I’m not sure they are so rare. They are constantly being born all around us.
Take Ycombinator as cohort / case study. It picks, twice a year, the best 100+ start-ups that apply. It screens them remotely, and then makes a quick 5–10 minute decision after a face-to-face. This is a pure process, a funnel, folks.
And of each class — several always are amazing and produce huge returns (Stripe, AirBnB, DropBox, Twitch, Cruise etc. etc. etc.). And many more are still substantial successes with strong exits (OMGPop, Heroku, etc etc).
Every. Single. Class. Or at least very close to it.
So … it’s not so much that they are rare. They are just rare in certain, in most, cohorts.
If you have amazing founders (really amazing, not pretend amazing), committed for 7–10 years, that can ship great products AND get customers, AND that are pointed in a good direction … they have a pretty good shot at getting somewhere.
The odds are misleading.