I love to read books, mostly business books, and I’m usually reading several different books at the same time. Right now, one of the books I’m reading is “Black Box Thinking” by Matthew Syed. In chapter two, Syed tells a story about a famous mathematician Abraham Wald, whose research during World War II saved the lives of dozens of brave airmen.
The Statistical Research Group (SRG), where Wald spent much of World War II, was a classified program that assembled the intelligence of American statisticians to the war effort — something like the Manhattan Project, except the weapons being developed, were equations, not explosives.
Working on behalf of the military, they were given the job of analyzing a whole range of issues, such as the most effective pattern of torpedo launching and the aerodynamic efficiency of missiles.
One of the key projects Wald was given, was studying bomber aircraft. American bomber pilots were considered remarkable and brave men, because at one point during the war, the probability of a pilot surviving a tour of duty was slightly better than fifty-fifty.
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.
The military came to the SRG with some data they thought might be useful. When American planes came back from engagements over Europe, they were covered in bullet holes. But the damage wasn’t uniformly distributed across the aircraft. There were more bullet holes in the fuselage and wings, not so many in the engines.
The military officers saw an opportunity for efficiency; you can get the same protection with less armor if you concentrate the armor on the places with the greatest need, where the planes are getting hit the most. But exactly how much more armor belonged on those parts of the plane? That was the answer they came to Wald for. Ironically though, the answer they got was not at all what they expected.
Wald’s insight was simply to ask: where are the missing holes? The ones that would have been all over the engine casing, if the damage had been spread equally all over the plane? Wald was pretty sure he knew. 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 at all. Whereas a large number of planes returning to base with a Swiss cheese 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.
You’d have planes coming back with bullet holes all over the wings, the fuselage, the nose — but none at all on the engine. The military analyst had two options for explaining this: either the German bullets just happen to hit every part of the plane but one, or the engine is a point of total vulnerability. One-shot to the engine was enough to bring the whole airplane down. Both stories explain the data, but the latter makes a lot more sense. The armor goes where the bullet holes aren’t.
I found this to be a very facinating story, but it also made me think. Why didn’t the military officers see this? I suspect they were not idiots, but just blinded by the data. This story makes me think about my own business and my own life. What am I blinded by that I’m just not seeing? What information am I missing?