The planes that came back were lying

In the middle of the Second World War, the US military studied its bombers after every mission and mapped where the bullet holes clustered: fuselage, wings… The obvious plan was to reinforce the most riddled areas.

The mathematician Abraham Wald, of Columbia's Statistical Research Group, turned the map on its head: the armour should go exactly where the returning planes had no holes. The missing hits — engines, cockpit — weren't missing because the enemy never struck there, but because the planes hit in those spots never made it back to be counted.

We call it survivorship bias: drawing conclusions from the survivors alone. And today it inflates, for instance, the apparent returns of investment funds: the bad ones get closed or merged away, vanish from the statistics, and the average you're shown is computed only from those still alive.

Before you admire a survivor — a fund, a company, a guru — always ask about the ones missing from the picture. That's usually where the real information is.