Jordan Ellenberg’s “How Not to Be Wrong: The Power of Mathematical Thinking” just went up on my summer reading list after reading this excerpt from a review of the book:
“During World War II, the U.S. military was trying to optimize the armor plating on its airplanes. Officials noticed that the bullet holes in planes returning from combat in Europe followed certain patterns: There were more per square foot in the fuselage than in the engine section. They figured that they therefore needed to add more protection to the fuselage, but wanted help in determining how much more — to balance the extra protection against the loss of fuel efficiency and maneuverability.
The military took this problem to Abraham Wald of the Statistical Research Group. Wald, who spent most of his career as a statistics professor at Columbia University, came back with a surprising answer: Add no plating to the fuselage. Instead, add it to the engine area.
Wald’s reason was that unless the enemy was for some odd reason successfully targeting the fuselages, the bullet holes on the returning planes showed where the planes could withstand attack and still survive. The paucity of bullet holes on the engine casings of the returning planes suggested that hits to that area tended to bring down the plane. Returning planes, in other words, were a biased sample of the planes that were attacked. The lesson: Think about where the bullet holes aren’t.“