Always Invert

“Invert, always invert”

It is a phrase coined by the mathematician Carl Jacobi and made famous by Charlie Munger. When you want to solve a difficult problem take the inverse.

It is the first thing that came to mind when reading about survivorship bias and where to armor allied bombers during WW2.

In World War 2 the allied nations had a problem, they were losing too many aircraft. At the most dangerous times of the war the odds of coming back were a coin flip.

The Navy decided that the best solution would be to add armor to the planes, but could only add so much, and didn’t know where to put it. They took this question (how much armor to add and where) to Abraham Wald, a mathematician working on the war effort. Wald applied his models to places where the plane hadn’t been shot.

This took everyone aback. Why armor where the planes hadn’t been hit?

Wald reasoned that if some planes were able to return after being shot in certain places, other planes had not been able to return after being shot in the inverse of those places. Wald found the survivorship bias in looking at only the planes that made it back.

Source:

Survivor Bias in WW2 Airplanes, NBA players, & Mutual Funds (The Waiter’s Pad)

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