User Retention (part 2)
This will be a fairly short post but in it I hope to explain simply and clearly one of the terms in my function that describes rate of user acquisition (and loss).
In my function described earlier dU/dt = f(t) + g(m,e,t) - aU the term -aU may seem a little mysterious to some readers.
If we remove the first two terms that represent growth due to organic and advertising methods we shall look at the case where an app has been withdrawn from sale and no further promotion is taking place. In such a case the function becomes dU/dt = -aU
What this tells us is that the rate of loss of users is proportional to the number of users we have, by a coefficient of proportionality labelled 'a'.
To understand it think of it much like radioactive decay which follows a similar mathematical model.
At a particular time there are 'U' total users with the app installed. We do not know when each user will uninstall the app but we do know that it is a fairly random event - a user could uninstall the app at any time and the likelihood of them doing so at any given time is shown by the value of 'a'. Large values indicate a high likelihood, low values indicate a lesser chance of uninstall.
As such - the more users you have the more likely that at any given time 1 of them will uninstall the app. If you double the number of users, by probability, you double the rate at which users uninstall the app.
This is what leads to the exponential decay curve those of you who are developers will see when you have finished a promotional period for a product as users gradually fall away and uninstall the app.
It is perfectly normal and mostly unavoidable.
I hope that helps understand the model I use to describe app user retention and loss.