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What distribution does the reputation points per user follow on math.SE (or on entire stackexchange)?

Is there a mathematical explanation/model of it?

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  • $\begingroup$ Can a query be made to get that distribution? Or at least the raw data? $\endgroup$ – Raskolnikov Mar 28 '12 at 10:55
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    $\begingroup$ OK, just made a query myself and it seems the data can be stored as a CSV-file. $\endgroup$ – Raskolnikov Mar 28 '12 at 11:02
  • $\begingroup$ @LLLLL What have you tried? :-) $\endgroup$ – user21436 Mar 28 '12 at 11:17
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    $\begingroup$ Related: When the site was much younger I tested user reputation against Benford's Law. The results are here. $\endgroup$ – Mike Spivey Mar 28 '12 at 20:36
  • $\begingroup$ This is a question that is appropriate on both Math.SE and Meta.Math.SE. $\endgroup$ – Abhimanyu Pallavi Sudhir Jul 20 '13 at 14:58
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Here's a histogram with 20 bins of the data contained in the CSV file. On the x-axis, I have plotted the logarithm base 10 of the reputation scores. We can see that many users just come here to ask one question and then never get much beyond 100 points (people who also use other SE's) or 1 point (throwaway accounts). Hence the peaks around 2 and 0. So we should filter these two peaks and look at the residual data to see if there's some well-known distribution emerging. I expect something with a long tail, hence the need to use the log-transformation.

Histogram

And here's the query I used to fetch the data.

Here's an extra plot of the rank-size distribution of the tail of the previous distribution. The slope of the line is about -0.92.

Rank-size distribution

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    $\begingroup$ That small circle at the bottom right point in the second graph... that's Arturo, right? $\endgroup$ – Asaf Karagila Mar 28 '12 at 20:32
  • $\begingroup$ Yes, that's him. And the second point on the left from that one is Arturo and Qiaochu. ;) $\endgroup$ – Raskolnikov Mar 28 '12 at 20:47

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