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.

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give some example data (even fake)....we could compare the proposals. –  user603 Jul 29 '11 at 14:25

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.

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thanks for the answer –  marcgg Jul 27 '11 at 11:54