Hidden History: Abraham Wald and a lesson in survivorship bias

Mon Mar 11, 2019

Image courtesy of Wikimedia Commons


Many of the Hidden History articles that have centered around humanity’s various wars have given undue attention to the frontlines of combat, whether it be the beloved dog that went to war or the British officer that refused to fight without his sword. However, it is important to note that just as much of a country’s victory in a war is due to the people operating behind the frontlines. While many stories (including many of the ones featured in this column) focus on the frontlines and battlefields of conflict and the tales of heroism and triumph that occur on them, this week’s Hidden History looks at another, equally important wartime setting: the quiet office of a mathematician.

Abraham Wald was born in October 1902 in the city of Cluj, located in Austria-Hungary (now known as Romania). A natural-born mathematician, Wald graduated from the University of Vienna with a Ph.D. in mathematics in 1931. However, Wald found difficulty finding a university position due to the discrimination he faced for his Jewish faith. This discrimination only got worse upon the Nazi invasion of Austria in 1938, prompting him to flee to the U.S.

In the U.S., Wald received an invitation to join the Cowles Commission for Research in Economics as part of the Statistical Research Group (SRG). As part of the SRG, Wald applied his vast mathematical and statistical knowledge toward solving various wartime problems throughout World War II (WWII).

One of the most notable problems that Wald helped solve (and the focus of today’s article) concerned the placement of armor on American bomber aircraft sent to campaigns over Europe. The SRG was faced with the task of increasing aircraft survivability without compromising flight range or maneuverability. Thus, the aircraft could not be covered entirely with armor. Instead, the SRG had to prioritize the most important parts to place armor plating on.

The initial approach of the SRG was to look at returning American B-29 bombers and note where they had taken the most fire. The SRG noted that the bombers they observed had fuselages (main bodies) riddled with bullet holes, taking almost twice as many hits as the engine platforms.

Thus, the SRG made a simple decision: apply more armor to the fuselage. After all, the crew were housed inside the fuselage, so adding extra protection here seemed to make the most sense.

However, Wald was the one to point out that this approach was completely wrong. He instead suggested that extra armor should be placed in all of the places that the SRG noted no bullet holes appeared. Why is this? It was because the only planes that the SRG looked at were the ones that actually survived out in the field, and they were therefore a sample showing the exact opposite end of the data pool for the problem at hand.

In other words, the planes that the SRG observed were actually able to continue flying despite having their fuselages riddled with bullets. If the SRG really wanted to place armor in ways that would save more American airmen, they should instead place extra armor everywhere EXCEPT for the fuselage. Aircrafts weren’t returning with bullet holes in their engines because they couldn’t; they were shot down and crashed in the European countryside.

Wald’s recommendations were adopted, and this basic premise continues to be used in applying armor to American aircraft. Wald’s story presents a textbook case study in survivorship bias: the logical error of only concentrating on a sample that survives or passes some kind of process and ignoring those who don’t. This form of bias can lead to optimistic beliefs and incorrect assumptions because failures are ignored, and in this case, the failures were most important to look at. Luckily, Wald was able to think beyond the data available and understand the full context of the situation, saving thousands of lives in the process.



Appears in
2019 - Spring - Issue 7