The Flaw of Averages

How many people really are “average”? Is it possible to design a system to fit the average person, and if not, what’s the alternative? A recent article published on examines this question, excerpting the work of L. Todd Rose from his recent book The End of Average. Rose’s narrative is somewhat massaged, but the central thesis about averages and their relationship (or lack thereof) to the individual user is well-developed and quite pertinent. We will explore these ideas through excerpts from the article, beginning with the one below:

Back in 1926, when the army was designing its first-ever cockpit, engineers had measured the physical dimensions of hundreds of male pilots … and used this data to standardize the dimensions of the cockpit. For the next three decades, the size and shape of the seat, the distance to the pedals and stick, the height of the windshield, even the shape of the flight helmets were all built to conform to the average dimensions of a 1926 pilot.

[In the late 1940s] military engineers began to wonder if the pilots had gotten bigger since 1926. To obtain an updated assessment of pilot dimensions, the air force authorized the largest study of pilots that had ever been undertaken. In 1950, researchers at Wright Air Force Base in Ohio measured more than 4,000 pilots on 140 dimensions of size, including thumb length, crotch height, and the distance from a pilot’s eye to his ear, and then calculated the average for each of these dimensions. Everyone believed this improved calculation of the average pilot would lead to a better-fitting cockpit and reduce the number of crashes — or almost everyone. One newly hired 23-year-old scientist had doubts.

Before the second half of the 20th Century, as well, this philosophy dominated firearms design. Weapons were typically produced with one gunstock length or grip size, created with some rough approximation of the “average” user in mind. Of course, in reality, these were a poor fit for many people, and a very good fit for only a scant few. A different type of thinking was needed.

It was not the first time Daniels had measured the human body. [His] field focused heavily on trying to classify the personalities of groups of people according to their average body shapes — a practice known as “typing.” For example, many physical anthropologists believed a short and heavy body was indicative of a merry and fun-loving personality, while receding hairlines and fleshy lips reflected a “criminal type.”

Daniels was not interested in typing, however. Instead, his undergraduate thesis consisted of a rather plodding comparison of the shape of 250 male Harvard students’ hands. The students Daniels examined were from very similar ethnic and socio-cultural backgrounds (namely, white and wealthy), but, unexpectedly, their hands were not similar at all. Even more surprising, when Daniels averaged all his data, the average hand did not resemble any individual’s measurements. There was no such thing as an average hand size. “When I left Harvard, it was clear to me that if you wanted to design something for an individual human being, the average was completely useless,” Daniels told me.

So when the air force put him to work measuring pilots, Daniels harboured a private conviction about averages that rejected almost a century of military design philosophy. As he sat in the Aero Medical Laboratory measuring hands, legs, waists and foreheads, he kept asking himself the same question in his head: How many pilots really were average?

The bit about hand size, particularly, should be loudly ringing bells through the collective heads of all my readers. None of the hands Daniels measured conformed to the average, so then what is the use of designing for the average hand?

He decided to find out. Using the size data he had gathered from 4,063 pilots, Daniels calculated the average of the 10 physical dimensions believed to be most relevant for design, including height, chest circumference and sleeve length. These formed the dimensions of the “average pilot,” which Daniels generously defined as someone whose measurements were within the middle 30 per cent of the range of values for each dimension. So, for example, even though the precise average height from the data was five foot nine, he defined the height of the “average pilot” as ranging from five-seven to five-11. Next, Daniels compared each individual pilot, one by one, to the average pilot.

Before he crunched his numbers, the consensus among his fellow air force researchers was that the vast majority of pilots would be within the average range on most dimensions. After all, these pilots had already been pre-selected because they appeared to be average sized. (If you were, say, six foot seven, you would never have been recruited in the first place.) The scientists also expected that a sizable number of pilots would be within the average range on all 10 dimensions. But even Daniels was stunned when he tabulated the actual number.


Out of 4,063 pilots, not a single airman fit within the average range on all 10 dimensions. One pilot might have a longer-than-average arm length, but a shorter-than-average leg length. Another pilot might have a big chest but small hips. Even more astonishing, Daniels discovered that if you picked out just three of the ten dimensions of size — say, neck circumference, thigh circumference and wrist circumference — less than 3.5 per cent of pilots would be average sized on all three dimensions. Daniels’s findings were clear and incontrovertible. There was no such thing as an average pilot. If you’ve designed a cockpit to fit the average pilot, you’ve actually designed it to fit no one.

And the world’s engineers and designers wept. There was no easy answer, no real “average”; not even a large body of people who were even roughly-speaking “average-sized”, even in only a few dimensions. It was and is impossible to force every potential user to conform to an arbitrary “average” measurement, so instead engineers had to adapt to the users, and develop a new type of fit.

By discarding the average as their reference standard, the air force initiated a quantum leap in its design philosophy, centred on a new guiding principle: individual fit. Rather than fitting the individual to the system, the military began fitting the system to the individual. In short order, the air force demanded that all cockpits needed to fit pilots whose measurements fell within the 5-per-cent to 95-per-cent range on each dimension.

When airplane manufacturers first heard this new mandate, they balked, insisting it would be too expensive and take years to solve the relevant engineering problems. But the military refused to budge, and then — to everyone’s surprise — aeronautical engineers rather quickly came up with solutions that were both cheap and easy to implement. They designed adjustable seats, technology now standard in all automobiles. They created adjustable foot pedals. They developed adjustable helmet straps and flight suits.

In the firearms world today, we have adjustable stocks, grips, sights, optics, cheekpieces, and most other accessories. The gun world has, wisely, adapted to the needs of the decidedly non-average user. The days of “one-size-fits-all” are not quite gone, but they are going quickly, and it’s to the great benefit of the company who can afford it to adapt their existing designs to be able to adjust even further to fit ever more perfectly every possible user – in other words, customer – who might benefit from it.

If I may extend the topic past its welcome, it’s this quality that I would identify as one of the key factors in the popularity of the AR-15 rifle, especially since the advent of the M4 Carbine. The adjustable buttstock and the general modularity with regards to optics, grips, and handguards means that any given buyer of an M4-style weapon will get the absolute most out of it in terms of accuracy, ease of use, and speed. The more people can use the weapon to its greatest effect, the more satisfied customers a company will have, and perhaps more importantly, the fewer unsatisfied customers there will be.

The FBI, too, has recognized this need, as its latest solicitation for a 9mm handgun requires that submissions must have frame sizes that accommodate all of three different hand sizes. Even the US Army has recognized the reality of this problem, and a major criteria in its Modular Handgun System program is that the new pistol must have interchangeable, adaptable backstraps to fit multiple hand sizes.


Nathaniel F

Nathaniel is a history enthusiast and firearms hobbyist whose primary interest lies in military small arms technological developments beginning with the smokeless powder era. In addition to contributing to The Firearm Blog, he runs 196,800 Revolutions Per Minute, a blog devoted to modern small arms design and theory. He is also the author of the original web serial Heartblood, which is being updated and edited regularly. He can be reached via email at


  • Great article Nathaniel.

  • Dickie

    Nice history lesson.

  • politicsbyothermeans

    “average” shooter, according to Beretta when designing the M92.

    • Paul White

      I’ve got largeish hands and even I find it clunky

    • mosinman

      correction: the only man who can CC a Desert Eagle

      • Ranger Rick

        Arnold & Dwayne “The Rock” Johnson can also.

      • Paul White

        I met a guy at a local gun range that WAS carrying one! He was an older guy–late 60s maybe? Wore a hoodie and carried it in a shoulder holster he said his son made for him. Strangest thing but also kind of cool.

      • politicsbyothermeans

        If you look closely, he actually has a Desert Eagle concealed in each sideburn. Don’t ask where he keeps the reloads.

    • PLK

      I gotta be honest, I’m a full 2 feet shorter than Andre was but I like the feel of the M9 in hand.

    • The funny thing is the italians were known for amost 100 years to have the best foot library for shoe design size/shapes. They were a bit narrower than US shapes, regardless.

      • 6.5x55Swedish

        Italians can’t make shoes even if you force them at gun point. You have to choose between getting shoes that are either two times too long but wide enough or the right length but half the width. And even if you do manage to get your foot inside the damn shoe you will only be able to use it for three days untill it falls apart.

        • DaveP.

          George Raft ON

          “Alright Tony, you’re gonna cobble for me, see? I’m gonna give ya three hours, then there’s gonna be one of two things on your workbench: a pair of men’s black leather casuals, size ten wide… or your brains, see?”

          George Raft OFF

        • Miguel Raton

          “It is better to LOOK good than to FEEL good, & dahling, you look MAHVELOUS!”

    • TheMaskedMan

      Never understood why they made the grip so large. Guns generally should be designed with small hands in mind, especially if they have removable panels. You can always go bigger with grips, but not the other way.

      • Anonymoose

        That’s why the Vertec exists. 😀

        • TheMaskedMan

          The Vertec is how the 92 should have been built in the first place.

    • SheriffJon

      At least he has a plentiful supply of ammo…..

    • SirOliverHumperdink

      They put the safety on the slide for Andre’s giant thumb.

  • M.M.D.C.

    Thanks for this! Well done.

  • Nigel Tegg

    This article nicely puts to point why I hate bullpups

    • Joe

      Pistol grip should be as rearward as possible to obtain a LOP shorter than an M16A2, instead of longer as we typically see.

    • Mazryonh

      Would it be at all possible to get a bullpup design that could have an adjustable stock to fit more users?

      • David

        Yes, the VHS 2 rifle

        • It’s adjustable from “normal bullpup length” to “Robert Wadlow”, yeah…

        • The VHS-2 with its stock collapsed has a longer length of pull than the original non-adjustable VHS-1. That is not a step in the right direction.

      • 624A24

        For that to happen, the base receiver length must be shorter than existing bullpup designs – current bullpups have excessive stock length, especially when wearing a vest with plates.
        Shorter actions (in the sense of what the M73 and M219 were to the M1919) have to be designed without compromising reliability, and many things can go wrong, eg. excessive wear, bolt group velocity exceeding magazine stack speed (whatever thats called) and sensitivity to fouling etc.

        • Mazryonh

          Hmm, sounds more complex than I thought. I hear that when the magazine is too close to the back of a bullpup it’s harder to change the magazine especially if you’re wearing a vest with plates.

  • oldman

    One size does not fit all.

  • Kevin Harron

    Heh. You referenced a TorStar article. 🙂 This amuses me greatly.

  • nova3930

    the whole 5-95 compatibility is a perpetual thorn in my side at work. nature of the work is modifying existing platforms, but our human factors people act like we’re going to rework the entire cockpit for them…

    • hkryan

      I feel your pain. It’s really bad when we must use 5% female to 95% male!

  • Joseph Smith

    Small deviations from the “average” are not a big deal. I think it’s safe to say that even with modular systems it’s hard to find the perfect Goldilocks fit for some. Shooters have to get used to their weapons and train to the weapon.

    It’s the large deviations from the “average” that are forcing change. I could go on but TFB is about firearms not politics.

  • Hinermad

    I’m a little surprised the military, or at least the engineers doing the measurement studies, didn’t figure the standard deviation of their results. Standard deviation gives an idea of how unlikely it is a member of a population will be close to the average. A big standard deviation means not bloody likely.

  • 624A24

    Pretty much why bullpups aren’t the “ultimate firearm solution” they were touted to be. The universal army rifle simply isn’t.

    • iHAL

      It’s also why the AR-15 pattern is as if right now. It is the only rifle with complete modularity on the market.

      • Fegelein

        You haven’t looked at what’s new for the AK and SCAR recently, no?

      • Mujaga

        Pfft, AR-15 stocks are barely adjustable. Only for length which is basically the easirst thing to adjust.

        It’s like saying somebody isn’t retarded due to an iq over 70 but under 100.

  • paulm53

    I’m 6’3″, wear size 15 shoes, my glovesize is 3XL (Trump eat your heart out!). I hate hate hate average sized people!

    • Rooftop Voter

      6’4″ with size 14 feet. Of late, I find socks in a “one size fits all” from size 6 to 12. Um, no, that won’t work for me but it seems to be the trend for many of the offshore makers of products. When the Japanese cars started coming into this country in force many eons ago, the seat track would not push back far enough for the large American person but was adequate for the large Japanese driver. At least that has been changed but as for the socks, still the same.
      Don’t get me going on airline seating.

      Trying to get the g/f into a 9 mm but her fingers are so short she cannot grip anything in 9 correctly. Not crazy about a 380 size though.

    • Brian M

      5’5″, size 9 shoes, no gloves I buy ever seem to fit quite right. You lucky giant.

      • Anomanom

        Try women’s size gloves. Seriously. I have smallish hands, and men’s gloves never fit right. Maybe you have the same problem as me.

  • Bill

    Averages, means, medians and modes are all classified as descriptive statistics for a reason – they were never meant to be used for individualization, but bureaucracies being what they are…

    • Anomanom

      The problem is that you can’t craft a weapon for each person, individually. Well, you can (see Holland & Holland), but it’s time intensive and expensive.

  • Roy G Bunting

    This is the real promise of 3D printing for firearms. With pistols like the Sig P250 where you could have nearly any grip size and shape that fits around the magazine. With post grip revolvers and rifles like that AR-15, you could have nearly any grip shape.

    With a robust 3d print method and some method to figure out the shape of the model, this would be the most personalized grip.

  • Geoff

    The irony of referencing an article in the Toronto Star, which makes the New York Times look like Guns & Ammo, in a firearms article is incredible.
    Good points in the article, though.

  • Rodford Smith

    I have long arms and large hands. A few years ago I heard a man of below average stature gripe good-naturedly to a gun store employee about the trouble he had with rifle stocks being too long. I grinned and held out my arms, and noted I had the opposit problem. We all three had a bit of a laugh.

    Of course, there are many gunsmiths who do a booming business in making rifle and shotgun stocks longer or shorter.

  • Blake

    Spiffy article, thanks.

  • kzrkp

    interesting article. love seeing tailored solutions above one-size-fits-all engineering.

  • George

    It’s true that nearly nobody is “average” (do you mean “mean”, “median”, “mode”?…?). But everyone has a workable effective and workable tolerance band, and loses comfort and effectiveness outside that band. Devices have bands of effective use as well.

    It’s not “Joe’s size is X” or “Mary’s is Y”; Mary can hold the pistol from 3.8 to 5.0 cm length from backstrap to trigger face, say, but comfort maximizes at 4.2 and is disconfortable faster on the longer side than on the shorter side. And she may be most accurate at 4.6 cm and rapidly lose accuracy shorter than that. What’s her best length?…? 4.4 cm?… It may be her average best spot, but she’s not maximally comfortable nor accurate there…

  • Patrick Karmel Shamsuddoha

    good article thumbs up

  • Dolphy

    What ever happened to adapt and overcome?

    • Mazryonh

      Because 9-pound M1 Garand rifles just aren’t for everybody.

      And because no amount of “can-do” attitude is going to make a person’s finger’s, or arms, or legs longer/shorter. Maybe if we had the super-soldier formula from the Captain America comic book series . . .

      • Cmex

        So people shouldn’t learn how to deal with guns that aren’t tailored to them? My despair grows by the day.

        • Mazryonh

          I didn’t say that M1 Garands were impossible to use properly for many people. Clearly the thousands of American conscripts in WWII who learned to use the M1 Garand are evidence that many could and did use it well despite not having ideal physical traits for it.

          I was talking about how, as a “one-size-fits-all” solution, it was far from a comfortable gun for many of its users. Of course most people can train to become strong enough to handle an M1 Garand as easily as they can handle a baseball bat, but while you can shop for and buy a baseball bat of a specific length and weight you find comfortable, you can’t do that with the M1 Garand. So today’s more adjustable/customizable long guns are generally more comfortable to use than “one-size-fits-all” platforms like the M1 Garand was.

  • Jake

    “Even the US Army has recognized the reality of this problem, and a major criteria in its Modular Handgun System program is that the new pistol must have interchangeable, adaptable backstraps to fit multiple hand sizes.”
    Ah yes, the pistols must have additional parts to accommodate varying users. I have two predictions:
    Prediction # 1. The backstraps not currently installed on the pistol will immediately become lost. Forever. Some motivated company supply sergeant will record this on a shortage annex to be annotated ad infinitum, but battalion supply will never order these parts because people keep losing them. Thus, the Army ends up with a bunch of pistols that are still either too large or too small to properly fit the hands of the end user.
    Prediction # 2. A similiar, but different, motivated company supply sergeant will force the armorer to install all the medium backstraps on the pistols. He will then secure all the additional pieces in the original packaging; he will then secure these in a storeroom or warehouse nobody else has access to or really knows exists. These items, like most Basic Issue Items (BII) or Components of the End Item (COEI) will be guarded and hoarded by generations of sergeants-de-logistique (made up French phrase; don’t quote me on that) like the Holy Grail and only accessed for change of command inventories. Thus, the Army ends up with a bunch of medium sized pistols that are also either too large or small to fit properly.

    • Jwedel1231

      That’s like saying that the supply sergeant will force everybody to wear medium sized pants, hoarding the larges and smalls in a supply room.

      • Jake

        No, it isn’t because people don’t often lose their pants. People do, however, lose plastic things small enough to fit into their pockets.

        • Jwedel1231

          Yes, it is. If I am only going to be using the small sized back strap, issue me a small back strap and not the other sizes. Treat them the same as pants, or shoes, and for the same reason.

    • Mouldy Squid

      France has an actual law that requires that foreign phrases that are adopted into the language MUST be translated into French. If no native French phrase exists, one is invented.

    • cwolf

      You’re right.

      My first week in RVN I went to supply to get sun screen, etc. There were hundreds of various personal items neatly stacked and organized in the room.

      He refused to issue me anything because he was afraid he’d flunk inspections.

      And so it goes.

  • Vitsaus

    Its nice to know that we gun owners can all be unique snowflakes too.

  • Modern handgun frames are pretty thin, to be honest, and fit most people.

    If you are really worried about it, you have HK’s system of a backstrap and two side panels, shown in the title image.

    • Mazryonh

      Sure, for a given value of “most,” and likeliest to be the case when using double-stack 9mm Parabellum handguns (those using smaller rounds like the Five-seveN). Otherwise, why would some smaller-handed FBI agents complain about their 10mm handguns being too large when that caliber was still in vogue with that agency?

      As I mentioned elsewhere on this blog, is it possible to make a STANAG magazine for NATO handguns? Assuming everyone agrees on a specific caliber it might provide the simplification to logistics some are looking for.

      • Pistols simply aren’t militarily relevant enough to justify the *huge* downsides to a STANAG on magazines.

        • Mazryonh

          The STANAG on 5.56x45mm magazines may be an informal standard, but there are plenty of rifles than can take them.

          • That misses the point.

            We never actually adopted a STANAG for *any* magazines, even for weapons that are significant. NATO nations are free to whatever magazine they choose in any of their rifles.

            Why would they bother with a STANAG for handguns, under those circumstances? The purpose of equipment STANAGs isn’t to ensure compatibility at the squad or platoon level, it is to ensure compatibility at the major depot level, where you are dealing with tonnes of supplies being issued out to a unit.while ammo incompatibilities frequently have created mahor problems in wars, magazine incompatibilities simply haven’t.

          • Mazryonh

            NATO was pretty close to adopting the 5.7x28mm cartridge as the replacement for 9x19mm back in the early 2000s. It would have been interesting to see whether they could have made a “standard handgun” in that caliber.

            If the STANAG experiment has failed, then the next best solution might be to issue universal rifle magazine speedloaders in the field, because if a unit has mixed rifles using magazines of the same caliber some personnel might need to use loose ammo to load their own magazines.

          • “Came close” as in “some advocates of the 5.7mm talked about it”. What they did do was look at whether NATO should adopt a PDW as *another* standardized round *in addition to and beside* the 9x19mm.

            After some cursory testing where they couldn’t get any kind of consensus (despite FN’s desperate hopes when they pushed for the idea originally,figuring they would be the only viable.choice and be selected by default) on whether or not PDWs even made sense (much less what caliber they should be in, or whether a new PDW caliber in the inventory would be logical), the PDW issue and the 5.7mm cartridge were quietly dropped from any serious consideration for NATO standardization.

            Why would units have mixed rifles that use incompatible magazines? Most countries tend to try to replace the rifles in each unit at the same time, when there are major incompatibilities. The situations where this would even be a concern would be so infrequent and strategically irrelevant that the effort spent “standardizing” would actually be counterproductive to the overall war effort.

            Remember, there isn’t even one standard NATO rifle caliber – *both* 5.56 and 7.62 are equally valid, NATO standard rifle rounds. And many NATO nations are reintegrating 7.62 rifles into lower echelon units. Heck, Turkey, (who never switched over to 5.56) just adopted a new 7.62 rifle for line troops, not specialty use.

            Gonna be a Hell of an interesting universal magazine speed loader that can handle 5.56 and 7.62 cartridges, in all the various magazine forms NATO nations use… Heck, at the *height* of NATO rifle standardization – I.e., before the US adopted the M16 – there were at least *five* different magazine patterns in major use that I can think of among NATO nations – G3/CETME, FAL, L1A1 (just because an L1A1 can fit an FAL mag in doesn’t make them interchangeable – it’s strictly one way), M14, and BM59.

            And you think worrying about handgun calibers and small arms magazine standardization is actually relevant to NATO’s mission?

            Exchanging ammunition internationally, at the tactical level, is *not* why STANAGs on ammo exist. It’s for logistics compatibility at the operational and theater level.

  • Jim

    I generally have no trouble with the grip size on most handguns. Where I run into trouble is with the length of pull on fixed stock long guns. I’m 5’6″ and most rifles and shotguns seem to be designed for folks who are somewhat larger than I am. A couple years back I bought an 870 youth model. The thing fit me perfectly.

  • cwolf

    Add in equipment interfaces. The M16A2 has a very long trigger to butt plate length. When the Army shifted to qualifying in IBA, short folks were failing to qualify.

    In a sense, the regular measurements (arm length, etc.) didn’t capture the dimension needed to get the eyeball behind the peep sight.

    • That’s because the M16A2 stock was optimized for bullseye shooting in the standing offhand position, without armor or gear. By the Marine Corps.

      • cwolf


  • CavScout

    The Army took dozens of us during MOB training for measuring. We were stripped down to some provided speedo type boxer briefs and measured and scanned every which way to get sizing data. We assumed for the next, next gen of uniforms. Fun times…
    In the Civil War era, hundreds or thousands of soldiers were measured; and we ended up with current mail sizing stuff.

  • Mazryonh

    The funny thing is, the fact that people generally aren’t “average-sized” with regards to their body proportions has been known for a long time and even been used as a form of individual identification before fingerprinting and other methods took over for that purpose.

    Alphonse Bertillon, one of the fathers of forensic science and the creator of the mug shot, used what he called “anthropometry” to measure bodily proportions. With 18 bodily measurements, the odds of misidentification were 4 million to 1. This was clearly ample evidence of the “flaw of average” established early in the late 19th century, which would have been useful to the military engineers mentioned in this article had they heard of Bertillon’s work.

  • Mazryonh

    How about skeleton folding stocks for certain long guns? Those seem popular in some circles, but they certainly can’t be adjusted.