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Is there a way to get "global" statistics on one's own MSE posts?

I'm particularly interested (if for no good reason) in total length - e.g. what's the average length of an answer I post? - but more generally, I don't know how to get any sort of overall data beyond the very coarse (e.g. how many answers/questions and how many of a given reputation - and even that latter I don't know how to do gracefully).

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As suggested in the comments, some statistics might be available using SEDE. In particular, you can see what data about the posts are available in Database schema documentation for the public data dump and SEDE. (Keep in mind that data in SEDE are only updated once a week, so they might be slightly behind the live stats. If you want to see similar stats on other sites, you can use "switch sites" in SEDE to change the site for which you are running the stats.)

Let's collect here some examples of queries which might be related to what the OP asks about:

Also running some queries over multiple sites at the same time might be interesting:

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  • $\begingroup$ I have made this answer community wiki so that other users can add other queries if they have something interesting to add. (And also since I was not sure what the OP means by "any any sort of overall data" which sounds a bit vague - perhaps the OP will clarify what he had in mind.) $\endgroup$ – Martin Sleziak May 15 '19 at 3:38
  • $\begingroup$ Thanks to rene for including some interesting queries. I will also explicitly mention that if you need some help with composing a SEDE query, you can also try to ask in the SEDE chatroom. $\endgroup$ – Martin Sleziak May 16 '19 at 4:46

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