How to determine an impact based on components

[Semidevilz]

I feel this is an easy arithmetic, but I can’t figure out how to get it to work out.
Let’s say I have an overall metric of sales data that can be broken down by 5 sales reps.

In 2016, each rep makes a certain number of phone calls and their success rate is # of sales divided by # of calls. I'm able to determine my overall 2016 performance by summing each reps sales and dividing by the total number of calls for a total success rate. so for example:
rep1: sales: 5; calls 10; success .50
rep2: sales: 3; calls 20; success .15
rep3 : sales: 2; calls 10; success .20
rep4: sales: 1; calls 10; success .10
rep5: sales: 8; calls 80; success .1
total: sales 19; calls 130; success .146

In 2017, the same 5 reps performance are available

rep1: sales: 5; calls 100; success .05
rep2: sales: 10; calls 20; success .5
rep3 : sales: 2; calls 10; success .20
rep4: sales: 1; calls 100; success .01
rep5: sales: 80; calls 2000; success .4
total: sales 98; calls 2230; success 4.3%
my goal is that I want to start at 14.6%(initial success) and mathematically determine how much each rep contributed to my final success of 4.3%.

Ideally, 14.6% + or minus rep1...rep2...rep3...rep4...rep5 = 4.3%. how do I do this calculation? I've tried a couple methods with weighting and such but I still can't get it to tie out.

 

[jbriggs444]

total: sales 98; calls 430; success 4.3%

How did you get 4.3% from 98 out of 430? I get 23%.

Also, I think that rep5 only made 200 calls, not 2000.

Edit: Oh, that's what happened. It's all that typo for rep 5. Fix that number.

 

[Semidevilz]

How did you get 4.3% from 98 out of 430? I get 23%.

Also, I think that rep5 only made 200 calls, not 2000.

Edit: Oh, that's what happened. It's all that typo for rep 5. Fix that number.

Whoops. Fixed! 2000 is correct for this exercise

 

[Mark44]

Whoops. Fixed! 2000 is correct for this exercise

How can 2000 calls for rep5 be reasonable when the other reps made between 10 and 100 calls?

Also, you can easily confuse yourself and others by being inconsistent with some success rates written as decimals and others as percentages.

Ideally, 14.6% + or minus rep1...rep2...rep3...rep4...rep5 = 4.3%. how do I do this calculation?

I don't know if it makes much sense. You can't really add averages if their bases are different. This works correctly in "baseball averages" if a batter is up 6 times with 2 hits in one game, and up 4 times with 1 hit in another game. His average would be $\frac 2 6 + \frac 1 4 = \frac 3 {10}$ or .300, but regular fractions don't work this way. Outside of baseball $\frac 2 6 + \frac 1 4 = \frac 4 {12} + \frac 3 {12} = \frac 7 {12}$, which is a lot larger than .300.

 

[Semidevilz]

How can 2000 calls for rep5 be reasonable when the other reps made between 10 and 100 calls?

Also, you can easily confuse yourself and others by being inconsistent with some success rates written as decimals and others as percentages.I don't know if it makes much sense. You can't really add averages if their bases are different. This works correctly in "baseball averages" if a batter is up 6 times with 2 hits in one game, and up 4 times with 1 hit in another game. His average would be $\frac 2 6 + \frac 1 4 = \frac 3 {10}$ or .300, but regular fractions don't work this way. Outside of baseball $\frac 2 6 + \frac 1 4 = \frac 4 {12} + \frac 3 {12} = \frac 7 {12}$, which is a lot larger than .300.

Thanks. I know there's some issues with calculating it the way I want, but was just wondering if there was a way to make it work.