The Relationship Between
Salary and Job Performance:
Major League Baseball as an Example
Jacob Bogardus
INFO 4470
Cornell University
May 13, 2011
Preliminary Thoughts
• If job performance can be a successful indicator of salary earned in a competitive market shouldn’t this be more widely used
• Health Care
• Education
Research Question
• Can a baseball player’s salary be predicted by on field performance? Are salary and on field performance closely correlated?
• Hypothesis: A player’s salary is based upon past on field performance.
Goals
• Quantify a player’s on field success using baseball statistics
• Track the relationship of a player’s on field success with the player’s salary
• Test for correlation between salary and on field success in a variety of different scenarios
Major League Baseball Market
• 1800’s – mid 1970’s little player mobility
– Player’s bound to team for life
• Mid 1970’s—Free Agency
– Player’s able to openly negotiate contract with any team after current contract had expired
– Player mobility increased
Quantifying On Field Success
• Traditional Statistics
– Batting Average
– Home Runs
– Runs Batted In
– Stolen Bases – Runs Scored
Problems with Traditional Statistics
• Batting Average‐ Luck
• Home Runs‐ Field dimensions, weather, altitude
• RBI’s and Runs‐ Functions of other team mates success
Moneyball Era
• Oakland Athletics‐ small market team
– General Manager‐ Billy Beane
• On Base Percentage (OBP)
• Slugging Percentage (SLG)
Problems with Moneyball
• On Base Percentage‐ Overvalues walks
• Slugging Percentage‐ Doesn’t adjust for parks
Sabermetrics
• Bill James – father of sabermetrics
– “the search for knowledge about baseball”
– Advanced statistics used to try to solve some of the inadequacies of traditional and Moneyball
statistics.
How Sabermetrics Help
•
•
•
•
BABIP‐ Batting Average on Balls In Play
Park Factor
On Base Percentage Plus Slugging (OPS+)
Adjusted OPS (OPS+)
Data Used
• Three sets of Data
– Team data‐ Payroll vs. Performance (Wins)
– Individual Data 2005‐2009 Salary vs. Performance
– 2010 Free Agent Data‐ Salary vs. Past Performance
Data Set 1
Average Player Salary vs. Average Wins per Year
$8,000,000.00
$7,000,000.00
Average Player Salary
$6,000,000.00
$5,000,000.00
R² = 0.4481
$4,000,000.00
$3,000,000.00
$2,000,000.00
$1,000,000.00
$0.00
0
20
40
60
Average wins per Year
80
100
120
Data Set 2
$35,000,000.00
Salary vs. OPS+
$30,000,000.00
Salary (in 2005 dollars)
$25,000,000.00
$20,000,000.00
$15,000,000.00
$10,000,000.00
$5,000,000.00
$0.00
0
20
40
60
80
100
OPS+
120
140
160
180
200
Rookie Contracts
$35,000,000.00
Salary vs. OPS+ no Rookie Contracts
$30,000,000.00
Salary (in 2005 dollars)
$25,000,000.00
$20,000,000.00
$15,000,000.00
$10,000,000.00
$5,000,000.00
$0.00
0
20
40
60
80
100
OPS+
120
140
160
180
200
Data Set 2: Adding Speed
Salary (in 2005 dollars) = b0 + b1OPS+ + b2SB + e1
Regression Statistics
Multiple R
0.415316792
R Square
0.172488038
Adjusted R Square
0.169137787
Standard Error
4472069.415
Observations
539
Coefficients
Intercept
‐3226926.459
X Variable 1
30922.18381
X Variable 2
86839.54804
Experience
Salary (in 2005 dollars) = b0 + b1OPS+ + b2SB + b3EXP + e1
Regression Statistics
Multiple R
0.629199457
R Square
0.395891957
Adjusted R Square
0.392542004
Standard Error
3847859.944
Observations
539
Coefficients
Intercept
‐8535622.292
X Variable 1
56326.92264
X Variable 2
76913.11271
X Variable 3
649540.9672
Data Set 3‐ Free Agents
$25,000,000
Free Agent Salaries vs. 3 year OPS+ Average
$20,000,000
Free Agent Salary
$15,000,000
R² = 0.4933
$10,000,000
$5,000,000
$0
0
($5,000,000)
20
40
60
80
3 year OPS+ average
100
120
140
160
Taking out the high prices
$16,000,000
Free Agent Salaries vs. 3 Year OPS+
$14,000,000
$12,000,000
Free Agent Salary per year
$10,000,000
R² = 0.5933
$8,000,000
$6,000,000
$4,000,000
$2,000,000
$0
0
20
40
60
80
($2,000,000)
($4,000,000)
3 Year OPS+ Average
100
120
140
160
Logarithm of Free Agent Salary
8.5
Log of Free Agent Salaries vs. 3 year OPS+ Average
8
Log of Free Agent Salary
7.5
7
R² = 0.6098
6.5
6
5.5
5
40
60
80
100
3 year OPS+ average
120
140
160
Adding Speed‐ Free Agents
LOG(Salary (in 2005 dollars)) = b0 + b1OPS+ + b2SB + e1
Regression Statistics
Multiple R
0.798385681
R Square
0.637419696
Adjusted R Square
0.623990796
Standard Error
0.259998111
Observations
58
Coefficients
Intercept
4.789012936
X Variable 1
0.00327468
X Variable 2
0.016883482
Adding Experience‐ Free Agents
LOG(Salary (in 2005 dollars)) = b0 + b1OPS+ + b2SB + b3EXP + e1
Regression Statistics
Multiple R
0.804486979
R Square
0.647199299
Adjusted R Square
0.627229448
Standard Error
0.258875979
Observations
58
Coefficients
Intercept
4.668238459
X Variable 1
0.003284876
X Variable 2
0.016541719
X Variable 3
0.013641242
Conclusions
• Data Set 1
– In general more money spent, more wins
• Data Set 2
– Weak correlations between salary and performance
• Data Set 3
– Moderate to strong correlations between salary and performance