Its that time of year (every year) to talk about this image which does the rounds on Linkedin about once a week.
What is it ?
Well the image itself, is something which is inferred was drawn by the statistician Abraham Wald. But in fact its something someone drew at some point in MS Paint or something, to talk about "survivor bias".
THE INTERNET wrote of this image and Walds work:
"The US military’s conclusion was simple: the wings and tail are obviously vulnerable to receiving bullets. We need to increase armour to these areas. Wald stepped in. His conclusion was surprising: don’t armour the wings and tail. Armour the engine."
The trouble, is this is all basically nonsense.
Wald published his early work in 1943, the conclusions after 100 pages of equiations, are not exactly staggeringly profound:
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"This analysis of the hypothetical data would lead to the conclusion that the plane is most vulnerable to a hit on the engine area if the type of bullet is not specified, and is most vulnerable to a hit by a 20-mm cannon shell if the part hit is not specified.
The greatest probability of being destroyed is .534, and occurs when a plane is hit by a 20-mm cannon shell on the engine area.
The next most vulnerable event is a hit by a 7.9-mm machine gun bullet on the cockpit.
These, and other conclusions that can be made from the table of vulnerabilities derived by the method of analysis of part VIII, can be used as guides for locating protective armor and can be used to make a prediction of the estimated loss of a future mission."
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Aircraft are extremely weight sensetive, and by 1943, all aircraft designers the world over already knew perfectly well which part of an aircraft to armour.
They put armour on the pilots cabin and the engine systems. You cant put any where else as then the plane becomes so heavy its useless and so slow its probability of being shot down skyrockets as its performance goes down.
All Allied aircraft followed this doctrine from early on in WW2. There was never an attempt by aircraft constructors to put armor all over tails, and wingtips.
USAAF aircraft were also about as heavily armoured as they could be, this is (along with defensive armament) the main reason why a B-17 has so much less bombload capability than a British Lancaster, the British believed that fewer bombers meant the best tactical results and so the Lancaster had a lot less armour and armament than a B-17.
This was offset by its massive bombcarrying capability.
So what WAS Abraham Walds work ?
What it really comes down to is the first major attempt to define a statistical probability based estimate of the proportions of a batch of aircraft on a mission which would be likely to be shot down, based on data gathered experimentally. Although Wald did state (see quote above) that it could also guide armor placement, this aspect of his work was already perfectly obvious to anyone who made aeroplanes and was already in effect being followed to the letter.
So yes, Abraham Wald was a clever statistician, whose work is likely important piece of early matematical history to anyone studying the topic at University today, but NO - none of this resulted in aircraft manufacturers in WW2 changing the position of any armour plate, because everything of critical value which could be armoured, already was.