No one has an actual number, but I expect it's A LOT.
The best thing folks can do is to NOT rely on just dropping their resumes into some anonymous web-based corporate application system. Instead, it's much better to network and to use your contacts (previous co-workers, folks you know, family, friends-- anyone really) to get get leads and bypass HR drones entirely or as much as possible.
The other thing that, IMHO, works really well is to specialize. Positioning oneself for "hot" in-demand jobs, ironically, just ends up putting people into an ocean of competition where each job has hundreds of equally qualified people going after it. That's awesome for employers who can then be absurdly picky, but it's terrible for candidates.
The way many technical candidates shoot themselves in the foot before even getting started is they fail to network and fail to specialize (or target their search properly). They're often honest to a fault and go up against competition that is unscrupulous. There's a reason why so many candidates completely flunk fizzbuzz.