Measuring value of free users I was wondering if the following scenario had a word for it (eg. Survival analysis...).
Suppose we have a company that has pro users (pay $10/ month) and free users. I want to calculate the worth of the free users to the company. Despite not spending any money with the company, they make the product more popular and therefore bring in more revenue.
Currently we frame the value of a user as a proportion of the $10 as follows:
$$
value = 10 \frac{activeness}{max\_activeness}
$$
where activeness is calculate as the number of logins per month. Logic being the more active they are the more valuable they are to the company.
While this is a start, I was wondering if there was a more statistically rigorous way of defining long term value of free users. What other data would be necessary to frame this question better?

This is a business question, not a Stats question in my opinion; the term you want is "customer value analysis". Just to point you towards some relevant bibliography:

*

*The Value of a 'Free' Customer by Gupta et al. (2006)

*Nonmonetary customer value contributions in free e-services by Anderl et al. (2016)

*Non-monetary social and network value: understanding the effects of non-paying customers in new media by Hollebeek & Brodie (2016)

Also I suggesting looking at publication/opinion pieces on "freemium online games".
In terms of datasets, one would most likely need to know location as well as timing of newer user joining. To state a hammy example: An established platform in a saturated market gains less from "free users" than a newly established platform in new market. Similarly an "old" free user is less likely to switch to a paid user than a "new" free user who might still be testing before buying; the "age" of the user matters.
