I want to measure the value of a client based on the average project fee and average length of the project in days. We combined the two to create a Revenue/Day metric - it's inelegant but works well enough for our purposes.

I want to determine the Average Revenue/Day for all projects with a specific client, but I am unsure about the best way to calculate.

Say we conducted 3 projects with a client

Project 1: Fee = 100,000 | Length = 100 days | Revenue/Day = 1,000

Project 2: Fee = 120,000 | Length = 90 days | Revenue/Day = 1,333

Project 3: Fee = 135,000 | Length = 75 days | Revenue/Day = 1,800

If we handle each discretely, and take the average of the revenue/day totals, it equals $1,378.

However, if you take the total fees and divide by total days, you get $1,340. This to me seems like the average of averages, so I think it's incorrect.

I think $1,378$ is the correct number, with the equation being something like: $$ \left(\frac{\text{fee}}{\text{day}}+\frac{\text{fee}}{\text{day}}+\frac{\text{fee}}{\text{day}}\right) / n = x $$ with $x=\text{average revenue/day}$.

Is that right?

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    $\begingroup$ isn't there any cost associated with a client? how is the cost not in the value? you can have a needy client who would generate a lot of revenue but at a very high cost $\endgroup$ – Aksakal Sep 1 '17 at 18:42

The correct average revenue must be total revenue / total days, with your numbers this becomes $$ \frac{100000+120000+135000}{100+90+75} $$ You can express this as an weighted average by reexpressing the fraction above as $$ \frac{100}{265}\frac{100000}{100}+\frac{90}{265}\frac{120000}{90}+\frac{75}{265}\frac{135000}{75} $$ which shows that the right weighted average have weight "the fraction of days worked" and data the revenue per day for each project.

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