OK, one more try at interpreting Matthew D. LaPlante's sentence
It is rare, Hamblin knows, for these kinds of situations to end better than they normally do.
My first idea was that "better" was being taken to imply "good", whereas the situations in question almost always end badly, so that even if about half the outcomes are literally better than average, few of them would qualify as good enough to be called "better". The next idea, due to Kenny Easwaran and some other readers, was that the author intended some kind of de dicto interpretation. As another option, Fernando Pereira suggests that "better" here means something like "significantly better" or "perceptibly better":
The Hamblin sentence could be taken to be about the rarity of large deviations from the norm. Let X be the random variable "outcome of these situations". Then, what Hamblin knows is
P(X - EX >= ε) <= δ
where ε is an appropriate (maybe just discernible) difference in outcomes, and δ is an appropriately small probability, and P and the expectation E are over the distribution of "these situations"). The relationship between ε and δ is the subject of many well-known theorems. For example, in the one-tailed Chebyshev inequality, δ = 1/(1+ε2/Var(X)).
This makes a lot of sense.
Anyhow, LaPlante's reporting from Iraq for the Salt Lake Tribune is some of the most consistently interesting stuff I've seen. In addition to the piece on Sgt. Ozro Hamblin, there's another on non-military interpreters. His most recent report deals with that "hillbilly armor" we all heard about during the last election campaign -- guess what, some of it's still there. And you should definitely read his Oct. 10 essay on sex in the military.
Posted by Mark Liberman at October 23, 2005 01:14 PM