Correlation between Basketball Players Performance and their Compensation
10 pages Paper. Topic is there positive Correlation between Basketball Players Performance and their Compensation. I attached the data, instructions, sample paper too.
Sheet1
| X Independent Predictor Variables | Y Dependent / outcome variable | ||||
| Height in ft | Weight in lbs | % Successful field goals | % Successful free throw | Compensation (Millions) | Avg pts scored per game |
| 6.8 | 225 | 44.20% | 67.20% | 31.38 | 9.2 |
| 6.3 | 180 | 43.50% | 79.70% | 33.83 | 11.7 |
| 6.4 | 190 | 45.60% | 76.10% | 37.98 | 15.8 |
| 6.2 | 180 | 41.60% | 65.10% | 30.35 | 8.6 |
| 6.9 | 205 | 44.90% | 90.00% | 43.28 | 23.2 |
| 6.4 | 225 | 43.10% | 78.00% | 48.07 | 27.4 |
| 6.3 | 185 | 48.70% | 77.10% | 31.65 | 9.3 |
| 6.8 | 235 | 46.90% | 75.00% | 38.17 | 16 |
| 6.9 | 235 | 43.50% | 81.80% | 25.81 | 4.7 |
| 6.7 | 210 | 48.00% | 82.50% | 37.10 | 12.5 |
| 6.9 | 245 | 51.60% | 63.20% | 42.49 | 20.1 |
| 6.9 | 245 | 49.30% | 75.70% | 30.91 | 9.1 |
| 6.3 | 185 | 37.40% | 70.90% | 28.94 | 8.1 |
| 6.1 | 185 | 42.40% | 78.20% | 30.08 | 8.6 |
| 6.2 | 180 | 44.10% | 77.50% | 42.49 | 20.3 |
| 6.8 | 220 | 50.30% | 88.00% | 47.06 | 25 |
| 6.5 | 194 | 50.30% | 83.30% | 42.49 | 19.2 |
| 7.6 | 225 | 42.50% | 57.10% | 23.76 | 3.3 |
| 6.3 | 210 | 37.10% | 81.60% | 33.62 | 11.2 |
| 7.1 | 240 | 50.40% | 71.40% | 33.33 | 10.5 |
| 6.8 | 225 | 40.00% | 76.50% | 33.05 | 10.1 |
| 7.3 | 263 | 48.20% | 65.50% | 27.73 | 7.2 |
| 6.4 | 210 | 47.50% | 24.40% | 37.65 | 13.6 |
| 6.8 | 235 | 42.80% | 72.80% | 30.91 | 9 |
| 7.2 | 230 | 55.90% | 72.10% | 44.47 | 24.6 |
| 6.4 | 190 | 44.10% | 75.70% | 37.10 | 12.6 |
| 6.6 | 220 | 49.20% | 74.70% | 26.5 | 5.6 |
| 6.8 | 210 | 40.20% | 73.90% | 30.91 | 8.7 |
| 6.1 | 180 | 41.50% | 71.30% | 28.4 | 7.7 |
| 6.5 | 235 | 49.20% | 74.20% | 44.12 | 24.1 |
| 6.4 | 185 | 48.40% | 86.10% | 33.83 | 11.7 |
| 6 | 175 | 38.70% | 72.10% | 28.33 | 7.7 |
| 6 | 192 | 43.60% | 78.50% | 33.00 | 9.6 |
| 7.3 | 263 | 48.20% | 65.50% | 28.1 | 7.2 |
| 6.1 | 180 | 34.00% | 82.10% | 37.10 | 12.3 |
| 6.7 | 240 | 51.60% | 72.80% | 30.91 | 8.9 |
| 6.4 | 210 | 47.50% | 84.60% | 37.63 | 13.6 |
| 5.8 | 160 | 41.20% | 81.30% | 33.67 | 11.2 |
| 6.9 | 230 | 41.10% | 59.50% | 22.77 | 2.8 |
| 7 | 245 | 40.70% | 57.30% | 23.50 | 3.2 |
| 7.3 | 228 | 44.50% | 72.60% | 31.65 | 9.4 |
| 5.9 | 155 | 29.10% | 70.70% | 35.45 | 11.9 |
| 6.2 | 200 | 44.90% | 80.40% | 37.95 | 15.4 |
| 6.8 | 235 | 54.60% | 78.40% | 28.10 | 7.4 |
| 7 | 235 | 48.00% | 74.40% | 42.49 | 18.9 |
| 5.9 | 105 | 35.90% | 83.90% | 28.74 | 7.9 |
| 6.1 | 180 | 52.80% | 79.00% | 36.93 | 12.2 |
| 5.7 | 185 | 35.20% | 70.10% | 33.62 | 11 |
| 7.1 | 245 | 41.40% | 77.80% | 22.68 | 2.8 |
| 5.8 | 180 | 42.50% | 87.20% | 35.45 | 11.8 |
| 7.4 | 240 | 59.90% | 71.30% | 40.06 | 17.1 |
| 6.8 | 225 | 48.20% | 70.10% | 33.83 | 11.6 |
| 6.8 | 215 | 45.70% | 73.40% | 27.30 | 5.8 |
| 7 | 230 | 43.50% | 76.40% | 28.95 | 8.3 |
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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
Testing Correlation Between Pitching Compensation and Performance
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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
Testing Correlation Between Pitching Compensation and Performance
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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)
Testing Correlation Between Pitching Compensation and Performance
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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
Testing Correlation Between Pitching Compensation and Performance
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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)
Testing Correlation Between Pitching Compensation and Performance
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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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Testing Correlation Between Pitching Compensation and Performance
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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 salari
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