Abraham Wald

Abraham Wald was born on 31 October 1902 in the Romanian city of Cluj, which was then part of the Austro-Hungarian Empire. Hungarian schools required their students to attend classes on Saturdays. As a Jew, Wald was unable to do so, so his parents educated him at home. He excelled academically and began studying mathematics at the University of Vienna in 1927. By 1931 he had earned a Ph.D in Mathematics. When Nazi Germany annexed Austria in 1938, persecution of Jews intensified, so Wald seized an opportunity to emigrate to the USA. In 1942, the United States’ Office of Scientific Research and Development made use of Columbia University’s Statistical Research Group (SRG), based in Manhattan, New York. By then, the USA had entered World War II. The purpose of the SRG was to employ notable mathematicians and statisticians to improve wartime procedures and strategies. Although technically from an enemy country and therefore lacking sufficient security clearance, Wald was employed by the SRG. It was a running joke that he was not allowed to read the documents he had written. As a statistician, Wald was a genius. In fact, in mathematics, several probability theories, equations and distributions have been named after him.

As American aircraft began to enter combat, military decision makers became increasingly concerned with aircraft losses. More armour could be added to make the aircraft safer, but that would reduce their ability to carry a heavy weapons load. It was therefore essential to build armour into the most vulnerable parts of the aircraft. The US Navy noticed that aircraft which had returned from combat had more bullet holes in their fuselages and wings, whilst there were comparatively few bullet holes in engine nacelles. High ranking naval officers concluded that more armour was required to protect an aircraft’s fuselage, whilst its engines did not need any armour. Abraham Wald was approached to verify this assumption. In response, he produced an 89-page document, in which he used statistical information to prove the exact opposite. In other words, he told the US Navy that they needed to place more armour where they could see no bullet holes. Aircraft which had fuselages described as resembling ‘Swiss cheese’ were in fact the survivors. Ironically, aircraft which had bullet holes around their engines were not part of the navy’s thought process, as they had not returned to their bases or ships and could not be analyzed.

Today, this phenomenon is referred to as ‘survivorship bias’ and is applied to dozens of fields of study. Through this example, as well as numerous other research tasks, Abraham Wald may have saved the lives of thousands of airmen in World War II.

Abraham Wald died in an Air India plane crash in southern India on 13 December 1950. He was 48 years old.