% Change for value that didn't exist before I want to record the percentage change of a value from one week to another.
For example: I deal with a client who brings in 10€ is week 1. In week 2, he brings in 30€. The percentage change is a 300% increase.
Say there's another client I hadn't yet dealt with in week 1, but am now working with him in week 2 and he brings 1000€.
What would be the best way to represent this new client's change coming in? I could say it is 100%, but that somehow does not seem reflective of the true value of this client. Indeed, had he brought in 10€ in week 1, like client 1, the % increase would have been 10,000%, and thus should be much more valuable than client 1.
Can I simply replace the 0 in week 1 with a 1? Or should I do the actual amount as the percentage increase or 100 times the new amount (1000, or 10,000). What is the best course of action?
Thanks
 A: Whatever value you choose, it would be equally arbitrary. If you don't know the previous value, you cannot say anything about the change.
A: Best course of action for what purpose? Purely mathematically, the client brought in either 0 (and 0 to 1000 is not a 100% increase but rather an infinite increase) or the income was missing (was perhaps not even a client). 
If you are interested in predicting future income, then perhaps trying different approaches (e.g. also average income from other - in some sense similar - clients could be something to try) and seeing the prediction performance in cross-validation could be an approach.
A: 
[...] that somehow does not seem reflective of the true value of this client.

... because percentages are to reflect changes or relative values and not absolute values.
If you want to highlight that this client has a higher absolute value than the one bringing in 10 or 30 € you can:


*

*use the absolute values

*use other indicators better suited for this purpose (eg. percentage of the total money brought in)


If you want to stick with percentages you won't have information regarding the relative worth of the clients between each other. Nevertheless, I would then recommend having no value in the first week and the relative value (as for other clients) in the following ones.
