The bomber-armor chart that pointed at the wrong parts

Plot the bullet holes on planes that made it home and the fuselage lights up while the engines look safe — so you armor the fuselage. The planes shot through the engine never came back to put a bar on the chart.

A. Wald, Statistical Research Group (1943); figures popularized by Jordan Ellenberg, “How Not to Be Wrong” (2014), 1943Added July 8, 2026

Bar chart titled “Where our bombers are getting hit” showing bullet holes per square foot on returning planes — rest of plane 1.80, fuselage 1.73, fuel system 1.55, engines 1.11 — with a red bracket over the two tallest bars labelled “add armor here” — Exhibit A — as published

The same four bars re-read Wald’s way: the engines bar, lowest at 1.11, is highlighted in blue with an “armor here” arrow, because the planes hit in the engine were shot down and never returned to be counted — Exhibit B — the honest redraw

The claim

The engines are the safest part of the plane — they take the fewest hits — so armor belongs on the fuselage, where the bullet holes actually cluster.

The trick

Every bar is measured on planes that came back. That sample has already thrown away its most important members: the aircraft hit in the engine that never returned to be counted. So the engine bar is short not because engines rarely get hit, but because a hit there tends to be fatal — the evidence removes itself from the chart. Reading the tall bars as “where the danger is” gets the lesson exactly backwards; the short bar is the danger. This is the story behind Abraham Wald’s WWII work for the Statistical Research Group, where he argued the Navy should reinforce the areas of returning planes with the least damage.

The honest version

Ask what a data point had to survive to appear on the chart. Here, a plane had to make it home — so the honest read is to armor the gaps in the survivors’ damage, not the clusters. Wald’s recommendation was to reinforce the engines, precisely because so few damaged-engine planes came back. (The per-square-foot numbers here are the illustrative figures from the popular retelling, not Wald’s raw memoranda, which worked in probabilities of a plane being downed — but the reasoning, and the counterintuitive answer, are his.)