# Marking The Hits

This fascinating tidbit was mentioned in an aside on TWIV. Even their digressions are often mind-blowing, and teach fundamental scientific thinking. I mentally bookmarked it under “more research” and “not miserably depressing” and started digging.

Abraham Wald was born in October 1902 in the city of Cluj, located in Austria-Hungary (now known as Romania). A natural-born mathematician, Wald graduated from the University of Vienna with a Ph.D. in mathematics in 1931. However, Wald found difficulty finding a university position due to the discrimination he faced for his Jewish faith. This discrimination only got worse upon the Nazi invasion of Austria in 1938, prompting him to flee to the U.S.

In the U.S., Wald received an invitation to join the Cowles Commission for Research in Economics as part of the Statistical Research Group (SRG). As part of the SRG, Wald applied his vast mathematical and statistical knowledge toward solving various wartime problems throughout World War II (WWII).

One of the most notable problems that Wald helped solve (and the focus of today’s article) concerned the placement of armor on American bomber aircraft sent to campaigns over Europe. The SRG was faced with the task of increasing aircraft survivability without compromising flight range or maneuverability. Thus, the aircraft could not be covered entirely with armor. Instead, the SRG had to prioritize the most important parts to place armor plating on.

Survivability and power-to-weight ratio are two of the most important determining factors of military aircraft’s success. I had never heard that there was a team of statisticians assigned to work on such problems, but it makes sense. When statisticians go to war, they’re likely to win! (84%!) #rimshot

Source: McGeddon, “Survivorship Bias,” Wikimedia Commons, https://commons.wikimedia.org/wiki/File:Survivorship-bias.png, accessed March 2019.

This is one of those judo flips of science, like the (original, simple) anthropic principle, that stand out to me as examples of scientific reasoning at its best. But, first, a mistake:

The initial approach of the SRG was to look at returning American B-29 bombers and note where they had taken the most fire. The SRG noted that the bombers they observed had fuselages (main bodies) riddled with bullet holes, taking almost twice as many hits as the engine platforms.

Thus, the SRG made a simple decision: apply more armor to the fuselage. After all, the crew were housed inside the fuselage, so adding extra protection here seemed to make the most sense.

Then, Wald steps in:

However, Wald was the one to point out that this approach was completely wrong. He instead suggested that extra armor should be placed in all of the places that the SRG noted no bullet holes appeared. Why is this? It was because the only planes that the SRG looked at were the ones that actually survived out in the field, and they were therefore a sample showing the exact opposite end of the data pool for the problem at hand.

The planes that got hit in a particular location, and made it home, must have been able to survive hits in that location. The places where no returning planes had hits were the places that caused the plane not to return at all. On the illustration above, that’d be the wings where the wing tanks were, the engines, the pilots’ seat, and the fuselage where the hydraulic pumps and control surface lines were run, etc.

Simple, brilliant, and so illuminating!

Other forms of surviorship bias are:

“Steve Jobs, Bill Gates, and Mark Zuckerberg dropped out of college and became millionaires, so will I.” [source]

Another variation I encountered was, I believe, in George MacDonald Fraser’s Royal Flash in which he’s looking at a nasty opponent with dueling saber-scars on his face and realizes that the guy he should be afraid of is not the fellow with the scars, but rather the fellow who gave that fellow his scars. It’s the student who graduates from Heidelburg Military Academy without any scars, who is the one to watch out for.

What are some other fun examples of survivorship bias?

I am not sure it was in Royal Flash but I’m not going to re-read the entire series to verify it. Sometimes, a blogger has to rely on their memory and hope for the best. I apologize to GMcDF or whoever, if I am mistaken.

1. says

Lindy Beige said a similar thing in a video on World War I helmets. After the British issued their troops metal helmets, the number of reported head injuries went up five times.

It wasn’t because the helmets were unsafe.

2. flex says

Having just re-read Royal Flash, I’d say your memory is correct,… but Flashman’s isn’t.

In Mark Twain’s A Tramp Abroad he describes the culture and practice of getting dueling scars at Heidelberg. According to Twain, who is a generally accurate observer if prone to exaggeration, part of the purpose of dueling was to acquire scars. To the extent that the protective gear worn only exposed the areas (cheek, temple, above the ear) where scars were desired.

As was mentioned in an early The Simpsons episode “Chicks dig scars.” Apparently that’s been true for a long time.

3. The initial approach of the SRG was to look at returning American B-29 bombers and note where they had taken the most fire. The SRG noted that the bombers they observed had fuselages (main bodies) riddled with bullet holes, taking almost twice as many hits as the engine platforms.

I spotted the error immediately, before I could read your big reveal. I even spotted the general problem just by glancing at the diagram. No red dots on the engines? That didn’t seem right. Why would the engines never get hit? I correctly predicted that we were looking at only surviving planes just from that.

On a completely different topic, it’s interesting that you’re writing about the Abraham Wald. I met my first member of the Wald family almost 3 decades ago & have met more since. They’re all good & interesting folks, from what I can tell.

4. komarov says

“It’s the student who graduates from Heidelburg Military Academy without any scars, who is the one to watch out for.”

What if they’re the Trump type, with very influential parents and a private doctor who’ll attest anything as needed, from bone spurs to steel allergies? Smoothskin might be a devil with a sword or an expert quitter and future far-from-the-trenches general. With scarface you can be quite certain that they’ll keep trying to hack you to bits even after being stuck with something sharp, which is no less terrifying to someone like me (who can’t afford that doctor).

Re: Crip Dyke

Apparently I, too, am a master statistician but won’t bet any lives on it. (I know better, probably a further sign of my skills)
To be fair, jumping to conclusions is the one sport I excel in so I would never dream of holding my one victory over the SRG against them.
Engines and the cockpit were probably priority targets, provided you can actually aim with that much precision. From the diagram the gunners appear to be critical, too. There, I admit, I would have expected some leeway but if you have enemy planes after you all the way there and back, maybe not so much.
What puzzles me is the gap along the wings. Wing tips and most of the wing surface are apparently unimportant, but you get those two bands. Is that where the fuel tanks are? It seems smallish. And yes, I’m totally overthinking the diagram yet can’t say for sure which bomber it’s supposed to be. My initial theory (other than fuel tanks) would be that it’s the maximum stress point of the wing. One hit too many and the structure goes. You (presumably) see the same thing just aft of the gunner where the tail section might just start to go if the narrower parts of the fueselage have one too many holes.

5. anat says

The same graphic was shared in response to women who had worked many years with James Watson speaking in defense of his behavior as their boss.

6. says

Survivor bias is one of the reasons why celebrity advice at succeeding in whatevah are not always useful. More often than not this advice are just a random list of what-to-do things but without reference to how many people did all those things and failed anyway, it is impossible to sort out which of those things were causal and which just coincidental with said success. Other good videos about survivor bias have been made by Veritasium – Survivor Bias and Is Success Luck or Hard Work?

The first one talks at the beginning about the same bomber issue as the op.

7. says

komarov@#4:
In those days, aircraft guns were not very accurate. You just sprayed a bunch of stuff at the target and hoped some of it hit.

To be fair, machineguns were not made to be precise; one does not want the whole stream of bullets to hit the same spot because it’ll just drill a great big hole. I believe that the barrels of an M-2 .50 HMG are made to a low spec, so that the bullets disperse.

8. snarkhuntr says

Marcus@7

Given that the M2 (and most other machine guns) fire off an open bolt, the slamming home of the bolt carriage and the recoil after the first shot provide all the dispersion you want in the gun. Purposely degrading a barrel that’s going to see tens of thousands of rounds during its service life does seem like a bad idea.

The M2 is actually a fairly accurate gun in the right hand. See here https://www.wearethemighty.com/articles/marine-made-historys-5th-longest-sniper-kill-machine-gun/

9. StonedRanger says

Gun barrels are made to high spec. Its the delivery system for the gun. If it fails due to being low quality the gun itself would be useless. Its the recoil cycle that makes the gun not hit in the same spot every time. I have fired my share of machine gun rounds and its nigh impossible to put two bullets in the same place. Even when fired in semi auto mode (one shot per trigger pull) you cant put two bullets in the same hole. Machine guns are made to deliver maximum amount of bullets downstream, but some degree of accuracy is required or you would never hit your target.

10. Ketil Tveiten says

Marcus (and others), I’m a little surprised you hadn’t seen that one before, it’s one of usual suspects for “here’s some classic infographics”-collections.

11. Steve Pells says

” the guy he should be afraid of is not the fellow with the scars, but rather the fellow who gave that fellow his scars”.
One of the Mexicans in The Magnificent Seven” makes the same point when they are recruiting professional gunfighters to protect their village from the bandits.
s.

12. Rob Grigjanis says

flex @2: Since you just re-read it, I’ll take your word, but my memory says that Flash knew about the facial-scars-as-mark-of-honour thing. Now I have to read the damn thing again. Oh well.

13. says

What are some other fun examples of survivorship bias?

“Bullying at schools is no big deal. I got bullied as a kid and learned to defend myself from attempted abuse as a result, which was a valuable life lesson.” This totally ignores all those other victims of bullying who got a depression or committed suicide.

Alternatively: “Sweatshops and minimum-wage jobs aren’t bad. As a young adult, I started my career with a miserable minimum-wage job and by now I have worked my way up to the point that I’m a millionaire. All those other people who complain about their minimum-wage jobs are just lazy.”

Granted, you asked for “fun” examples, and these aren’t exactly fun.

14. sonofrojblake says

One of the corporals who trained me (a chap who’d been five years in the British SAS and three in the Australian version) didn’t like the LSW (the current section support weapon for infantry). “Too accurate” he said. He preferred the GPMG, which fired bigger rounds (7.62 instead of 5.56) and spread them over a wider area. It could also fire more than 30 at once… Belt feed ftw. (I’m aware there are bigger, drum mana available, but we were never issued such toys in the Toy Army).

15. John Morales says

re the duelling scars: https://en.wikipedia.org/wiki/Dueling_scar#Social_significance

In short,

Another variation I encountered was, I believe, in George MacDonald Fraser’s Royal Flash in which he’s looking at a nasty opponent with dueling saber-scars on his face and realizes that the guy he should be afraid of is not the fellow with the scars, but rather the fellow who gave that fellow his scars.

has it backwards.

Re the substantive part of the post, I was aware of this long ago, and myself put it into a similar category of clueyness as Feynman’s insight about the O-rings.

16. says

Komarov,

How you attack may affect the areas you hit. If I remember right the Japanese had trouble shooting down B29s until they switched to head on attacks.

17. flex says

@10, Rob Grigjanis,

I wasn’t clear. From the novel, Flashman knew they were scars of status, but it was not clear in the novel that there was a specific, almost ritualistic, manner of acquiring them in which there was no actual danger to the recipient (aside from sepsis).

I only re-read it recently because I was looking for something to read which didn’t take much cogitation. Of all the Flashman books, Royal Flash is my second least favorite. The one I’ve enjoyed re-reading the most is Flashman in the Great Game. I know that the history as portrayed by Fraser of the Indian Rebellion, AKA the Sepoy Mutiny, is incomplete and biased, but the story is well written. I also have a soft spot in my heart for Kipling’s Kim which may help explain why I like that particular Flashman book the best.