I am analyzing data for an email marketing company.

We have x amount of subscribers that come in at some point in time.

We promote zero or more emails to these individuals daily, for several months.

I want to determine what the "best performing" emails are, as a function of Revenue per subscriber (RPS).

  • revenue per subscriber = revenue for that email/number of subscribers that email was sent to

Where I am facing difficulty is factoring the natural decline in revenue that occurs as the email list becomes old. Average RPS declines naturally over time for several reasons (people unsubscribe, people stop opening emails, etc.)

The natural decline means that I cannot simply rank the RPS over time and look at what values are the highest, because this would not account for the natural decline. i.e. and RPS of 100 is much more valuable when the list is 6 months old, than when it is 1 week old.

Hopefully that makes sense, and I apologize if this question is simple. I am pretty new to statistics and data analysis, so bear with me.

I would appreciate if you could tell me how to arrive at an answer (what are the best performing emails) as opposed to just giving me a straight answer.


There's a ton of marketing science literature now on "customer lifetime value." For instance, there's a paper from 2004 by Gupta, Lehmann and Stuart Valuing Customers that is one of the first papers by academics. Wharton has it's Customer Analytics Initiative that is quite actively developing CLV models today.

What you're describing as a "natural decline" in response is simply a survival (or attrition) curve which could be fit with a Cox hazard model or any number of other parametric and nonparametric forms beginning with an exponential curve (constant decay rate) and extending from there.

So, at its simplest for a given time period (e.g., weekly, monthly, quarterly), Revenue (or net profit) can be a function of (Expected Revenue - Costs (acquisition, fulfillment, creative, etc.)) * Probability of Survival.

The models become more complicated as more factors are introduced. For instance, the Wharton guys try to improve and augment financial models of corporate valuation by introducing customer metrics such as these.

  • $\begingroup$ Will have to do a lot of reading before I can fully grasp your comment, but that is exactly what I wanted, a lead. Thank you $\endgroup$ – Alibaba Jan 20 '16 at 18:52

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