Observations on the odds of becoming a tenure-track professor

The odds of surviving 'Hell Week' during the Basic Underwater Demolition / SEAL training? About 33%.

Classes typically lose around 70–80% of their trainees, either due to DORs (drop on request) or injuries sustained during training, but it is not always easy to predict which of the trainees will DOR during BUD/S. Winter class drop out rates are usually higher due to the cold. SEAL instructors say that in every class, approximately 10 percent of the students simply do not have the physical ability to complete the training. Another 10–15 percent will definitely make it through unless they sustain a serious physical injury. The other 75–80 percent is 'up for grabs' depending on their motivation. There has been at least one BUD/S class where no one has completed the program. Most trainees are eliminated prior to completion of Hell Week, but trainees will continue to DOR in the second phase or be forced to leave because of injuries, or failing either the diving tests or the timed runs and swims.

Pen y Fan -- looks a little harder than a candidacy exam, maybe.
Credit: Wikipedia

Odds of surviving from the Special Air Service's (the UK's most prominent special operations unit) hill phase selection? About 15-20%.

On arrival candidates first complete a Personal Fitness Test (PFT) and a Combat Fitness Test (CFT).[nb 5] They then march cross country against the clock, increasing the distances covered each day, culminating in what is known as the Fan dance: a 14 miles (23 km) march with full equipment scaling and descending Pen y Fan in four hours. (at right)[73] By the end of the hill phase candidates must be able to run 4 miles in 30 minutes and swim two miles in 90 minutes.[73] ...Typically, 15–20% of candidates make it through the hill phase selection process. 

Odds of getting a tenure track assistant professor position at a US university? From folks on Twitter (btw, these are mostly non-chemists talking:

@labroides: more news on the Irvine position, "only" 185 applicants, 5 selected for short list.
@sciencegurlz0: That is similar to the UT-Arlington jobs that I applied for. Both had approx 150 applicants. :(
@fianros:  That's better than the 600 applicants for TT chem/biochem positions past couple years.

Now I'm being tricky here, in that there's wild selection bias in special operations selection. Militaries will usually pre-announce their minimum physical standards (and pre-screen their candidates) to ensure that they're not wasting their time with the total number of applicants. Universities requesting applicants for tenure track positions, of course, seem to advertise for anyone with a pulse and a Ph.D.

It is my opinion that the classic "short list" of the 5 or 6 interviewees should be really called a "really short list", with the true "short list" being the various applicants that actually have a real shot at the professor position to begin with. It's my guess that the maximum number of people that a search committee can seriously consider hiring (i.e. applicants given more than a cursory glance) is probably in the 40 to 50 candidate range.

In some sense, applying for a tenure-track position is probably more like running for office or winning a golf tournament than passing an arduous test of physical ability and mental toughness.  In the end, there can only be one -- and that makes things much more daunting for the applicant.