Happy New Year, everyone!

I just realized that I only moved once in 2012. A good year indeed.
Actually, 2012 wasn’t too bad. At least the latter half. I think Vancouver Karma is finally reversing itself. I really hope 2013 is as good or better.

Anyway. To the blog!

Abraham Wald was a mathematician born in Austria-Hungary (present day Romania) in 1902. He studied mathematics and statistics and worked for the Statistical Research Group (SRG) during WWII. Wald’s job was to estimate the vulnerability of aircraft returning from battle.

To do so, he made note of the location of bullet holes on a ton of returning Allied aircraft to determine the best places to reinforce the planes to promote survival. He made several diagrams showing where the planes were most bullet-ridden (which was pretty much everywhere but the cockpit and the tail).

Showing these diagrams to his supervisors, the supervisors concluded something a lot of us would probably expect—that the best course of action to increase the rate of survival of the planes was to reinforce the areas that were the most damaged.

But Wald came to a different conclusion. He stated that rather than adding reinforcing armor to the bullet-ridden areas of the planes, the plane manufacturers should instead reinforce the areas that were bullet free. His reasoning behind this? The planes survived the battles because the cockpit and tail were undamaged. That is, the parts most vital for the planes’ survival were untouched by bullets. The planes that had been damaged to the point of being destroyed, of course, would not be able to make it back and be observed by Wald and his team. Since only planes whose cockpits and tails were undamaged were returning to be sampled, Wald concluded that it was likely planes sustaining damage to the cockpits and tails were the ones that were not surviving the battles—thus, those two parts of the airplane were the most vital to the survival of the plane overall. The wings/body/etc. were sustaining damage, but the planes were able to return even after sustaining this damage. Wald concluded, therefore, that extra armor should be added to the components of the plane that had to remain undamaged for the planes to survive.

Wald’s observation actually helped to prevent the SRG from making conclusions under the influence of “survival bias”—including only the aircraft that survived the battles and not including the planes that were damaged beyond repair and did not return to be included in the sample.

How cool is that??

There is a paper by Mangel and Samaniego discussing Wald’s findings and the math behind them. It gets pretty technical pretty quickly, but if anyone’s interested, here you go!