Scores and normal distributions

Question

I'm in the process of designing a system.

So basically, every day users on my site rack up points based on their activity on my website. So whatever they do on my website, they rack up points.

So on 8/3, a user might do multiple things on my website so that they rack up 10 points.

Every day, I figure out the number of points for the user for that day and add a row in the database with the number of points for that day.

I want to give each person a score. Basically a score from 0 to 10 just like in school, but I want that score to depend on the mean score of all the users.

I was thinking of finding the average number of points per day for each user (so user 1 might have an average of 10 points per day) and then finding the average ($X$) of these averages. And using $X$ to create a normal distribution to give each person a score from 0 to 10.

But if the person is 2 standard deviations from the mean, how does that translate to a score?

I'm not a statistician. Any advice would be greatly appreciated. What's the best way to calculate a score like this? Also I know with normal distributions that the distribution has to be normal. What if the average scores are right skewed? What should I do? Determine whether there is an outlier? Anyway help would be appreciated.

Answer 1

I agree with the general drift of @m0skit0's comments that there is no clear "should" to your situation. Also, you have to make a choice among the various things that you've said you want: 1) to have the scores range from 0 to 10; 2) to have the scores be based on standard deviations; and 3) to have the scores be (ultimately) normally distributed. Which of these is most important to you--or are you just looking to set up a scale so that is seems credible to others? If the latter is the case, you'll need to consider and perhaps share with us something about who those people are and what their criteria might be for credibility.