interesting little thought question

[Azazello1313]

During WWII, statistician Abraham Wald was asked to help the British decide where to add armor to their bombers. After analyzing the records, he recommended adding more armor to the places where there was no damage!

 

The British were initially confused. can you explain?

[BeeR]

Yes but I cheated.

[Deathpig]

Best I can think of... if he was examining damaged bombers that had returned to England, then clearly the damaged areas of those bombers weren't severe enough to cause the plane to crash. Hence, the undamaged areas on those bombers were the likely places damaged on the bombers that did not return, and hence those areas were likely more vulnerable and needed the protection.

 

Not sure if that makes sense to anyone else, but it made sense to me.

[BeeR]

And I'm sure you didn't cheat.

[Big Country]

Best I can think of... if he was examining damaged bombers that had returned to England, then clearly the damaged areas of those bombers weren't severe enough to cause the plane to crash. Hence, the undamaged areas on those bombers were the likely places damaged on the bombers that did not return, and hence those areas were likely more vulnerable and needed the protection.

 

Not sure if that makes sense to anyone else, but it made sense to me.

 

 

This is the correct answer and I didn't cheat because I had learned of this some time ago, thus it was via memory, not cheating.

[Deathpig]

Shall I interpret your comment to mean we now commence with the requisite Huddle gainsay on whether or not I was capable of deducing the answer to a lateral thinking question without the use of the Internet?

[Ursa Majoris]

Best I can think of... if he was examining damaged bombers that had returned to England, then clearly the damaged areas of those bombers weren't severe enough to cause the plane to crash. Hence, the undamaged areas on those bombers were the likely places damaged on the bombers that did not return, and hence those areas were likely more vulnerable and needed the protection.

 

Not sure if that makes sense to anyone else, but it made sense to me.

Well done.

[Pope Flick]

And I'm sure you didn't cheat.

 

 

Many, many people are smarter than you. Many.

[Azazello1313]

Best I can think of... if he was examining damaged bombers that had returned to England, then clearly the damaged areas of those bombers weren't severe enough to cause the plane to crash. Hence, the undamaged areas on those bombers were the likely places damaged on the bombers that did not return, and hence those areas were likely more vulnerable and needed the protection.

 

Not sure if that makes sense to anyone else, but it made sense to me.

 

that is indeed the answer, elaborated upon here:

During WWII, statistician Abraham Wald was asked to help the British decide where to add armor to their bombers. After analyzing the records, he recommended adding more armor to the places where there was no damage!

 

This seems backward at first, but Wald realized his data came from bombers that survived. That is, the British were only able to analyze the bombers that returned to England; those that were shot down over enemy territory were not part of their sample. These bombers’ wounds showed where they could afford to be hit. Said another way, the undamaged areas on the survivors showed where the lost planes must have been hit because the planes hit in those areas did not return from their missions.

 

Wald assumed that the bullets were fired randomly, that no one could accurately aim for a particular part of the bomber. Instead they aimed in the general direction of the plane and sometimes got lucky. So, for example, if Wald saw that more bombers in his sample had bullet holes in the middle of the wings, he did not conclude that Nazis liked to aim for the middle of wings. He assumed that there must have been about as many bombers with bullet holes in every other part of the plane but that those with holes elsewhere were not part of his sample because they had been shot down.

 

my first thought in reading that, though, was that I wondered how accurate the assumption in bold actually was. a bomber can a pretty big thing to aim at. and even if the luftwaffe fighter pilots couldn't necessarily aim at one part of the plane, it seems like certain parts of the plane would be more susceptible, due to firing angles and whatnot. a totally random hit pattern just doesn't seem like a safe assumption here.

Edited September 14, 2011 by Azazello1313

[Pope Flick]

that is indeed the answer, elaborated upon here:

 

 

my first thought in reading that, though, was that I wondered how accurate the assumption in bold actually was. a bomber can a pretty big thing to aim at. and even if the luftwaffe fighter pilots couldn't necessarily aim at one part of the plane, it seems like certain parts of the plane would be more susceptible, due to firing angles and whatnot. a totally random hit pattern just doesn't seem like a safe assumption here.

 

 

There's a bit of detail missing from what you posted (I haven't followed the link) - in that you're assuming nazi fighter planes were doing the shooting. There are the fighter bomber escorts to be considered here, along with the fact that a lot of bombing was done at night which was mainly flak gun defense, and I am going to assume that led him to the random pattern theory, since flak guns are general aiming devices if ever they existed...

[Ursa Majoris]

There's a bit of detail missing from what you posted (I haven't followed the link) - in that you're assuming nazi fighter planes were doing the shooting. There are the fighter bomber escorts to be considered here, along with the fact that a lot of bombing was done at night which was mainly flak gun defense, and I am going to assume that led him to the random pattern theory, since flak guns are general aiming devices if ever they existed...

Yep.

 

Also, in support of what Pope says above, while it was theoretically possible to aim for a specific part of a bomber, it is likely that in reality the choice was largely between "bottom" and "top". The aim of a fighter would be to hit the bomber with as many bullets as possible, rather than be specific.

 

I wonder if the statistician divided the planes into "sections" and looked at the number of damage points within each?

[Azazello1313]

There's a bit of detail missing from what you posted (I haven't followed the link) - in that you're assuming nazi fighter planes were doing the shooting. There are the fighter bomber escorts to be considered here, along with the fact that a lot of bombing was done at night which was mainly flak gun defense, and I am going to assume that led him to the random pattern theory, since flak guns are general aiming devices if ever they existed...

 

the number of bombers lost to both enemy fighters AND flak was substantial. it doesn't sound like he differentiated, he just assumed complete randomness. and even with flak guns, wouldn't basic physics suggest that forward facing and downward facing surfaces would be far more likely to be hit than say rearward or skyward facing surfaces? maybe he took all that into account somehow, but this particular account doesn't necessarily make it sound like he did.

[Pope Flick]

the number of bombers lost to both enemy fighters AND flak was substantial. it doesn't sound like he differentiated, he just assumed complete randomness. and even with flak guns, wouldn't basic physics suggest that forward facing and downward facing surfaces would be far more likely to be hit than say rearward or skyward facing surfaces? maybe he took all that into account somehow, but this particular account doesn't necessarily make it sound like he did.

 

 

I just think it's lacking on details. If he only considered night bombers, then he had no reason to assume anything was really aimed.

 

Also, I believe flak guns aren't meant to hit a plane directly but blow up nearby throwing shrapnel in their direction. Which would only lead to more randomness.

[Deathpig]

I doubt he suggested they armored every single inch that wasn't damaged, but rather looked at the undamaged areas of the returning planes and kinda of stack-ranked those locations based on how important those areas likely were to the plane's survival.

 

So if you looked at a plane, and noticed the wing tips had no damage, and the paneling around a section of the fuselage that contained important fuel hoses had no damage, you'd probably not be as worried about the former as compared to the latter. It's an extreme example, but I'm trying to convey the concept.

 

It might seem silly that certain areas weren't already sufficiently armored, but strange things like that do happen. In addition, they knew the engineering required for the plane to function (it's not like they were trying to reverse-engineer a UFO) so it makes the job a bit easier to do a sort-of forensic investigation like this.

[Ursa Majoris]

It might seem silly that certain areas weren't already sufficiently armored, but strange things like that do happen.

Gotta remember when this was (1940s), the small size of the planes, the power of the engines and, critically, that the planes be light enough to get to Germany and back. Bombs took priority over armor.

 

It's astounding how much damage those planes could absorb and also the amazing skill of their pilots and crew, never mind their stratospheric bravery.

Edited September 14, 2011 by Ursa Majoris