How The Allies Used Math To Save Bomber Crews During WWII

When retelling stories of war, our focus tends to fall where the physical action was. Tales of battlefield bravery have been around for as long as there has been language and battlefields, but securing victory over a powerful foe requires more than the strength of will and courage under fire. Often, it takes the calm, calculating mind of strategic leaders, the tireless efforts of scientists and researchers, and as was the case in the skies above World War II... the unusual approach of an Austrian mathematician.

Abraham Wald was born in Austria-Hungary in 1902, and by 1931, he had completed his Ph.D. in mathematics. However, despite possessing a gifted scientific mind, Wald couldn't find work in his home country upon his return. The difficulty? It was 1931, and Wald was Jewish.

By 1938, the Nazis were invading Austria, and Wald and his family were on their way to the United States, where Wald had no trouble securing a job at the Cowles Research Commission in Economics, and then with the American government assisting with the war effort.

math save bomber crews during wwii — Abraham Wald.
Photo Credit: Wikimedia Commons

Wald quickly proved to have a powerful analytical mind, making a name for himself with the U.S. government's Statistical Research Group (SRG) where he worked on classified programs despite his status as a "potentially hostile immigrant". Just as his Jewish heritage made him a pariah in Austria, his Austrian heritage made Wald a bit of an outcast in Uncle Sam's ranks. He wasn't even allowed to look at his own equations after submitting them, as the programs Wald worked on were classified. Wald's secretary was even known to joke that her job was to yank Wald's pages away as soon as he finished writing them "for the sake of national security".

Despite this looming prejudice, Wald thrived in his role as a mathematician for the Allies, contributing to multiple programs over the years and securing a place in history thanks to his groundbreaking work in "survivorship bias".

Allied forces were feverishly working on ways to help their B-29 bombers survive anti-aircraft fire, but knew that limitations on weight and available resources would bar them from adding armor to the entirety of the aircraft. So they began collecting data on returning B-29s in hopes that the data would eventually produce a working theory. Soon enough, it did.

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Officials took note of how the B-29s that made it back were often riddled with holes in specific areas. Some of these bombers were even described in official documents as looking like "swiss cheese," but the heaviest concentration of holes were always all over the aircraft's fuselage. By the time they had translated their observations to hard data, they had confirmed that the fuselage and wings of the aircraft took rounds at nearly twice the rate of the aircraft's engines.

The data seemed to be pointing at a clear answer to their problem: if the fuselage was taking the brunt of the of damage, they should add armor to that portion of the aircraft. After all, it housed all of the plane's internal systems and its crew, it made perfect sense that taking so much fire to the fuselage must be what was bringing these bombers down.

Wald, however, knew immediately that placing armor on the fuselage of these bombers wasn't going to solve the problem. He asserted instead that additional armor needed to be placed on the parts of the aircraft that had the smallest number of recorded bullet holes, rather than the highest. His assertion, and the premise of survivorship bias, was basically that these airplanes could survive taking a great deal of fire to the wings and fuselage because they were making it back riddled with holes all over both. Instead, Wald posited, it's the places they didn't see holes that couldn't handle direct fire.

Wald believed that these planes were getting hit in the engines just as often as the fuselage or wings, but because the bombers that got hit in the engines didn't survive, no data could be collected from them. Lacking data from the aircraft that didn't make it back had skewed the numbers to show the exact opposite of what they had been looking for.

Wald proposed adding armor to the engines, rather than the fuselage and his premise was swiftly adopted, and soon that premise was proved true. Bombers that had additional armor added to their engine shrouds saw much higher rates of return, and before long, armoring the engines of B-29s became standard practice.

In fact, Wald's approach continues to be employed in military aircraft design today, making it hard to even guess just how many aircraft, missions, and lives Abraham Wald is ultimately responsible for saving... all through his unique combination of perspective and arithmetic.

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