Yet networking, in one form or another, is how many if not most people land their jobs. Perhaps a poll is in order here?
I suspect your definition of what constitutes "a network" is what makes the odds you calculate look like a search for extraterrestrial intelligence. It's nothing like that.
If we did a poll right here, I would wager that more people got their current position through a third party lead or inside contact than through submission to an online job application.