I Have Been Guilty of Spreading Wrong Info... Here is the True Legacy of Abraham Wald

Ever heard of the story that mathematician Abraham Wald and the Statistical Research Group at Columbia University was asked by USAAF in WW2 to "optimize" the location armor in the B-17 bomber, due to heavy losses of B-17s over the skies of Germany in 1943. Wald allegedly told all the generals "you are doing it all wrong", because they only concentrated on armoring where the survivors (that made it back to base) got hit, and presumably, he did it right, and the bombers started surviving... Nerd triumphs over dumb military. Great story. Right? 

I just learned that was a lie, an urban myth. 

Photo by Gary Wann on Unsplash

But they story is far more nuanced than that. So... let me start from the beginning. My current citing is mostly coming from this blogpost by Bill Sweetman for Hush-Kit, and a feature column by Mathematician Bill Casselman for American Mathematical Society. 

First, did US suffer tremendous bomber losses in 1943? Yes, but the PRIMARY reason Americans were suffering tremendous losses was because Americans insisted on conducting day-time bombing raids. Both British and German air forces have switched to night-time raids against each other as they can't sustain such losses with day-time raids. 

Second, did Wald wrote a study on survivability? Well... the SRG *did* help write *something* in 1943, and we based this on the autobiographical memoir by W. Allen Wallis, who was with Wald in the Statistical Research Group at Columbia University. But the memoir was really two short and vague mentions and mostly about his own work on aircraft vulnerability calculations. And we did find actual memoranda written by Wald. That's it, that's all the evidence.

As for Wald's own memos, it's a series of very dry equations on how to more accurately calculate the vulnerability of an aircraft based on variety of factors, It's NOT about how to redesign the armor.

Indeed, B-17 actually entered service back in 1938. B-24 entered service in 1941. By 1943, both designs have been long finalized. There were NO evidence that armor were shifted in bombers manufactured after 1943. Indeed, NO version of the Wald story can actually point out WHAT EXACTLY was changed in B-17 or B-24 post-1943. 

Unfortunately, Wald died in 1950 in a plane crash, so we can't ask him about it. We have to rely on whatever paper or recollections left behind. And the memos left behind by Wald was collected by Wallis when SRG shutdown in 1946, but was not rediscovered until 1980, when it was edited by Phil DePoy and published under Wald's name posthumously in 1981 by Center of Naval Analyses, along with an explainer article on what it meant by Marc Mangel and Francisco Samaniego. 

In the late 1990s, statistician Howard Wainer started using that story in his lectures and and books. This is when the "chicken pox bomber" diagram got attached to the story, but the diagram is usually of a 2-engine plane with a bunch of red dots all over it. (B-17 and B-24 are FOUR-engine bombers!)

Sometime in 2010s, writer / mathematician Jordan Ellenberg included a section about Wald's work in his book "How Not to Be Wrong", where he used as non-technical explanation as possible. However, he wrote it in a way that could have been misinterpreted:

 “The officers saw an opportunity for efficiency; you can get the same protection with less armor if you concentrate the armor on the places with the greatest need, where the planes are getting hit the most. But exactly how much more armor belonged on those parts of the plane? That was the answer they came to Wald for. It wasn’t the answer they got.”

Presumably, someone read this and concluded that Wald had told the Generals how to redesign the bomber's armor allocation. We have no evidence that Wald ever said such thing. Indeed, in Wallis' memoir, he stated that SRG only do math, and reallocating armor is not what they do and it wasn't what the USAAF asked for any way. 

Unfortunately, Jordan Ellenberg went on to include this whopper:

“Wald’s recommendations were quickly put into effect, and were still being used by the navy and the air force through the wars in Korea and Vietnam.”

There was no evidence that Wald ever made any recommendations (for aircraft redesign or otherwise). Perhaps Ellenberg meant that Wald's equation to estimate survivability was still in use in subsequent wars? Given that the book this passage appeared in was "How not to be Wrong", it is extremely ironic. 

And now you know everything I know about this.