Split up bonus inversely to errors
$begingroup$
I have five teams, A-E, who have made errors as follows (errors are percentages):
A 30
B 20
C 12
D 22
E 16
I have to allocate a bonus of $50 in inverse proportion to their errors.
I initially tried a naive approach to allocate based on existing percentages, and then subtract that from 50, in which I ended up with a bonus distribution of 200 against 50, which is obviously not feasible.
My current approach is to take 1/Percentage, then take the percentage of each team's inverse over the total, and use that to split up the $50, which gives me:
Score Point Adjusted Adjusted Percent Allocation
A 30 0.3 3.3333333 0.1213793103 6.068965517
B 20 0.2 5 0.1820685 9.103448276
C 12 0.12 8.3333333 0.3034482759 15.17241379
D 22 0.22 4.5454545 0.1655172414 8.275862069
E 16 0.16 6.25 0.2275862069 11.37931034
Now, this works, and does give me something that feels right, but I'm wondering if there is a better approach to splitting up the bonus.
This is not a homework problem, or one I found in a textbook, so I don't have a solution or topic based hint to check against.
percentages
asked Dec 9 '18 at 8:30
JeremyJeremy
61
$endgroup$
add a comment |
$begingroup$
I have five teams, A-E, who have made errors as follows (errors are percentages):
A 30
B 20
C 12
D 22
E 16
I have to allocate a bonus of $50 in inverse proportion to their errors.
I initially tried a naive approach to allocate based on existing percentages, and then subtract that from 50, in which I ended up with a bonus distribution of 200 against 50, which is obviously not feasible.
My current approach is to take 1/Percentage, then take the percentage of each team's inverse over the total, and use that to split up the $50, which gives me:
Score Point Adjusted Adjusted Percent Allocation
A 30 0.3 3.3333333 0.1213793103 6.068965517
B 20 0.2 5 0.1820685 9.103448276
C 12 0.12 8.3333333 0.3034482759 15.17241379
D 22 0.22 4.5454545 0.1655172414 8.275862069
E 16 0.16 6.25 0.2275862069 11.37931034
Now, this works, and does give me something that feels right, but I'm wondering if there is a better approach to splitting up the bonus.
This is not a homework problem, or one I found in a textbook, so I don't have a solution or topic based hint to check against.
percentages
asked Dec 9 '18 at 8:30
JeremyJeremy
61
$endgroup$
add a comment |
$begingroup$
I have five teams, A-E, who have made errors as follows (errors are percentages):
A 30
B 20
C 12
D 22
E 16
I have to allocate a bonus of $50 in inverse proportion to their errors.
I initially tried a naive approach to allocate based on existing percentages, and then subtract that from 50, in which I ended up with a bonus distribution of 200 against 50, which is obviously not feasible.
My current approach is to take 1/Percentage, then take the percentage of each team's inverse over the total, and use that to split up the $50, which gives me:
Score Point Adjusted Adjusted Percent Allocation
A 30 0.3 3.3333333 0.1213793103 6.068965517
B 20 0.2 5 0.1820685 9.103448276
C 12 0.12 8.3333333 0.3034482759 15.17241379
D 22 0.22 4.5454545 0.1655172414 8.275862069
E 16 0.16 6.25 0.2275862069 11.37931034
Now, this works, and does give me something that feels right, but I'm wondering if there is a better approach to splitting up the bonus.
This is not a homework problem, or one I found in a textbook, so I don't have a solution or topic based hint to check against.
percentages
asked Dec 9 '18 at 8:30
JeremyJeremy
61
$endgroup$
I have five teams, A-E, who have made errors as follows (errors are percentages):
A 30
B 20
C 12
D 22
E 16
I have to allocate a bonus of $50 in inverse proportion to their errors.
I initially tried a naive approach to allocate based on existing percentages, and then subtract that from 50, in which I ended up with a bonus distribution of 200 against 50, which is obviously not feasible.
My current approach is to take 1/Percentage, then take the percentage of each team's inverse over the total, and use that to split up the $50, which gives me:
Score Point Adjusted Adjusted Percent Allocation
A 30 0.3 3.3333333 0.1213793103 6.068965517
B 20 0.2 5 0.1820685 9.103448276
C 12 0.12 8.3333333 0.3034482759 15.17241379
D 22 0.22 4.5454545 0.1655172414 8.275862069
E 16 0.16 6.25 0.2275862069 11.37931034
Now, this works, and does give me something that feels right, but I'm wondering if there is a better approach to splitting up the bonus.
This is not a homework problem, or one I found in a textbook, so I don't have a solution or topic based hint to check against.
percentages
percentages
asked Dec 9 '18 at 8:30
JeremyJeremy
61
asked Dec 9 '18 at 8:30
JeremyJeremy
61
asked Dec 9 '18 at 8:30
JeremyJeremy
61
asked Dec 9 '18 at 8:30
JeremyJeremy
61
asked Dec 9 '18 at 8:30
JeremyJeremy
61
61
add a comment |
add a comment |
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