Abraham Wald and the Missing Bullet Holes

This Medium article is an excerpt from a book titled “How Not to be Wrong,” by Jordan Ellenberg. He discusses Abraham Wald, and the story of the missing bullets – my first introduction to Wald, and Wald’s particularly gifted insight with his work during WWII.

The article is a great, compelling read. The writing just pulls you in:

So here’s the question. You don’t want your planes to get shot down by enemy fighters, so you armor them. But armor makes the plane heavier, and heavier planes are less maneuverable and use more fuel. Armoring the planes too much is a problem; armoring the planes too little is a problem. Somewhere in between there’s an optimum. The reason you have a team of mathematicians socked away in an apartment in New York City is to figure out where that optimum is.

Mapping the damage done to planes that returned from battle, researchers looked at the bullet holes to try to determine where they should apply additional armor. But when Wald looked at the damage, he deduced that the armor shouldn’t go where the bullet holes are; the armor should go where the bullet holes aren’t.

The missing bullet holes were on the missing planes. The reason planes were coming back with fewer hits to the engine is that planes that got hit in the engine weren’t coming back. Whereas the large number of planes returning to base with a thoroughly Swiss-cheesed fuselage is pretty strong evidence that hits to the fuselage can (and therefore should) be tolerated. If you go to the recovery room at the hospital, you’ll see a lot more people with bullet holes in their legs than people with bullet holes in their chests. But that’s not because people don’t get shot in the chest; it’s because the people who get shot in the chest don’t recover.

Re-reading this article again now, as I’m writing up this post. Really tempted to get Ellenberg’s book now.

The Turn: Elegant, Mysterious and Deceptive
Mathematics During a Fire
Math Graf

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