Tune into weak signals in a world of data dominance

World War II saw the full fury of air power in battle, first exercised by Axis forces and then by the Allies, culminating in American B-29 bombers dropping atomic bombs on Hiroshima and Nagasaki.

- PAVAN SONI

But before that, as the US sent warplanes behind enemy lines in Europe, most were shot down by German tanks and air fighters. A pressing need was to armour these planes. But this made these craft heavy. It was a classic optimization problem: How much of the plane should be armoured?

In came Abraham Wald, a mathematician working at the Statistical Research Group of Columbia University. His first task was to call in data, specifically on the surviving fighters’ bullet holes, which was duly presented to him. On average, the plane’s engine had 1.11 bullet holes per square foot, the fuselage 1.73, fuel system 1.55 and rest of the body 1.8. The military personnel were convinced that precious armour must be used for the worst hit areas, namely the fuselage and rest of the plane; the engine didn’t seem to be that badly hit. But after one glance at the data, Wald famously declared, “The armour doesn’t go where the bullet holes are. It goes where the bullet holes aren't: On the engines.” His argument was that the most relevant data was what the numbers had missed: the bullet holes on missing planes, the ones that did not return. After all, planes with fewer engine hits had survived. Thus, he toppled conventional thinking and saved the day for the Allied powers.