliever Outs Recorded as a Reliever OBP On-Base Percentage OPA Offensive Performance Average PA Plate Appearance RBI Runs Batted In SB Stolen Base SLG, SA Slugging Percentage TBB Total Walks WHIP Walks plus Hits per Inning Pitched

TABLE OF CONTENTS

ABSTRACT

1 INTRODUCTION...... 1

2 LITERATURE REVIEW...... 2

3 PERFORMANCE VARIABLES...... 7

4 DATA...... 9 Pre-Arbitration Players...... 9

5 METHODS...... 11 Determining a Difference in Denver...... 12 Regression Equations...... 14 Predicting Expected Salary...... 15 Comparing Actual vs. Expected Salary...... 15

6 RESULTS...... 15

7 CONCLUSIONS...... 18

APPENDIX A...... 22

APPENDIX B...... 24

APPENDIX C...... 25

REFERENCES...... 27

Introduction

The Colorado Rockies represent an anomaly in the Major League Baseball industry. The

29 other current teams play at an average elevation of 313 ft. above sea level. The

Rockies currently play 5197 ft. above sea level at which is over 4,000 ft. higher than the next highest . There is plenty of speculation surrounding Rockies players each year linking their success or struggles to the altitude of their home stadium.

Currently, there is no publicly available measure to analyze the effect on performance due to high elevation of Denver, Colorado. Evidence suggests that there is a significant effect on player performance in Denver as compared with player performance at any of the other in the league. Rockies players, who play half of their games in

Denver’s “thin air”, are especially subject to the altitude effect. Rockies players face a bias to their statistics which do not accurately measure their true ability. This paper attempts to understand whether or not the Colorado Rockies create a market inefficiency by the way they compensate their players when confronted with the altitude effect. The null hypothesis is that the Rockies do not pay their players any differently than the league standard despite statistically significant evidence to suggest that the altitude effect exists.

The alternative hypothesis is that the Rockies pay their players differently than the league standard suggests players should be paid. In this paper, the league standard for a player will be referred to as their market value which is determined by modelling players’ salaries across the league. The results conclude that hitters on the Rockies are underpaid compared to their market value, while pitchers receive salaries which are not significantly different than their market value. Due to the altitude effect, the Rockies are able to leverage their players into deals that may not match their market value or maintain

1 market efficiency. The market for baseball players is efficient when players receive compensation which reflects their true ability. Since the altitude affects performance statistics, the salary for Rockies players’ must be adjusted to maintain market efficiency.

The Rockies maintain efficiency in the market for hitters by adjusting their salary from their market value, but they create an inefficient market for pitchers by paying them similarly to the league standard.

The paper is organized in the following manner. In Section 2 the literature surrounding the effects of altitude on a baseball, as well as literature pertaining to firms which face unique effects within an industry will be discussed in relation to the altitude effect faced by the Rockies. Section 3 provides an explanation of the performance variables to be used in the regression models for salary. In Section 4 the criteria for data selection is introduced. Section 5 outlines a four-part approach to comparing the actual salary of Rockies players to a league-generated expected salary. In Section 6 the observations of the results are recorded. Finally, Section 7 concludes the findings of the paper.

Literature Review

The purpose of this section is to first discuss the findings of two articles which conclude that there is a significant effect on the baseball during play that is a result of playing at high altitude. These articles are Park Elevation and Long Ball Flight in Major League

Baseball by Bloch, Coe, Ebberson and Sommers (2006) and Atmosphere, Weather, and

Baseball: How Much Farther Do Really Fly at Denver’s Coors Field by

Chambers, Page, and Zaidins (2003).The second portion of this section will analyze the research regarding firms which face uncontrollable micro-economic effects that are

2 unique to the industry. The third segment will discuss the issues of compensation with respect to the labor market, as well as to the baseball industry.

Coors Field has long been perceived as a hitter’s park and offensive statistics over the last 10 years support the perception (ESPN Park Factors). Using econometric modeling, Bloch et al. (2006) conclude that the perception is actually a realistic effect which causes fly balls to carry further resulting in more home runs. The authors even go so far as to call Coors Field “a veritable power hitter’s paradise” (Bloch et al. 2006). The advantage of Coors mainly lies in its expansive which is very generous to hitters.

However, the significance of the home run figures in the model, and the significantly higher number of them hit at Coors Field imply that there is some force allowing the balls to travel farther. Even the Rockies’ website admits that altitude plays a role in aiding fly balls claiming that batted balls travel “9 percent farther at 5,280 feet than at sea level”

(Coors Field History). Much is made of the “hitter’s park”, which implies that the variation in an average hitter’s performance can sometimes be attributed to the venue in which they play. The “thin air” resulting from lower atmospheric pressure at Coors Field increases offensive numbers put up by both the home team and visitors.

The Rockies have had their fair share of pitchers struggle in Denver. In their article titled, Atmosphere, Weather and Baseball: How much Farther Do Baseballs

Really Fly at Denver’s Coors Field?, Chambers et al. (2003) argue that the Rockies hitters who have thrived during their time in Denver should attribute their success towards the struggles faced by opposing pitchers in addition to their own ability. The authors dispute the claim that objects one mile above sea level will travel approximately

10% further (a generally accepted estimate) than the same object at sea level. Using

3 atmospheric and meteorological research they conclude that the effect is really closer to

6% which can sometimes even be negated by prevailing winds from the northeast during game time (directly into the batter’s face). Regardless, they conclude that there is an effect on the baseball in Denver which is not present at other ballparks due to the high altitude. Their conclusion, however, maintains that the magnitude of the effect is greater on pitchers, who struggle, than on hitters, who thrive. The low atmospheric pressure causes pitches to behave differently at high altitude, and the dry air allows dehydrated balls to be hit farther. The effect of the low average humidity in Denver was mitigated in

2002 with the introduction of a , but the low atmospheric pressure cannot be adjusted for. Many professionals feel the effects, and prefer to remain pitching at low altitudes. was once quoted saying, “I can’t imagine having to pitch a whole year there” (Verducci, 1998).

Teams that play in Denver face a unique environment which none of their competitors must account for on a regular basis. In a 1998 Sports Illustrated article, then general manager of the Rockies said, in regards to scouting pitchers, that

"the first thing I have to do is find out how a guy has pitched here--you tell me, what other general manager has to do that?” (Verducci, 1998). While the altitude effect can be accounted for, it still creates an uncontrollable micro-economic effect on the firm. Such effects can sometimes result in significant differences in individuals’ wage earnings across different firms in an industry. While measuring performance among general laborers can be difficult at times, the sports industry provides plenty of performance indicators in the form of statistics that can be linked to a publicly known salary. As a result of the 1981 strike in Major League Baseball, the use of performance indicators was

4 necessary in classifying the degree of compensation (Bennett and Fluek, 1983). However, statistically analyzing the more qualitative aspects affecting teams has been much harder.

The effect of altitude remains extremely hard to quantify, but is still widely recognized as a legitimate effect. The effect of a player’s ability and the altitude effect together create the output of a player’s performance. The sum of performance in many industries can be divided between the “person effect” and the “firm effect” and the relationship is discussed in a study carried out by Abowd, Kramarz, and Magolis (1999) titled High

Wage Workers and High Wage Firms. The findings attribute the variation in compensation among these laborers either to person effects (“wage heterogeneity…related to permanent unmeasured differences among the individuals”) or firm effects (“wage heterogeneity…related to permanent differences among the employers”). The authors conclude that the variance in compensation among these high wage laborers can be attributed more to person effects relative to firm effects. The major difference between the findings in this article and the wage variation in professional baseball is that there should not be an abundance of heterogeneity in salaries for major league players. The paper claims that labor market outcomes are extremely heterogeneous meaning that “observably equivalent individuals earn markedly different compensation”. Since compensation in Major League Baseball is based heavily on performance statistics and the salaries of comparable players, all of which is readily available, there should not be the same sort of heterogeneity in ballplayers’ salaries as there is among the employees discussed by Abowd et al (1999).

The person effect on display in the baseball industry is the talent of an individual player. Talent in baseball is simpler to quantify than talent in other industries since the

5 sport is rooted in individual actions by players that can be readily recorded as statistics.

This measurable version of the person effect has a great impact on compensation because it is information which can be used to pay players relatively to each other.

Firm effects for a baseball team can vary from weather patterns, to ballpark dimensions, to playing surface, and certainly to altitude. The altitude effect on the

Colorado Rockies creates a discrepancy between the player’s actual ability and his observed performance through a permanent, unmeasurable difference unique to the

Rockies.

There are findings in labor market research which suggest that a unique aspect of a firm could result in varying compensation for comparable level workers across an industry. The altitude effect is certainly profound enough to raise the question of whether or not this is the case between the Rockies players and players from other teams across the league. In an article titled The Recognition and Reward of Employee Performance, author John Bishop (1987) addresses “productivity differentials” from one firm to another within an industry. Bishop acknowledges that these differentials can often be difficult to measure accurately. Such is the case with the altitude differential affecting the

Rockies. Bishop also mentions that it can be difficult to base wages and job offers off of such differentials. This sort of analysis would require a measurement which could quantify the unique firm-specific aspect in order to compare it to the industry. Despite the vast amount of data, and the increasing presence of statistical analysis in baseball, there is no publicly accepted measure to account for the altitude effect. According to Bishop’s research paper, it is in the best interest of the Rockies to refrain from making a private analysis of the altitude effect public. Bishop states that “productivity differentials

6 between workers might reflect differences in skills that are specific to the firm or known only by the firm” (Bishop, 1987). Naturally the Rockies are more cognizant towards the altitude effect than any other team who may only visit Denver briefly during the season.

It is necessary for the Rockies to build their team with the altitude effect in mind because they play 81 games in the unique environment. This is a chore not shared by any other team.

Performance Variables

The goal in choosing a performance variable with which to measure the players in the data set is to find a statistic that mirrors individual performance while excluding as much of the bias contributed by teammates as possible. There are plenty of hitters’ statistics which can effectively eliminate bias. Therefore, offensive performance can be relatively easy to compute for an individual. The pitching performance of an individual is much more difficult to quantify. A pitcher’s statistics can be heavily biased due to the defense around him. The performance variables discussed in this section have been chosen based on previous research by others, and theoretical hypotheses stemming from knowledge of the game of baseball.

The performance indicator being used for hitters is called Offensive Performance

Average (OPA). It combines On-Base Percentage (OBP) which measures a player’s ability to reach base with a weighted version of Slugging Percentage (SLG) which accounts for the total number of bases achieved per At-Bat (AB). OPA was developed by

Mark Pankin (1978) and outlined in his publication, Evaluating Offensive Performance in

Baseball. The statistic reflects the impact of a certain outcome as it pertains to the

7 probability of scoring an additional run. These probabilities are then converted into relative values for each outcome.

[1퐵+2(2퐵)+2.5(3퐵)+3.5(퐻푅)+0.8(푇퐵퐵+퐻퐵푃)+0.5(푆퐵)] 푂푃퐴 = (1) (퐴퐵+푇퐵퐵+퐻퐵푃)

G. R. Lindsey developed the modified SLG statistic which discounts triples and home runs from its predecessor to better model their relative effect on the probability of an additional run. This model makes much more sense than simply using SLG because the value of an additional base is diminished after a player reaches 2nd base since it becomes much easier to score. Hence, runners on 2nd and 3rd base are often considered to be “in scoring position”. The model was developed based on the probability of outcomes in the

Major Leagues for offensive players over the 1959 and 1960 seasons. This is not a concern because the probability of a given type of outcome was very similar in 2014 compared to the seasons used in creating the relative probabilities as seen in Table 1.

Table 1

Year H 2B 3B HR SB BB IBB HBP 2014 8.56 1.67 0.17 0.86 0.57 2.88 0.20 0.34 1960 8.67 1.39 0.27 0.86 0.37 3.39 .029 .20 Source: Baseball-Reference.com

Table 2 displays the significance of OPA in comparison to other performance indicators used in Pankin’s research.

Determining a pitcher’s level of performance presents multiple problems. There are issues of teammate bias that appear to weigh heavily on certain statistics, and some performance indicators can be more important than others depending on the situation. A pitcher faces enough situations throughout the course of season that the variation in his

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Table 2

Source: Pankin, 1978 performance is smoothed out and can be simplified into a ratio, or average. The statistic used for overall pitcher performance in this model was Walks plus Hits per Inning

Pitched (WHIP). The purpose of the statistic is to use one all-encompassing statistic that measures a pitcher’s ability to record outs and prevent runs. WHIP records the act of a batter reaching base on a walk or a hit as a failure by the pitcher to prevent baserunners.

WHIP measures the failure of a pitcher to prevent runs as well because baserunners are generally necessary in order to score. Other overall performance indicators only punish pitchers for one of these two failures, both of which WHIP successfully accounts for.

In addition to WHIP, (IP) was included in the equation. IP is not an indicator of a player’s performance in the traditional sense as an indicator of success the way WHIP is. However, it does help to further explain the performance value of a pitcher. The standard IP statistic is broken down into outs recorded by pitchers in order to avoid issues arising from the decimal measures used for recording IP (for example 21 1/3

IP is often indicated as 21.1 IP in stat sheets). The number of outs recorded by a pitcher while they were a starter and a reliever were separated creating two variables for the model: Outs Recorded while a Starter (IPouts_starter) and Outs Recorded while a

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Reliever (IPouts_reliever). The ability of a pitcher to pitch more innings demonstrates value since it reduces the number of additional pitchers which a team must use in a given game and in an entire season. The durability of a pitcher is very valuable and is measured through the accumulation of outs recorded.

Data

The data was retrieved from Baseball Reference and the Lahman Baseball Database which Baseball Reference heavily relies upon for data. Player data was consolidated for pitchers and hitters for the years spanning 1993-2014. The 1994 season was shortened by a strike, but the data is included in this model because the performance measures are averages which remain relevant even in a shortened season. Hitters were required to have at least 106 Plate Appearances (PA) in a given season to qualify for the data set. Daryl

Kile had the most PAs of any pitcher in baseball for a single season within the data set recording 105 PAs in 1997 (Fangraphs). Setting the limit at 106 PAs automatically excluded all pitchers from the offensive data set. No players who are considered hitters pitched more than 10 innings in any year of the data set. Therefore, pitchers had to throw more than 10 innings in order to qualify, thus, excluding all hitters from the pitching data.

This kept compensation consistent as it assumes hitters are paid primarily on their ability to hit and pitchers are paid primarily to pitch.

Pre-Arbitration Players

Pre-arbitration eligible players must be removed from the data for all parts of the model following part 1, Determining a Difference in Denver. These players are not afforded the right, under MLB’s Collective Bargaining Agreement, to negotiate their salary regardless of their performance or any other factors. The team he is under contract with is free to set

10 his salary so long as it exceeds the minimum salary for the given year (see Appendix B).

Arbitration eligibility is attained, generally, once a player has reached 3 full years of service time in the major leagues. Players who do not reach this criterion present a real bias to any MLB salary model since they tend to put excessive significance upon age. By removing pre-arbitration eligible players the model will only represent those who are able to negotiate their salary which removes some of the age/experience bias that would otherwise exist.

Simply using the minimum salary as a cutoff would not be a sufficient means of removing pre-arbitration eligible players from the data set. Every team has their own elevating pay scale often based on the years of service accumulated for such players.

Instead, the salary level of pre-arbitration players was estimated using a percentile cutoff.

Based on the USA Today MLB salary database, on average 40% of a team’s roster is made up of pre-arbitration eligible players. After cutting out non-qualifying hitters who reach less than 106 PAs and pitchers who recorded 10 innings or less, almost all of whom were pre-arbitration players, the percentile cutoff for pre-arbitration players fell to 25%.

The cutoffs are not exact methods for determining arbitration eligibility. However, with each year containing 250-300 observations it is likely that the few players who were wrongly included or excluded will not have a significant effect on the results. In order to test the 25th percentile cutoff theory, the regressions were also run using a 20th percentile and 30th percentile cutoff. There were no significant differences between the regressions formed by the different cutoffs.

Methods

First, it needs to be determined whether there is, or is not, an effect on performance as a

11 result of the high elevation of Denver, Colorado. Second, a linear quantile regression will be performed for each individual year from 1993-2014 for players on all MLB teams excluding those who played for the Colorado Rockies for the given year. These models regress the player performance indicators as well as other player attributes and explanatory variables against his salary for that year. The quantile regression fits the data by minimizing the absolute deviations from the median as opposed to a linear regression which attempts to minimize deviations from the mean. The median salary in professional baseball is much less than the mean salary due to the skewed distribution of players’ salaries. The quantile model serves as a more robust method than its linear counterpart.

The use of the median to create the model is more effective at accounting for outliers and skewed tails that arise in salary distributions where there is a minimum salary, but no salary ceiling.

The model is used to approximate the market value of a player equal to the predicted compensation from the model. Market value in this paper refers to the league standard for compensation which is determine by the quantile regression equations. The market value compensation is predicted for all players. The predicted market value salary for Rockies’ players will then be compared to their actual salary using a non-parametric sign test in order to understand the effect, if any, that playing for the Rockies has on a player’s compensation.

Determining a Difference in Denver

It is necessary to first assess whether the high altitude and resulting low atmospheric pressure in Denver, where the Colorado Rockies play their home games, has a distinct effect on hitters’ and pitchers’ performance. Only players in the data set who had played

12 in Denver and at least one other ballpark in the Majors were included for this test. The exclusion of players who played in only one of the two possible “sites” (Denver or

Elsewhere) maintains consistency when comparing the two sub groups. A two group t- test was used to determine any significant difference between the normal distribution of players’ statistics when they played in Denver as compared to their statistics from other ballparks. When using OPA to account for hitters’ performance there is a significant difference in a player’s performance between the two locations with players performing much better at high elevation in Denver as seen in the higher mean OPA (Table 3).

Table 3

Pitchers were analyzed in a similar fashion as described for the hitters in order to determine any statistical significance with respect to playing in Denver. The two group t- test for WHIP is shown in Table 4. The test reports a significant difference, above the

99% level of confidence, for pitchers who have a higher WHIP when they pitch at high altitude. The higher mean WHIP reported for Denver suggests that pitchers perform worse at high altitude than at lower altitudes elsewhere.

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Table 4

Regression Equations

The purpose of the regression equations is to predict the dependent variable for salary using performance and explanatory variables. Rockies players were excluded from the dataset used to generate the two equations for the model. In doing so, the model does not include players who were heavily affected by playing many games at high altitude. The market values generated by the equations will, therefore, not contain any significant bias due to the altitude effect as a result of excluding the team most likely to create inefficiencies. A quantile regression model will be used for hitters and pitchers separately for each year spanning 1993-2014. The variables for each model will contain performance statistics as well as relevant descriptive statistics. The model for hitters is show in equation 2, followed by the model for pitchers in equation 3:

푆푎푙푎푟푦 = 훼 + 훽(푂푃퐴) + 훽(퐴𝑔푒) + 훽(퐻푒𝑖𝑔ℎ푡) + 훽(푊푒𝑖𝑔ℎ푡) (2) +훽(퐵푎푡푠푙푒푓푡푦) + 훽(퐵푎푡푠푠푤𝑖푡푐ℎ) + 훽(푇ℎ푟표푤푠푙푒푓푡푦)

푆푎푙푎푟푦 = 훼 + 훽(푊퐻퐼푃) + 훽(퐴𝑔푒) + 훽(퐻푒𝑖𝑔ℎ푡) + 훽(푊푒𝑖𝑔ℎ푡) (3) +훽(퐼푃표푢푡푠푟푒푙𝑖푒푣푒푟) + 훽(푇ℎ푟표푤푠푙푒푓푡푦)

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Predicting Expected Salary

The equations above create the model for determining market value compensation. The data for each player was fit to the corresponding equation and the output was reported as an expected salary equivalent to their market value. All players in the data set were paired with their predicted salary reflective of a league standard which excluded Rockies players. The significant results of these equations are included in Appendix C.

Comparing Actual vs. Expected Salary

A non-parametric sign test was used to measure the difference between players’ real salary and their expected salary throughout the time series. The test does not make assumptions about the data as parametric tests do. This is important for this model because the mean of salary distribution is not centered around the median of the distribution as is the case with normal distributions of data. The test simply pairs each player with his actual and expected salary and records a positive or negative result based on the difference. The results from non-Rockies players were run through a sign test to serve as the baseline for league compensation trends. The results from Rockies players were then run through a sign test, and were compared to the league standard results. The null hypothesis for this test states that there is an even distribution between positive and negative differences. A significant P-value results in the acceptance of the alternative hypothesis which states that the distribution of positive and negative differences is significantly altered from an even distribution.

Results

The sign test rejects the null hypothesis and accepts the alternative hypothesis for

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Rockies’ hitters suggesting that they are systematically underpaid. The test does not reject the null hypothesis for Rockies’ pitchers indicating that they are not paid any differently from their market value. The sign test accepts the null hypothesis for both non-Rockies pitchers and hitters are paid closely in accordance with an even distribution of differences (see Appendix A).

Out of a total of 180 Rockies hitters who had enough Plate Appearances and met the salary cutoff for arbitration eligible players, only 75 hitters reported a positive difference between their actual salary and their expected salary. 105 hitters reported a negative difference implying that they were underpaid compared to comparable players

Table 5

16 on all other teams. The sign test reported a probability value for the null hypothesis of

0.0304 which states that the results are statistically significant at any level greater than

96.96% confidence (Table 5). It is safe in this case to accept the assertion that hitters are paid significantly less on the Rockies than a player with comparable statistics on another team.

A sign test for pitchers reported a probability value for the null hypothesis of

0.3006 which means these results are statistically significant at any level greater than

69.94% (Table 6). The level of significance is too low to confidently reject the null hypothesis that there is no significant difference between the compensation received by

Rockies pitchers and the market value set by pitchers of all the other MLB teams.

Table 6

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Conclusions

The model tests the validity of the hypothesis that there is a difference between league standard salaries and Rockies’ salaries against the null hypothesis that there is no difference in compensation for players on the Rockies. The alternative hypothesis supports the hypothesis for market efficiency. It implies the salaries of Rockies players will be adjusted accordingly to remove the bias of the altitude effect on performance output. An “efficient market”, as defined by Aswath Damodaran of the Stern School of

Business at New York University, “is one where the market price is an unbiased estimate of the true value of the investment” (Damodaran). As reported in the results, the hitter’s salaries are adjusted so that they are no longer biased. The pitchers salaries are unadjusted from market value, and remain biased estimates of value due to the altitude effect.

The Rockies are paying their hitters significantly less than their market value because the high elevation of their home games creates a discrepancy between the player’s ability and his statistics. The discrepancy between his ability and his biased performance indicators would affect the efficient market for baseball players’ services if his salary was not adjusted. The Rockies paying their hitters based on the league-standard compensation would create an inefficient market since the player would be paid for performance which had been inflated by playing many games at high altitude. The player would be receiving compensation in part due to his ability, but also in part due to an effect which had no relation to the player. In order to pay only for the player’s personal service contribution, the Rockies adjust their pay scale downwards from the league average.

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Pitchers face opposite results than hitters when competing at high altitude. Instead of succeeding beyond their ability level, they struggle at a level below their true ability.

Because hitters receive less than market value for their overstated performance indicators it is fair to hypothesize that the market would adjust causing Rockies pitchers to be compensated at a rate greater than the league standard salary. However, teams systematically avoid paying players more than their approximate market value. A player has very little basis to demand a salary upwards of the standard rate established by the league as a whole, especially when playing in Denver which is considered a small market. Therefore, the Rockies can pay their pitchers along the same lines that pitchers are paid throughout the league. The conclusion of the sign test for Rockies pitchers suggests that the players do not receive a salary from the team which is any different from the league’s market value. Without a definitive means to quantify the altitude effect on players, pitchers resolve to accept a salary congruent with market value. By not adjusting the player’s salary to fit his actual ability, the Rockies create inefficiency in the market because they are able to buy the services of a player at a rate which is lower than their services are worth independent of any altitude effect.

The Rockies are able to use the altitude effect to adjust hitters’ salaries so that they maintain market efficiency. Pitchers’ salaries are not adjusted for the altitude resulting in compensation that is biased below an accurate representation of their ability.

John Bishop’s explanation of “productivity differentials” between firms could be the reason why both groups of players essentially have their salaries reduced. The productivity differentials for Rockies players are the result of their home field’s altitude.

This is an effect that the Rockies naturally need to comprehend as they play 81 games in

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Denver, and which other teams are less invested in understanding. Rockies hitters have their salaries reduced from market value to levels that more properly reflect their actual ability. Rockies pitchers have their salaries reduced from levels of actual ability to the market value. In both instances, the Rockies choose between paying a player based on ability or based on the corresponding market value. They systematically choose the basis which is less costly to the team. The cost saving method appears to be the method of choice based on the results of the sign-tests.

The results of the model rest on the assumption that the Rockies determine the salary for each player on their roster. This is not true of the data since the Rockies inherit salaries for players acquired by way of trade and are bound to paying the player a salary determined by playing at a much lower elevation. However, the Rockies must agree to any trade. By agreeing to a trade, the Rockies are accepting to take on the salary of the player they are acquiring. While they are not setting the player’s salary outright, they are accepting the salary as a reasonable rate of compensation. Therefore, the results of the model could also be viewed more broadly as a test for the methods upon which the

Rockies accept player salaries whether by acquiring contracts or signing players to new contracts.

There is statistical evidence that the Colorado Rockies pay their hitters at a rate which is significantly different from the market value while their pitchers are paid in accordance with market value. The significant altitude effect on both groups of players would suggest that Rockies players should always be paid differently than market value in order to adjust for the effect. An efficient market would result in the Rockies underpaying their hitters and overpaying their pitchers. The Rockies own attempts to

20 maximize efficiency by producing an output at the lowest possible cost conflicts with the market efficiency for professional baseball players. This results in the Rockies paying their pitchers less than the player’s actual ability suggests he should be paid in order to reduce costs and maximize the firm’s efficiency. Since the cost saving method causes the

Rockies to underpay their hitters, maximizing firm efficiency actually maintains market efficiency. The Rockies pay their hitters a salary which they would likely receive if they played for a team playing at low elevation. By neglecting to adjust their pitchers salaries for altitude, the Rockies actually pay their pitchers less than what that pitcher would make for any other ball club given his actual ability. Despite this inefficiency, the

Rockies are not likely to change their methods for paying pitchers. To restore an efficient market, the Rockies would need to over pay all of their pitchers, and this would be a highly unlikely thing for a profit maximizing firm to do.

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Appendix A Sign Test Results: Hitters League

Rockies

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Sign Test Results: Pitchers League

Rockies

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Appendix B MLB Minimum Salary

1993 109,000 1994 109,000 1995 109,000 1996 109,000 1997 150,000 1998 170,000 1999 200,000 2000 200,000 2001 200,000 2002 200,000 2003 300,000 2004 300,000 2005 316,000 2006 327,000 2007 380,000 2008 390,000 2009 400,000 2010 400,000 2011 414,000 2012 480,000 2013 490,000 2014 500,000

Sources: Statista (2015) & Average Salaries in Major League Baseball 1967-2009

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Appendix C

Hitter Quantile Regression Results

Year of Pseudo R2 Significant Variables Coefficient of # of Observations Regression (95% Confident) Variable 1993 .1515 OPA 6314130 270 Age 174565 1994 .1835 OPA 8106733 256 Age 149889 1995 .0877 OPA 8174943 285 1996 .1500 OPA 1.03e+07 285 Age 82166.45 1997 .1689 OPA 1.30+07 293 Age 140510.1 1998 .1854 OPA 1.31e+07 304 Age 156243.9 1999 .1712 OPA 1.41e+07 314 Age 174237.5 2000 .1946 OPA 1.58e+07 287 Age 186964.9 2001 .1479 OPA 1.67e+07 276 Age 209395.5 2002 .1480 OPA 2.05e+07 280 Age 192791.5 2003 .1508 OPA 2.64e+07 270 Age 236007.9 2004 .1695 OPA 2.43e+07 265 2005 .1093 OPA 2.24e+07 270 2006 .0924 OPA 1.81e+07 275 Age 203549.5 2007 .1309 OPA 2.41e+07 271 Age 288581.5 2008 .1893 OPA 2.26e+07 269 Age 553144.3 2009 .1365 OPA 2.56e+07 293 Age 447068.8 Bats_Switch 1825647 2010 .0883 OPA 2.08e+07 269 Age 311033.4 2011 .1162 OPA 2.47e+07 271 Age 291152.6 2012 .1333 OPA 2.58e+07 271 Age 344254.2 2013 .1412 OPA 3.02e+07 276 Age 377894.3 Bats_Left -1944931 2014 .1696 OPA 2.81e+07 274 Age 571018.8

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Pitcher Quantile Regression Results

Year of Psuedo R2 Significant Variables Coefficient of # of Observations Regression (95% Confident) Variable 1993 .2136 Age 95860.17 269 IPouts_starter 2569.511 1994 .2129 Age 115086.7 257 IPouts_starter 4442.774 1995 .1535 Age 60366.42 302 IPouts_starter 2344.792 1996 .1731 Age 65583.78 282 IPouts_starter 1653.349 1997 .1780 Age 80301.37 290 IPouts_starter 2356.102 1998 .1644 Age 87315.78 303 IPouts_starter 2601.174 1999 .1936 Age 146573.9 309 IPouts_starter 2732.946 2000 .1939 Age 236789.5 270 IPouts_starter 3351.423 2001 .1528 Age 207792.4 248 IPouts_starter 2467.531 2002 .1534 Age 288941.9 262 IPouts_starter 4009.667 Throws_Left -926185.1 2003 .1361 Age 255210.3 253 2004 .1412 Age 198177.9 259 IPouts_starter 3040.121 2005 .1616 Age 130413.7 265 IPouts_starter 3994.294 2006 .2129 Age 185527.8 255 IPouts_starter 7328.695 2007 .2493 Age 225790.1 278 IPouts_starter 5719.795 2008 .2167 Age 350199.4 271 IPouts_starter 3471.839 2009 .1674 Age 275498.1 339 IPouts_starter 3065.386 2010 .1642 Age 290124.6 270 IPouts_starter 5110.423 2011 .1173 Age 298157.2 276 IPouts_starter 6617.277 2012 .1607 Age 262562.5 277 IPouts_starter 6189.803 2013 .2139 Age 325220.4 276 IPouts_starter 6197.175 2014 .1979 Age 390356.7 278 IPouts_starter 5433.357

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