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User Rank -or- User Percentile Rating

Entirely editing my answer to try and make sense here ...

Wikipedia page on Standard Deviations.

I suggest that we display a value that represents the number of standard deviations from the norm that a user is.

The Y axis is the % of users with that reputation score, the X axis plots scores from 0 to n. You could then determine where the user is in terms of rarity with regards to the entire user-base, rather than looking at a reputation score that a large volume of users could be in. So I could show up as 101 rep, and we can identify just how rare (or common) that range is in the deviations of users on SO meta (about 8,750/21,000 = 41.7% have a lower reputation than me), where as someone at 0 would be

alt text

This is similar to how people are ranked as "genius" with IQ scores, as they are in the top 2% of IQ scores.

We could give users titles for being at specific deviations.

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marked as duplicate by Jon Seigel, Pops, Rosinante, Ladybug Killer, Tobias Kienzler Sep 24 '10 at 10:34

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That's funny, I don't ever seem to recall seeing the word "karma" on Stack Overflow. –  Aarobot Sep 23 '10 at 15:55
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It's not karma, it's exp. –  mmyers Sep 23 '10 at 16:02
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The distribution is quite different. The vast majority of users (~96%) have less than 1000 points. –  NullUserException อ_อ Sep 23 '10 at 16:09
    
Maybe he's talking about the up/downvote ratio when referring to karma –  Yi Jiang Sep 23 '10 at 16:11
    
Updated so it says reputation not karma. I'm talking about the reputation point system score. –  Incognito Sep 23 '10 at 16:39
    
I'm talking about representing how many standard deviations you are from the norm user. –  Incognito Sep 23 '10 at 16:41
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The distribution on Stack Overflow reputation is neither Normal nor Poisson nor Lorentzian, so while the standard deviation from the mean can be defined it does not have a obvious interpretation –  dmckee Sep 23 '10 at 16:53
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Where are these users with 1,000,000 (1000k) rep? –  raven Sep 23 '10 at 16:55
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Is there any chance we can get some terminology in here that's English, as opposed to Greek or French or Dutch? If not, some explanations, perhaps? –  Grace Note Sep 23 '10 at 16:55
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@Grace Note, he is not talking Dutch else I would understand. ;-). –  Toon Krijthe Sep 23 '10 at 19:11
    
@Gamecat Unless I am mistaken, the nomenclature of Lorentzian distribution comes from a Dutch physicist. –  Grace Note Sep 23 '10 at 19:19
    
@Jon Seigel that's exactly what I'm asking, but rather than showing percentage distribution represent it as the SD. –  Incognito Sep 23 '10 at 19:34
    
@Grace Note, thats right: en.wikipedia.org/wiki/Hendrik_Lorentz, sorry thought your comment was about the question and there wasn't a Dutch word (with no meaning in english) there. –  Toon Krijthe Sep 23 '10 at 19:36
    
Updated to make sense. –  Incognito Sep 23 '10 at 19:52
    
@Grace Note - Bais non! J'aime [ les poissons ](youtube.com/watch?v=XuuEDDyvzuE)! –  Peter Ajtai Sep 24 '10 at 2:49
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2 Answers

Standard deviations describe points in a specific type of distribution, a normal distribution.

Standard deviations cannot be used to describe (untransformed) scores on Stack Overflow, since scores on Stack Overflow do not follow a normal distribution.

How many standard distributions away from the "average" a point is basically describes how different the point is from that "average." This "average" is not really meaningful in the sort of one-tailed distribution that Stack Overflow scores have:


alt text


You could try some transformations...

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you should invert the x-axis, you suggest Jon Skeet has so little rep that even new users outrep him –  Tobias Kienzler Sep 24 '10 at 10:36
    
...or do you want to suggest Jon Skeet's rep finally overflowed? –  Tobias Kienzler Sep 24 '10 at 10:41
    
@Tobias - Whoops... done. –  Peter Ajtai Sep 24 '10 at 16:06
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Jon Skeet is not an outlier. All the other points are outliers. –  mmyers Sep 24 '10 at 16:47
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Aside: The standard deviation (or some similar "widthy" number) is actually meaningful on a number of peak-like distributions (not just the Gaussian). Now, time-averaged reputation velocity might have a peaked character for which a width number makes sense. Though the rep-cap may cause a discontinuity in the shape. –  dmckee Sep 24 '10 at 21:55
    
@dmckee - Maybe, but probably only if you discard velocities of 0. –  Peter Ajtai Sep 24 '10 at 22:21
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This would be awesome... if you exclude the many many users with <12 rep.

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It's Definitely not a normal distribution. –  C. Ross Sep 23 '10 at 20:34
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Not just <12. Especially with the new Stack Exchange Network sites, people who have done naught but association to get 101 are also a thing to watch out for. However, it's a good question how to differentiate them from people who started at 1 and actually worked up to get 101 reputation... –  Grace Note Sep 23 '10 at 20:37
    
You would definitely need to run some sort of transformation. –  Peter Ajtai Sep 24 '10 at 2:42
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