We found statistics on many different players on the Los Angeles Dodgers in 2012 and 2013. For pitchers, they had to have at least 40 innings pitched (IP) and batters had to have at least 200 at bats (AB). Using the statistics, we made an equation to calculate the salary efficiency values (SEV). These values ranged from 2.37 to 152.2.
Here are the formulas used to calculate SEV for:
Pitchers (2012): IP*1.7^(0.25*WAR)*(10000000/Salary)^0.7/(11(log(ERA+1)/log(5.01))^0.6)
(2013): IP*1.7^(0.25*WAR)*(10000000/Salary)^0.7/(11(log(ERA+1)/log(4.86))^0.6)
Batters: AB*(2*OPS)^(0.3*WAR)*(10000000/Salary)^0.5/20+0.03(BB-SO)+0.05(SB-CS)+0.1(HR+Rtot)
Here are the formulas used to calculate SEV for:
Pitchers (2012): IP*1.7^(0.25*WAR)*(10000000/Salary)^0.7/(11(log(ERA+1)/log(5.01))^0.6)
(2013): IP*1.7^(0.25*WAR)*(10000000/Salary)^0.7/(11(log(ERA+1)/log(4.86))^0.6)
Batters: AB*(2*OPS)^(0.3*WAR)*(10000000/Salary)^0.5/20+0.03(BB-SO)+0.05(SB-CS)+0.1(HR+Rtot)
Questions
1. Make a scatterplot of salary vs. salary efficiency.
1. Make a scatterplot of salary vs. salary efficiency.
2. What does the correlation in the graph above show us?
-The correlation between salary and the SEV values was -0.49, which suggests the risky nature of paying players higher salaries. However, it must be noted that players with high SEV's in 2012 who also played for the Dodgers in 2013 maintained a high level of play, including Clayton Kershaw, who had impeccable numbers that year.
3. How does a player's second-year effort compare to the first given a comparable salary?
-In the vast majority of cases, returning players' SEV's decreased going from 2012 to 2013. This was partly due to increased salaries for some players, but overall performance also showed signs of diminishing. This suggests that players are more content to play less feverishly knowing that they have secured a contract, and it's not just wear and tear.
4. What was the average salary efficiency value?
-The mean of all the SEV's is approximately 40.2. This is actually lower than the national average of about 45 which suggests the Dodgers' players' performances have not been meeting up to their salaries.
5. What was the best signing that the Dodgers made during the 2012-2013 seasons?
-The best signing was undoubtedly Clayton Kershaw, who posted SEV's of 66.74 and 72.61, well above the team average of around 40. His consistency is invaluable, especially concerning his role as pitching ace. His dominance was welcome and certainly warranted his yearly salaries of $7.5mil and $11mil.
6. What was the worst signing that the Dodgers made during the 2012-2013 seasons?
-In the news-breaking trad between the Dodgers and Red Sox, LA acquired Josh Beckett, who was supposed to provide much needed depth. However, Beckett's inability (or dead arm) fell short of his guaranteed salary of $15.75mil, throwing not much more than would be expected of a relief pitcher and serving up mediocre numbers.
7. What is the median of the SEV's?
-The median is 38.91. The median is less than the mean which suggests that the data is skewed right.
8. Is there a difference between the SEV's for the pitchers and the SEV's for the batters?
-Yes, but it is pretty slight. The pitchers have an average SEV of 38.1 while the batters have an average SEV of 42.3.
9. Are there any outliers?
-The most important outlier is batter A.J. Ellis in 2012 with an SEV of 152.2. He was definitely not paid enough for his incredible performances that year. In 2013 his SEV went down to 54.93 while his salary went from $490,000 to $2,000,000!
10. What is the most surprising part of this dataset?
-Some players begin with very high salaries which makes them feel more comfortable and they may not generally work as hard as those with lower salaries (they may have very low SEV's). Those that begin with very high SEV's generally have their SEV go down when they get a raise.
-The correlation between salary and the SEV values was -0.49, which suggests the risky nature of paying players higher salaries. However, it must be noted that players with high SEV's in 2012 who also played for the Dodgers in 2013 maintained a high level of play, including Clayton Kershaw, who had impeccable numbers that year.
3. How does a player's second-year effort compare to the first given a comparable salary?
-In the vast majority of cases, returning players' SEV's decreased going from 2012 to 2013. This was partly due to increased salaries for some players, but overall performance also showed signs of diminishing. This suggests that players are more content to play less feverishly knowing that they have secured a contract, and it's not just wear and tear.
4. What was the average salary efficiency value?
-The mean of all the SEV's is approximately 40.2. This is actually lower than the national average of about 45 which suggests the Dodgers' players' performances have not been meeting up to their salaries.
5. What was the best signing that the Dodgers made during the 2012-2013 seasons?
-The best signing was undoubtedly Clayton Kershaw, who posted SEV's of 66.74 and 72.61, well above the team average of around 40. His consistency is invaluable, especially concerning his role as pitching ace. His dominance was welcome and certainly warranted his yearly salaries of $7.5mil and $11mil.
6. What was the worst signing that the Dodgers made during the 2012-2013 seasons?
-In the news-breaking trad between the Dodgers and Red Sox, LA acquired Josh Beckett, who was supposed to provide much needed depth. However, Beckett's inability (or dead arm) fell short of his guaranteed salary of $15.75mil, throwing not much more than would be expected of a relief pitcher and serving up mediocre numbers.
7. What is the median of the SEV's?
-The median is 38.91. The median is less than the mean which suggests that the data is skewed right.
8. Is there a difference between the SEV's for the pitchers and the SEV's for the batters?
-Yes, but it is pretty slight. The pitchers have an average SEV of 38.1 while the batters have an average SEV of 42.3.
9. Are there any outliers?
-The most important outlier is batter A.J. Ellis in 2012 with an SEV of 152.2. He was definitely not paid enough for his incredible performances that year. In 2013 his SEV went down to 54.93 while his salary went from $490,000 to $2,000,000!
10. What is the most surprising part of this dataset?
-Some players begin with very high salaries which makes them feel more comfortable and they may not generally work as hard as those with lower salaries (they may have very low SEV's). Those that begin with very high SEV's generally have their SEV go down when they get a raise.