One thing I learned from my colleague Julio Martinez last week was that an average of 27.5 shows opened every week last year. Read another way, that was 1,430 shows total. His source, if I recall, was Lynne Heffley of The Times, who edits the theatre listings. No word on the geographical boundaries under consideration, or how many of those shows included short-run special presentations. Still, that's a nice fat number.
My colleague Dany Margolies, upon hearing that number, ventured that on average she sees about "2.5 shows a week." I'd love to catch one of those .5 shows with her some time.
CORRECTION: Lynne Heffley reached me to say that she wasn't the source for Julio's numbers; she stopped being listings editor at The Times midway through last year. I did reach Julio to confirm the numbers, however, and his source was someone at the "Thursday Calendar" desk.