I just had a thought: I gather that when there's a change of editors at a major magazine, it's fairly common for writers to resubmit stories that the previous editor rejected, in case the new editor might like those stories better.
I would guess that Gardner has been rejecting an average of at least 500 stories a month for at least the past 15 years, to pick conservative numbers. (I don't know quite when Asimov's started getting a high volume of submissions, but I vaguely recall getting the "850 submissions a month" rejection letter when I was in college, in the late '80s. Maybe it said 800 in those days, I'm not sure.)
That's a likely minimum of 90,000 stories, and probably quite a lot more.
Now, surely a large number of those stories ended up being published elsewhere. Let's even guess that 400 of those 500 a month ended up being published elsewhere, though that seems unlikely. (Rich Horton reads about 125 published sf stories a month; even if there are twice that many in small-press markets that Rich doesn't read, that's still a bit short of 400.)
That leaves at least 100 stories a month that Gardner's been rejecting that haven't found homes elsewhere. Which means that there are at least 18,000 stories out there that Gardner has rejected over the years that remain unpublished. (With less conservative guesses at numbers, it comes to more like five times that number.)
I hope that Sheila Williams doesn't receive all 18,000 of them in her first month as editor. Even if she only receives a tenth of those (on top of the regular volume of Asimov's subs), that's an awful lot of stories.
Yeah, yeah, there are plenty of ameliorating factors I'm not mentioning. My real point is: I suspect Ms. Williams will be receiving an awful lot of stories in her early days as editor.