Abraham Wald , Survivorship bias and armoring warplanes

You would have heard of “the legend of Abraham Wald”; his name often comes up in many talks and webinars, specifically as an illustration of lateral thinking or outside the box thinking. If you haven’t, let me quickly introduce him to you. He was a Hungarian mathematician who emigrated to the US during WW2 escaping religious persecution by Nazi Germany. As a gifted statistician, he became a part of the war math team of allied forces. Probably that was his way to get back at the repressive regime he ran away from in the first place.

Although formally not named that way, war math is applied mathematics, influencing battle strategies for optimal results. Being part of it is a highly under-celebrated and thankless job. These guys are equally crucial to the outcome of the battle, as much as that of a captain of that platoon, if not less — for example, Debora Morgan vs Dexter Morgan.

Anyways, back to Abraham Wald. He worked on analyzing and optimizing the damages sustained by returning warplanes. His decision would make or break the battles, save lives for the pilots and war machines themselves. In the below scenario, the optimization simply meant armoring the planes like battles tanks do. An extra layer of metal that can simply resist anything and everything thrown at it. But he cannot ignore the economics behind it. Armoring an entire plane is going double its weight and hence impacts its aerodynamics. The plane might not even take off. The decision is to armor a particular area of the aircraft or two without severely compromising the plane’s potency. The question is “Where?.”

With his guidance, the ground crew pulled beautiful statistics on the bullet holes the planes sustain upon returning from the mission. Please refer to the image below. The pattern was clear. Everyone had a straightforward answer. Engineers can clearly observe where the bullets holes were, armor them and problem solved!

The damaged portions of returning planes show locations where they can sustain damage and still return home; those hit in other places do not survive.

Abraham told “Eine Minuten, bitte,” or something like that. I do not know what Jewish Austrio-Hungarian genius mathematics spoke during then, Yiddish is it? Anyway, his argument was the engineers are actually looking at the planes that have returned. That simply indicates that planes can actually sustain the damage at these parts. The rest of the aircraft, which got hit in the area not on the map, did not even survive. Hence those parts should be armored. Basically, armor the regions where there are no bullet holes. This was a radical idea during then. It apparently worked, and it became one of the most celebrated legends on survivorship bias.

As its name unambiguously indicate, survivorship bias is a logical fallacy we tend to commit while recognizing a pattern entirely based on those who have survived. That, too, while discounting the disproportionately large instances indicate otherwise.

These are the few examples I can think of. I am sure you will find more when you give it a thought.

  1. There are colossal fandom on an idea of few Silicon Valley legends who became billionaires after quitting school, such as Bill Gates, Steve jobs, so on and on. It is a highly problematic argument. These folks became great despite leaving school, not because of! It is a classic case of survivorship bias. There are thousands of examples of kids who quit school who could not achieve anything remotely similar. In these cases, because of it.
  2. While celebrating centurions scoring 100 years, the most common topic of discussion is how people born in the first two decades of the last century have the best health. Again, this is a survivorship bias. Ask the centurion how many siblings and cousins they had and how many of them survived beyond the age of 5.
  3. Another example I came across is about Mud huts of Asia and Africa and their counterparts as wooden log houses in the west. When people come across one which is old, it is about 75 years. They immediately jump into the praise of the “engineer” who built it and how it survived despite harsh weather conditions. Also, “how we no longer make such strong ones anymore.!!!”. That mud hut was probably one among the millions which somehow survived.

P.s. Abraham Wald died in a plane crash in India, the kingdom of Travancore!!

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