Today's statistical fallacy (slightly redacted by editor) comes from Joel on Software:
Everyone thinks they're hiring the top 1%. Martin Fowler said, "We are still working hard to hire only the very top fraction of software developers (the target is around the top 0.5 to 1%)." I hear this from almost every software company. "We hire the top 1% or less," they all say. Could they all be hiring the top 1%? Where are all the other 99%? General Motors?
When you get 200 resumes, and hire the best person, does that mean you're hiring the top 0.5%? Think about what happens to the other 199 that you didn't hire. They go look for another job.
The entire world could consist of 1,000,000 programmers, of whom the worst 199 keep applying for every job and never getting them, but the best 999,801 always get jobs as soon as they apply for one. So every time a job is listed the 199 losers apply, as usual, and one guy from the pool of 999,801 applies, and he gets the job, of course, because he's the best, and now, in this contrived example, every employer thinks they're getting the top 0.5% when they're actually getting the top 99.9801%.
I'm exaggerating a lot, but the point is, when you select 1 out of 200 applicants, the other 199 don't give up and go into plumbing (although I wish they would... plumbers are impossible to find). They apply again somewhere else, and contribute to some other employer's self-delusions about how selective they are.
This might explain some other phenomena I've heard of, such as the "slush heap" of inconceivably awful stories received in the mail by every fiction publisher that accepts unsolicited manuscripts. When a story is good enough to be published, it's accepted and removed from the system. Otherwise the hapless author sends it to another publisher!
Perhaps most novice writers aren't quite as dreadful (on average) as editors seem to believe? Editors will disproportionately encounter the work of novice writers who are not only awkward, but so incompetent as to be unaware of their own incompetence, and so proud that they can't take a hint.
PS: Two other areas where this might apply: Students who apply to your program/department for admission. And, grant proposals.
PPS: Robert Scarth comments, "This might also explain why some women often think that 'all men are bastards' - there are a few cads out there in continual circulation and with no intention to settle down, whereas men with honourable intentions have much fewer relationships, and settle down more quickly."