In 1942 the probability of an Allied pilot surviving a tour of duty was only 50%. America alone was losing 220 pilots a day.

After the US entered the war they established an organization called the Applied Mathematics Panel (AMP) within the Office of Scientific Research and Development (OSRD) in order to solve mathematical problems related to the military effort in the war. The panel's headquarters were in Manhattan and recruited academics from Princeton and Columbia Universities.

They were asked to use their mathematical skills to reduce the number of pilots being shot down over enemy territory. The air force had been collecting a large amount of data about their wartime efforts. This included examining in detail every aircraft that returned to base to assess the extent of the damage. You can see the pattern in the diagram below:

After inspecting the evidence what advice do you think the mathematicians gave to the air-force?