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A common story about the British "Brodie helmet", issued first in World War I, is the following: After introduction of the helmet, the number of reported head injuries increased. This called the efficacy of the helmet into question among "high military ranks", "high command", or "upper echelons". An unnamed mathematician, or statistician, or scientist, finally concluded that the reports were due to survivorship bias: The helmet seemed to have caused more head injuries, since soldiers with head wounds were now more likely to survive when wearing the helmet.

The story is reported (unsourced) in the Wiki article on survivorship bias, but not in the article on the Brodie helmet itself. It is reported by history youtuber Lindybeige in a video with a million views, in this article published by the Royal North Shore Hospital in Sidney, this article from the open journalistic platfrom medium.com, and multiple blogposts such as this one.

I can't find any primary source regarding this phenomenon, and a primary source is never mentioned when the story is told.

Sometimes the helmet is not explicitly named or goes by another name. I would be convinced by good evidence for this story being true about any helmet.

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    I heard this story 60 years ago, and there was a similar argument over the compulsory wearing of car seat belts and motorcycle helmets. In a similar vein, a plan to add armour plate to fighter planes based on an analysis of bullet holes was scrapped when it was realised the planes surveyed were those that had not been shot down, but survived. – Weather Vane Dec 17 '20 at 13:49
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    @Weather Vane I looked into the claim about the airplanes already, and the evidence seems quite dubious. As far as I understand it, Abraham Wald indeed researched hits sufferend by WWII airplanes and took survivorship bias into account in his research. The claim that there had been plans to armour the planes at the most commonly hit locations based on bullet hole analysis is however only supported by one sentence written 40 Years after the incident: Wallis, a colleague of Wald, apparently wrote in the 80s that the army "was inclined" to armour the planes at the respective locations, ... – EpicBroccoli Dec 17 '20 at 14:36
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    but it is unclear to me who was inclined in the army (a single person? some gremium?) and what "inclined" exactly means here (where there actual plans?). Also, Wallis wrote this one sentence only in passing, and it seems likely to me that he simply constructed a little anecdote which would shine a favorable light on the research group he was part of as well. Basically, the intention of the respective article from the 80s was to explain what a great job Wald and Wallis did, so I think that this one sentence is given undue weight. – EpicBroccoli Dec 17 '20 at 14:40
  • @WeatherVane bullet holes to WW2 bombers and sealife being mutilated (but surviving) by motorboat propellers are the two classical examples. Yet what baffles me is if a team can design a fighter plane (very expensive), can't they do better stats than some random dudes on the Interwebz?! – Vorac Dec 17 '20 at 18:53
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    @Vorac The thing about issues like survivorship bias is that they're only really obvious after someone else has pointed it out to you. That's the problem with bias. – Shadur Dec 17 '20 at 23:48
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This looks like a made up claim, perhaps for educational purposes. I found it made in Paul Sloanes: "Lateral Thinking Puzzles", 1991. On page 24, "Historical Puzzles, 3.7 War Aims" and that exact solution on p83. No source given, just a puzzle to teach stats. (Like re-used here.)

Biggest problem in this detail: The British helmet went into service after the French were already convinced it was worth it.

When World War helmets were introduced, it was specifically to reduce head injuries from shrapnel. Which actually went down by 75%. Says the Imperial War Museum..

With such a number of direct improvement and helmets always seen by all sides, French, British, and Germans, from top brass down to the average grunt as "highly desriable", the claim seems to be quite ahistorical and improbable. There were some complaints in the British Army that a Brodie would make the men look "unsoldierly" and "go soft", but nowhere are records found that it increased head injuries over all compared to no helmet and over all survivorship.

It was designed primarily to absorb blasts and shrapnel, coming from above onto and into the trenches. It was quite good at that. A gunshot or rifle bullet protection was only a secondary role, and there it was still a vast improvement over felt caps, but far from perfect for that. Indeed, while almost all-around better than the French Adrian, the Brodie still had significant weaknesses.

These weaknesses then led to statistically relevant shift in relative distribution of the head wounds recorded, while overall casualties from head wounds still were much lower than otherwise expected, but caused or enabled by a known design weakness:

With some study at the time going like this:

Holmes’ Studies During WWI

A decade after the Russo-Japanese War, WWI produced particularly large numbers of occipital and cerebellar head injuries. Although shellfire caused the majority of head injuries in WWI, some of the injuries caused by bullets produced relatively restricted deficits whose extent could be estimated based on the trajectory of the bullet through the skull. Compared with earlier wars of the previous century, the muzzle velocity of rifles was moderately faster, and the bullets were smaller and much less deformable, allowing easy penetration of the skull without producing severe shock waves and cavitation in the brain.

In addition, the heads of soldiers had relatively greater exposure than other body areas above the parapets in the European trench warfare of that period, and the British “Brodie” helmet and the nearly identical U.S. Marine Corps Doughboy helmet gave insufficient protection to the back of the skull (in contrast to the protection afforded by German helmets and later American helmets) (Fig 1A, B).

As a result, more soldiers sustained and survived occipital bullet wounds than ever before, often with fairly discrete lesions, prompting studies of the visual pathways by a number of investigators, among which the work of British neurologist Gordon Holmes (1876–1965) was the most influential.
[…]
enter image description here enter image description here
Fig 1. (A) Wounded arriving from a train at a triage station in Suippes, France, during WWI. Note how the British helmets leave the lower posterior portion of the cranium exposed, making soldiers more susceptible to occipital and cerebellar injuries. [Photograph courtesy of the National Museum of Health and Medicine, Washington, DC.] (B) Comparison of cranial protection provided by different helmet styles during WWI. The standard British model (thin line) provided no protection for the sides and base of the cranium, whereas these areas were protected by the newer American helmet, Model 2A.
— Douglas J. Lanska,: "Historical Perspective: Neurological Advances from Studies of War Injuries and Illnesses", Ann Neurol 2009;66:444–459, DOI: 10.1002/ana.21822

Further source: — G. Kurt Piehler: "Encyclopedia of Military Science", SAGE Publications, 2013, p628.

And these statistics were recorded immediately from the battlefields at the time: head injuries increased with trench warfare; with helmets head injuries to be treated increase, while fatal head injuries decrease:

The statistics given the author by Leriche are of interest. […]
The author comments on the fact that since the introduction of steel helmets the number of head injuries has increased considerably. He explains this by the fact that before their introduction many of those injured were killed outright.

— P Gulldall: "War-Surgical Impressions Gained in France" (1916), Clinical Congress of Surgeons of North America: "International Abstracts of Surgery", Volume 24, 1917. (p 619, gBooks, archive.org)

Since such statistics were collected from the start and from the bottom up, it is very unlikely that anyone higher-up the food chain would ever question the practical utility of helmets for long.

Notably in the French army, the tests were already quite convincing, albeit mentioning the earliest form of 'this' among other criticisms:

Good reports soon came in from the front. Thereupon, he developed the regular helmet which was manufactured in great numbers for the French Army. […]

Investigation showed that the new helmet was of actual value in the field; hence it became a part of the regular equipment and was used by every soldier on active duty. Its use naturally added to the burden of each wearer, causing at first considerable grumbling. During the period of probation of the helmet, some of the critics pointed out that the number of casualties with head wounds increased notably, but the advocates of the helmet, referring to statistics, replied that the vast percentage of those who were formerly wounded in the head found their way not to hospitals but to cemeteries !

It is interesting to note that almost from the beginning the “casque Adrian” was a successful experiment. It protected a measurable portion of its wearer; it was light and soldiers of all classes shortly “took to it.” […]

There is no better evidence that armor is of practical importance in actual warfare than the testimony of physicians as to the value of the “shrapnel” helmet. In this case, at least, all criticism was overcome, although in the beginning there certainly were many objections to its use. Indeed, so severe was the criticism that had the French helmet not been introduced in very large numbers (the first lot included over a million copies), insuring it a thorough trial and under many conditions, the experiment might not have succeeded.

Various estimates have been made as to the number of casualties saved by the use of the shrapnel helmet. But these estimates are based on statistics obtained in different localities under different conditions, hence they are apt to be discordant. In a general way, however, hospital records (French, 1915) show that before the introduction of helmets about one head wound in four proved fatal. After the introduction of the helmet, however, statistics indicate that head wounds were fatal in, at the worst, one case in four and a half, and at the best one case in seven, a bettering of condition which is certainly appreciable. Add to this the saving of those men — and their number, although unreported, is great — whose helmets had resisted missiles which would otherwise have inflicted serious, if not fatal wounds.*

As a protection against missiles of low and middle velocity, there is no better evidence that armor has a definite usefulness in modern warfare than the fact that one type of armor ( i.e ., the helmet) is accepted by many nations as a part of their military equipment; for if such a defense, even when made of light metal, is capable of resisting small missiles of middle and low velocity, it is clear that similar defenses must have a definite value when worn on chest, abdomen, or extremities.
— The Metropolitan Museum of Art: "Helmets and Body Armor in Modern Warfare", 1920.

Early French sources:
— L Devraigne: "Les plaies par ‘crapouillots’", Presse Médicale, 1915; 23: 223–4.
— B Roussy: "Role protecteur du casque métallique de guerre", Presse Médicale 1916; 24: 122–3.
(Presse Médicale on archive.org, full article, p126)

From Roussy:

The protective role of the helmet is clearly demonstrated. Undoubtedly it preserves, intact or without serious functional disorders, the lives of many of our admirable soldiers. All of them are convinced of this and proclaim it. They are convinced of it and proclaim it. They do not want to part with it.
The confidence that it will surely increase their warrior value and thus contribute to ensuring the final victory.
The development of offensive weapons must always be accompanied by the development of defensive weapons.
Hygiene and prophylaxis must always take precedence over therapy: it is better to prevent harm than to cure it.

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    Can you please add some structure to this answer? It jumps around, has very long citations which don't clearly support the main argument and is hard to follow. Are you saying the claim was completely invented in 1991? Are you saying the story is substantially true, but has been transposed from the French Army to the British Army? Are you saying it is substantially false? – Oddthinking Dec 18 '20 at 12:01
  • At least part of the claim on the french evidence suggest they were aware of arguments where survivorship bias was an issue, so that hardly refutes the idea that it was irrelevant. – matt_black Dec 20 '20 at 17:41

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