A big part of the "DARPA formula" that doesn't seem to get much treatment here is
consistency. DARPA is going to spend a few billion this year, and it spent a few billion last year, and it spent a few billion twenty years ago, and you can feel confident they'll spend a few billion next year. That means that if an academic researcher or similar can position their lab in an area that DARPA likes, they have a good shot at reliable funding for the length of a career. With all the economic uncertainties around research, this is
tremendously appealing and will cause a lot of smart people to re-orient their entire research programs around DARPA-friendly subjects [0]. A funding organization that might disappear in a few years, by contrast, will get plenty of grant applications, but won't attract nearly the same level of researcher devotion.
(As a side note, I want to pull out a quote I thought was really nice, hidden a ways in:
"DARPA funds wacky things that go nowhere. DARPA programs have a 5—10% success rate and have included things like jetpacks, earthworm robots, creating fusion with sound waves, spider-man wall climbing, and bomb detecting bees. You can’t cut off just one tail of a distribution.")
[0] Which may, incidentally, go a ways towards explaining why DARPA heads describe their projects as "idea-limited"