Seeing the Unseen

Abraham Wald was a Jewish mathematician in the early twentieth century who was born in Austria-Hungary (now Romania). He later immigrated to the United States and started a new life there. One of his greatest contributions to the United States was helping the U.S. military to design their planes. During the Second World War, the B-29 bombers of the Allied were being shot down from time to time. They would like to fortify their aircraft, but if they did, it would sacrifice the mobility of the planes by adding weight to them. Therefore, the additional armour must be added to only the most fatal areas so that they could keep the increase in weight to a minimum.

The military presented Wald with a large amount of data taken from the planes returning from battle. It showed the distribution and frequency of different parts of the planes getting hit by enemy gunfire. The researchers at the Centre of Navy Analyses recommended that they should add armour to the most damaged area. Wald studied the data, assessed the overall situation, and disagreed with the Centre of Navy Analyses. He thought the protection should be added to the least damaged area instead.

It was a surprising recommendation. If the data showed a particular area was getting hit most often, is it not a logical reaction to first protect it first? Is it not a waste of material to add armour to the least attacked areas, where protection are not as needed? What was Wald thinking?

Wald criticised the Centre of Navy Analyses that the researchers there only looked at the plane which returned, but neglected the planes which did not. If those planes got most frequently hit in certain areas and were still able to make their way home, it only meant that those areas were not fatal. On the other hand, their unfortunate counterparts, who did not contribute to the data, were unlikely to be hit in the same areas before they went down. Instead, it must be those least attacked areas which caused their downfall, thus requiring extra protection by adding plates to them.

There is a simple yet meaningful message in this episode. The observed facts can only tell you a small part of the story. To look at the whole picture, you must look at things from a broad perspective, and consider the information which is invisible to you, as it often holds the key to solving the entire puzzle.

REFERENCE: Wald, A. (1943). A Method of Estimating Plane Vulnerability Based on Damage of Survivors. New York, NY: Statistical Research Group, Columbia University.