Seems like the list usually has about 500 openingsHere's my stab in the dark that I have been formulating in my head for a while:
Schools seem to get 100-300 applications per opening
Postdocs seem to apply to 10-20 opening each
so estimate 10x more applicants than openings
the talent pool seems to have about 5000 people looking for a job
Each year, about 2,500 people graduate with a Ph.D. in chemistry; in 2015, it was 2,675 according to the Survey of Earned Doctorates. Of those, 826 (30%) got a postdoc and 478 (18%) got jobs. (Of the 478 who got jobs, 70% went into industry and 22% went into academia.) The rest (936 people) were still looking for a position, either in industry or academia. I am going use 2015 as my model year - this is probably wrong.
Assumption 1: of those remaining as Ph.D./not-postdocs, 60% apply for industrial positions, 40% apply to academic positions.
Assumption 2: of postdocs remaining, 50% apply for academic positions.
Assumption 3: each year, 20% of remaining postdocs for each year are hired for academic positions
Assumption 4: postdocs drop out of the running after 4 years.
Assumption 5: we're not counting international Ph.D.s who have come to the US to do postdocs yet
So it quickly becomes a question of "how many postdocs are remaining on the market after X number of years?" And so through quick math, my guesstimate is 2430 applicants at any one time (number of graduate students applying + 2016 postdocs + 2015 postdocs + 2014 postdocs + 2013 postdocs.) After you add in more grad students and all the international postdocs, etc., I bet you wander into the 3000-3500 range, but that's just a guess.
Readers, what do you think?