Testing Correlation Between Pitching Compensation and Performance

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Testing Correlation Between Pitching Compensation and Performance

Student:

Hellenic American University

BUS6110 Operations Research

Professor Jeffrey Hansel

5/14/2020

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Introduction

In Major League Baseball (MLB) there is often the competitive comparison between the rich and

the poor, large market and the small market teams and of course National League (NL) and

American League (AL) baseball. Large market teams such as the New York Yankees, Boston

Red Sox and the Los Angeles Dodgers annually sign free agents to multi-million, multi-year

contracts to play baseball for their team. Many of these high-paid contracts are for pitching

talent such as Red Sox signing David Price in 2016 to a 7-year for $217,000,000 contract or

Gerrit Cole signing a 9-year $324,000,000 contract with the New York Yankees in 2019. Small

market teams like the Tampa Bay Rays, Milwaukee Brewers and San Diego Padres cannot afford

those high-priced contracts, so they deploy a competitive strategy to develop ‘home’ grown or

‘cast-offs’ players whom at some point if they do well, may become targets for the high spending

large market teams.

League style of play may impact the compensation and player acquisition and investment,

depending on the league. Pitchers bat in the NL, they don’t in the AL. The AL has a Designated

Hitter role, though not a position player, the only purpose is to bat. The NL doesn’t have a DL.

AL pitchers may pitch deeper into the game since the AL does not have to deploy double switch

strategies with pinch hitters replacing pitchers.

In May 2002 in the Journal of Sports Economics article written by Stephen Hall and Stefan

Szymanski of Imperial College and Andrew S. Zimbalist of Smith College, “Testing Causality

Between Team Performance and Payroll, The Cases of Major League Baseball and English

Soccer” (2002 Study), was a statistical analysis was performed linking team payroll to the

competitiveness of MLB. Interestingly in the 2002 Study, the findings were weak correlation

between team performance and payroll in MLB from 1980 to the mid-1990’s. The 2002 Study

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referenced the Quirk and Fort 1999 article, “Hard ball: The abuse of power in pro team sports”

published in the Princeton University Press, analyzing the correlation between the rank of

regular-season winning percentage and the rang of the player payroll cost by team for a 7 season

average (1990 through 1996), finding a correlation coefficient of .509 in the AL and 0.135 in the

NL, of which they interpreted as not statistically significant to interpret that payroll variability

significantly impacted winning percentages. They concluded that payrolls “were essentially

worthless in explaining the won-lost records in baseball”. A related study by Zimbalist in 2002,

“Competitive balance in sports leagues: An introduction” published in the Journal of Sports

Economics, is another source finding a low correlation coefficient for baseball and concludes

that ‘average team salary has been related only tenuously to team performance”.

My study focuses on the pay and performance on the role of a MLB pitcher, analyzing any

correlation of the pitcher’s compensation to the pitcher’s performance in key measurements such

as lower Earned Run Average (ERA) or Innings Pitched (IP). This study also narrows the 2002

Study total salary correlation to the specific investment in the pitching compensation and the

team pitching salaries correlation to the team winning percentage. The study covers the period

including the 2009 through 2019 MLB seasons.

Consistent with the findings of the 2002 Study, the hypothesis of my project should statistic find

little correlation to pitching salaries on performance. The test will address the below

relationships.

– Investment in large pitching salaries may not have a direct correlation to winning percentage

– The Pitcher’s salary may not correlate to the Pitcher’s Earned Run Average (ERA)

– The Pitcher’s salary may not correlate to more Innings Pitched (IP)

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Study process

The process followed in this study was to collect payroll and performance data on MLB pitchers,

perform exploratory analysis through the collection and statistical analysis of the data that

provide a basis of inference to interpret the results. Since the population is so vast to collect

data, I utilized a sample designed to be representative of the vast population of MLB pitching

salaries, performance and team results. The sample criteria identified two (2) teams from a

stratified simple random sample selection from (i) one large market team and (ii) one small

market team. Also, the sample criteria was to have a team from each league, AL and NL. The

teams selected for this study were identified as representative of the overall MLB population

without any inherent bias. Though unintended, the sample design may have some unintended

lurking variables that may provide unknown bias.

Selection process

After reading several studies, it is apparent that there is not a standard definition of a large and

small market team. The reason for clarifying a definition was to ensure that my sample selection

of a team from each stratum has unbiased statistical significance. The variables utilized in the

definition of large and small market are primarily team value, though I also reference team

revenue and population in the analysis.

Below are a listing of the team values as reported by Forbes Magazine’s April 6, 2020 issue

(https://www.forbes.com/sites/mikeozanian/2020/04/09/despite-lockdown-mlb-teams-gain-

value-in-2020/#52cbdb552010).

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Using descriptive statistics, an unbiased interpretation of large market team would have a value in

the upper quartile of league value and small market team in the lower quartile of team value. The

assessment is the top 8 teams outside the third quartile (Q3) would be classified as large market

and the lower 8 teams below the first quartile (Q1) would be classified as small market. Further

assessing the spread between the Yankees valued at $5 billion and the Marlins with a $980 million

value, the descriptive statistics found a median of $1,623 million for all 30 teams. The high value

Yankees and Red Sox pulled the mean of $1,852 million to the left of the median. Using a

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histogram, bins of value ranges skew left with some larger outliers such as the Boston Red Sox

and the New York Yankees skewing the mean right.

Finally, I found an interesting statistical analysis is The Hardball Times

(https://tht.fangraphs.com/baseball-revenues/), regarding metropolitan area population and team

revenue (except for the top four (4) metropolitan populations). Though the R-Squared value of

.08 is statistically insignificant, the large markets are skewing the correlation upward to the right,

0

2

4

6

8

10

12

14

N um

be r o

f T ea

m s

Value in Millions

Team Values (in Millions)

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suggesting that lurking variables besides population are increasing team revenue and market

value for the large market teams.

Metro Area Populations with Revenue from all MLB Teams in Area | R-Squared 0.08 (Top 4 Metros Excluded)

The result of the comprehensive analysis on small market and sample size is that the below

teams are identified as small and large market. Since six (6) of the eight (8) large market teams

are in the NL, I randomly selected an AL team for my analysis, the Boston Red Sox. Also, since

five (5) of the eight (8) teams in the lowest quartile are from the AL, I randomly selected an NL

team for my analysis, the Milwaukee Brewers.

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Variables and Methodology

The study is focused on finding correlation between the independent variable, pitching salary,

and performance dependent variables such as (i) ERA, (ii) IP and (iii) team wins. All variables

are quantitative.

Table 1. Variable Rational

Pitching salary Compilation of comprehensive pitching salaries for the Boston Red Sox and the Milwaukee Brewers for a period of 11-years, commencing for the 2009 through the 2019 MLB season. This is the independent variable test to correlate pay for performance.

Earned Run Average (ERA)

ERA is a dependent variable in this study. The test was to determine if a pitcher’s salary correlated to a lower ERA performance.

Innings Pitched (IP) IP is a dependent variable in this study. The test was to determine if a pitcher’s IP correlated to a higher IP performance.

Team winning percentage

Teaming winning percentage is a dependent variable in this study. The test was to determine if a larger aggregate team pitching salary correlated to more team wins.

Data Compilation

Using the criteria using the stratified simple random sample selection described above, salary

data was collected from the USA Today (www.usatoday.com) and performance data was

collected from the Baseball Reference (https://www.baseball-

reference.com/teams/BOS/2009.shtml). Data was collected for the 2009 through 2019 baseball

seasons, or for eleven (11) consecutive years. The data population of the sample was 100% for

the two (2) teams included in the sample, specifically all Red Sox and Brewer pitcher salaries

and performance results for the variables in this study were compiled for the sample population.

The design was intended to coverage a sufficient period to represent the MLB population for the

study period. Also important in the design, the study period was design objective was to

statistically analyze the inferences from the 2002 Study in the most recent decade.

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Consistent with the expectations of the large market and small market classification, the data

clearly illustrates that the Red Sox team pitching salaries are significantly larger than the

Brewers pitching salaries. The investment in the pitching salaries during the11-year study

period, shows that the Red Sox won 63 more games for an overall incremental winning

percentage of .036 while spending 127% more in pitching salaries than the Brewers in the

comparable time period. Though the Red Sox won 63 more games over the 11-year period, their

pitching cost per win was 112% more than the Brewers and 116% more for all salaries. Even

without further statistical analysis we may infer that pitching salaries may not correlate to more

regular season wins.

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Specific data collected for both the dependent and the independent variables is listed in

Appendix A (attached excel file). The raw data evidences a collection of 286 pitcher salaries and

performance covering the sample period.

Pitching Salary collation to the Innings Pitched independent variable Data Analysis

In this presentation, I was looking to prove a relationship between the pitcher’s salary and the

number of innings pitched. The dependent variable (y) was set as the innings pitched per season

per pitcher. The independent variables (x) is the annual salary for the specific pitcher. By using

the regression tool in Excel, I found that the R, or correlation coefficient, is 0.478. Since R is

near .5, we can interpret the relationship between the inning pitched and pitching salary, is

moderately positive. Excel computed the R-squared value of 0.229, which represents the percent

change in the dependent variable (y-IP) that is explained by the independent variables (pitchers

salary). R-squared tells us that the salary for the pitcher accounts for about 23% of the

variation/change in the innings pitched per season. The value of the slope was .000005 (or 5.1

innings pitched for each $1,000,000 of pitching salary), and the confidence intervals indicate that

we are 95% confident that the slope will fall between .000004 (or 4.1 innings pitched for each

$1,000,000 of pitching salary) and .0000062 (or 6.2 innings pitched for each $1,000,000 or

pitching salary). In order to predict annual innings pitched for an individual pitcher, the formula

would be annual innings pitched = 58.9 + (5.1 * annual pitcher salary in millions of USD). As

you can see, there is moderate relationship between the progression of annual innings pitched to

the pitcher’s compensation. My conclusion is that though a pitcher’s salary has a slightly

moderate correlation to annual innings pitched, there are also many lurking variables that may

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influence this outcome, such as the AL pitches do not bat, so no need to utilize a pinch hitter as

needed in NL baseball.

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Pitching Salary correlation to the independent variable ERA data analysis

In this presentation, I was also looking to prove a relationship between a pitcher’s salary and the

number of innings pitched. The dependent variable (y) was set as the ERA per season per

pitcher. The independent variables (x) is the annual salary for the specific pitcher. By using the

regression tool in Excel, I found that the R, or correlation coefficient, is 0.068. Since R is near 0,

we can interpret there is no relationship between the pitcher’s ERA and the pitcher’s salary.

Excel computed the R-squared value of 0.005, which represents the percent change in the

dependent variable (y-ERA) that is explained by the independent variables (pitcher’s salary). R-

squared tells us that the salary for the pitcher accounts for just less than .5% of the

variation/change in the pitcher’s season ERA. The value of the slope was -.00000003 to an

intercept of 4.76. As you can see, there is no statistical relationship between the progression of

the pitcher’s ERA to the pitcher’s compensation.

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Pitching Salary correlation to the independent variable team wins data analysis

Finally, following up on the 2002 Study, I was looking to prove a relationship between the

team’s pitching staff salaries and winning percentage. The dependent variable (y) was set as the

team’s winning percentage. The independent variables (x) is the annual aggregate team pitching

salaries. By using the regression tool in Excel, I found that the R, or correlation coefficient, is

0.088. Since R is near zero, we can interpret little relationship between the winning percentage

and aggregate pitching salaries. Excel computed the R-squared value of 0.008, which represents

the percent change in the dependent variable (y-winning percentage) that is explained by the

independent variables (team aggregate pitching salaries). R-squared tells us that the salary for

the pitcher accounts for about .7% of the variation/change in team winning percentage. The value

of the slope was .058, and the confidence intervals indicate that we are 95% confident that the

slope will fall between -.248 and .364. In order to predict the team winning percentage based on

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aggregate pitching salaries, the formula would be winning percentage = .499 + (.058 * aggregate

team pitching salaries). As you can see, there is little relationship between the progression of

winning percentage to the team’s pitching compensation. My conclusion is that these results are

consistent with the 2002 Study and there is little correlation between compensation, in this case

team pitching compensation and the team’s winning percentage.

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Conclusion

The inferences from this study are findings of the 2002 Study that payroll has little correlation to

performance may be a statistically supported finding. The inferences from the analysis

performed in this study support this hypothesis.

– Investment in large pitching salaries may not have a direct correlation to winning percentage

– The Pitcher’s salary may not correlate to the Pitcher’s Earned Run Average (ERA)

– The Pitcher’s salary may not correlate to more Innings Pitched (IP)

In conclusion, these findings are good news for the future competitiveness of Major League

Baseball. Small Market teams can compete on the baseball diamond with the rich Large Market

teams. We can only hope to see the Milwaukee Brewers play and beat the Boston Red Sox in a

World Series in the very near future.

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References

Stephen Hall, Stefan Szymanski, Andrew S Zimbalist. (2002, May). Testing Causality Between

Team performance and Payroll. The Cases of Major League Baseball and English Soccer,

Quirk J, Fort, R (1999). Hard ball: The abuse of power in pro team sports. Princeton, NJ:

Princeton University Press

Zimbalist, A.S. (2002). Competitive balance in sports leagues: An introduction. Journal of

Sports Economics, 3(2), 111-121

9 April 2020, Fortune Magazine, Despite Lockdown, MLB Teams Gain Value in 2020

https://www.forbes.com/sites/mikeozanian/2020/04/09/despite-lockdown-mlb-teams-gain-value-

in-2020/#52cbdb552010

USA Today https://www.usatoday.com/sports/mlb/brewers/salaries/2019/player/all/

Baseball Reference.com https://www.baseball-reference.com/teams/BOS/2009.shtml

The Hardball Times (https://tht.fangraphs.com/baseball-revenues/)

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