How to form a meaningful statistical indicator to reflect user interaction with a website A given user can interact in multiple ways with a website. Let's simplify a bit and say say a user can:


*

*Post a message

*Comment a message

*"like" something on the website via Facebook


(after that we could add, following the site on twitter, buying something on the site & so on, but for readability's sake let's stick to these 3 cases)
I'm trying to find a formula that could give me a number between 0 and 100 that reflects accurately the user interaction with the given website.
It has to take the following into account:


*

*A user with 300 posts and a one with 400 should have almost the same score, very close to the maximum

*A user should see his number increase faster at the beginning. For instance a user with 1 post would have 5/100, a user with 2 would have 9/100, one with 3 would have 12/100 and so on.

*Each of these interactions have a different weight because they do not imply the same level of involvement. It would go this way: Post > Comment > Like

*In the end, the repartition of data should be a bit like the following, meaning a lot of user around 0-50, and then users really interacting with the website.


This is quite specific and data-dependent, but I'm not looking for the perfect formula but more for how to approach this problem.
 A: Suggestion: Assign values to each post, "like" and etc. For example, one post is worth $0.1$. So if I have posted eight times, I have $0.8$ points.
Now, display my score as $S=100-\frac{100}{P+1}$ where $P$ is the sum of my points. In our example, $S=100-\frac{100}{1.8}\approx 44$. Note that if I haven't done anything, $S=0$. If I have posted $50$ times, my score will be $S=98$.
More generally, I suggest a function $S=100(1-f(P))$ where $f(0)=1, f(\infty)=0$ (and $f$ is monotonically decreasing). Other examples could be $S=100-\frac{100}{\sqrt{P+1}}, S= 100-\frac{100}{(P+1)^2}$ and so on. I suggest playing around with these until you find one that seems to match what you want out of the score.
A: Collect all the indicators and try to combine them as described here: How do I develop a metric for comparisons that involves a combination of variables at different scales?
There is no general advice as the distribution of the scores will depend on the population of your visitors and will tend to change as it changes whatever metric you choose.
