There are people who post their first drafts. I am not one of them.
I'm probably more on the OCD end of the rewrite spectrum. More of a gardener than an architect in my approach, I'll keep trying things until I get that "Ahhhhh" feeling, with a tendency to go triple-000 grit wordsmithing in the final polish. (And I have no compunctions against tweaking a chapter after it's posted, either.)
I have to ask if you're making a distinction between a 'rewrite' — involving substantial changes to the plot like throwing out the opening chapter and doing something entirely different— and a 'revision,' where you stick to the original idea but keep fiddling until you get it to work.
By that definition, I've only done a "rewrite" a handful of times out of 300 or so pieces. Every time it's happened it's been after I felt the story was really fighting me (or, when I had an editor or take-charge beta, when they told me the opening didn't work at all and to come up with another.) In those cases I set the story aside until I saw more clearly what the problem was.
As for "revisions" ... I used to do a "Save As" and number my document after every writing session that involved revisions, but after realizing how scarily high those numbers were getting (in one case over 100 :p), I made myself write in GoogleDocs and revise freely until the chapter is ready for beta. I tend to do several passes through a fic, too; the first to block out the narrative and add rough unpunctuated dialog, the second to add description and tidy punctuation, the third to tweak characterizations. Some fics/chapters go though maybe 1 or 2 more passes to make sure everything flows well and that the transitions and nuances are smooth. ~ And then I always do a re-read whenever I get a review, and almost always find some rough edge to smooth over.
tl;dr: on average, 3-10.