The Bullet Holes That Didn't Matter

Kevin Drum waxes counterintuitive:

Back during World War II, the RAF lost a lot of planes to German anti-aircraft fire. So they decided to armor them up. But where to put the armor? The obvious answer was to look at planes that returned from missions, count up all the bullet holes in various places, and then put extra armor in the areas that attracted the most fire.

Obvious but wrong. As Hungarian-born mathematician Abraham Wald explained at the time, if a plane makes it back safely even though it has, say, a bunch of bullet holes in its wings, it means that bullet holes in the wings aren't very dangerous. What you really want to do is armor up the areas that, on average, don't have any bullet holes. Why? Because planes with bullet holes in those places never made it back. That's why you don't see any bullet holes there on the ones that do return. Clever!