With regards to reputation on Stack Exchange, I did a [very short analysis](https://meta.stackoverflow.com/a/357336/4751173) last year on the distribution of reputation on [Stack Overflow](https://stackoverflow.com). Thanks to the [Stack Exchange Data Explorer](https://data.stackexchange.com), I can easily run the same analysis for [MathOverflow](http://data.stackexchange.com/mathoverflow/query/734355/reputation-distribution-log-log-scale#graph):

[![enter image description here][1]][1]

<sub>x-axis: logarithm of reputation; y-axis: logarithm of number of users; logarithms are base-10, so the 2.0 on the x-axis corresponds to $10^2 = 100$ reputation and there are about $10^{4.25} \approx 18000$ users with this much reputation.</sub>

Some interesting points, caused by 'oddities' in the Stack Exchange reputation system:

1. are the many no-activity users with just 1 reputation
2. the sawtooth until x = 2.0 (±100 reputation) looks strange, but makes sense once you realize how hard it is to get a total reputation of 2 (1 question upvote followed by 2 downvotes).
3. a peak on and just after x = 2.0, corresponding to 101 reputation; these are mainly users from other Stack Exchange sites who have the [association bonus](https://meta.stackexchange.com/q/141648/295232) on Math Overflow plus some optional minor additional activity.
4. the peak at 300 reputation is also caused by the association bonus. Users with 200-300 reputation either don't have other accounts on the network, or have another site where they have more reputation.

Feel free to [fork](http://data.stackexchange.com/mathoverflow/query/fork/734355) the query to experiment yourselves with the data.

  [1]: https://i.sstatic.net/ZnvcM.png