If I am reading the article correctly, they claim that they should usually be able to repair in less than an hour in the case of disk failure.
Thus the probability of losing 50 (or whatever their N-K value is) disks within an hour is how you get 27 nines of durability.
Of course, the probability that one of your software engineers introduces a durability bug is WAY more likely than those disks experiencing a coordinated failure.
Or say, the probability that a terrorist organization targets your datacenters. Even if those odds are one in a billion, that's still not even close to 27 nines.
We've very strong believers that an effective replication strategy is just table stakes and that from there the real risks to durability are the "black swan" events that are much harder to model.
I gave at talk at Data@Scale recently where the main premise is about "Durability Theater" and how to combat it in a production storage system. In case you're interested: https://code.facebook.com/posts/253562281667886/data-scale-j...
No criticism of Dropbox here; they know that number is just math games, too. I'm just putting some numbers on how true that is. Because I find tossing about big numbers like this as if they mean something a bizarre, nerdy sort of fun.