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As a fellow Analytics pro and man of data in general, I REALLY like what you're trying to do. From the skim I took, you're trying to determine a metric for lean muscle mass / height.
However, I think where you'll eventually be hamstrung (no pun intended) is data purity; by your own statement a lot of this is estimation and guesswork. The raw, base data is largely self-reported, sadly with much temptation to exaggerate, and can hinge upon fluctuations in water weight, as well as the adeptness of s/he who wields the BF calipers. Don't get me started on those annoying bathroom scales that shoot a current through you and pretend to extract accurate Fat/water qty/%.
I have more faith in current/future DEXA testing, where some exciting developments are being made, as the scan can now give a value for the amount of LMT you have in a bodypart, though I think it'll be some time before it can discern biceps weight from Triceps, even longer still Biceps/Brachialis etc. It's expensive, but like any tech, cheapens over time, hopefully becoming as commonplace as tape-measured Breast/Waist/Hips. On the glorious day we have that granularity and accuracy of data widely available, some pretty exciting ideas blossom, like using comparisons of legs considered stunning, vs other legs of the same length/muscularity/fat% on another girl being awful, and using analytics to infer optimum proportionality.
However, I think where you'll eventually be hamstrung (no pun intended) is data purity
Honestly I don't think it's that bad. The dominant source of error should be from the estimation of bodyfat assuming a halfway decent weight measurement. In this case, the overall error is directly proportional to the error (not the fractional error) in bodyfat. This means the overall error can be kept fairly low if you just look at competition photos with corresponding weight measurements. (I think they would record weight before the competitions and post the stats somewhere, right? e.g., found this when looking for Ramsteiner's height, but it looks like whoever did the measurements really slacked off when it came to the women.)
The formula for FMME basically just came from that paper, which does mention DEXA a lot, though I can't be bothered to read it. If it's good enough for her diploma it's good enough for a random funny. I do find it mildly amusing that we are applying a statistical rule to all the anomalies out there.
Honestly I don't think it's that bad. The dominant source of error should be from the estimation of bodyfat assuming a halfway decent weight measurement. In this case, the overall error is directly proportional to the error (not the fractional error) in bodyfat. This means the overall error can be kept fairly low if you just look at competition photos with corresponding weight measurements. (I think they would record weight before the competitions and post the stats somewhere, right? e.g., found this when looking for Ramsteiner's height, but it looks like whoever did the measurements really slacked off when it came to the women.)
The formula for FMME basically just came from that paper, which does mention DEXA a lot, though I can't be bothered to read it. If it's good enough for her diploma it's good enough for a random funny. I do find it mildly amusing that we are applying a statistical rule to all the anomalies out there.
Before I decide to unpack the rest, can I ask what you find humorous about quantifying this - or indeed anything else to do with admiring muscular women?
Before I decide to unpack the rest, can I ask what you find humorous about quantifying this - or indeed anything else to do with admiring muscular women?
Apologies, I meant no offense. Please allow me to clarify.
According to statistics over the entire population, mass can be taken to be proportional to height^2, and hence mass/height^2 should give an index reflecting how obese (or in this case, how muscular) one is that is independent of height. Since this is a statistical rule, it only works well near the average. This is not the case for most of the women here, therefore the square dependence might not work well. Basically, I fear two gwm with a significant difference in height and the same FMME will have quite different muscularity, which somewhat defeats the purpose of this. (I haven't really looked into the effect of this, so I don't know if it will potentially become a problem.)
What I find amusing is that far more intricate things (as can be seen from the factors 1.282 and 7.6) are being corrected for without addressing the problem above. To me, this feels analogous to attempting to measure the length of something with laser accuracy while the table is shaking.
With that said, I really do appreciate and is impressed by what Thessel has done so far. I also find myself enthusiastic to do whatever contribution possible. I realise mass/height^2 is probably as good as we can do to remove height dependence. Decreasing the error in body fat percentage is definitely important as well.
tldr, one aspect of the problem has been corrected very well, nothing can be done about the other aspect, so I rant.
Thank you for your interest. I am fully aware of how prone the FMME calculation is to errors. Rounding errors alone can change the FMME-value by as much as 10 points. The formulas may sound very scientific (such as the 1.282 factor for fat mass), but the FMME-project is purely a hobby. Of course, I am happy when better methods, like the InBody measurements for skeletal muscle mass, become more widespread and improve the data basis. I also know that I will have to revise the FMME-value diagrams several more times. It is possible that the average value will change with better measurements, and all previous FMME-values may need to be divided by 1.1 (or something similar).
On the other hand, I didn’t want to wait until (nearly) perfect measurement results are widely available but wanted to get a rough overview now. Even in the future, such perfect measurements will not be available for all girls with muscles. Instead, they will be compared to women with similar muscularity and BF percentage, and an (optical) FMME-value range will be estimated.
(Another application might be to later review old Miss Olympia competitions from the 1980s and 1990s, estimate FMME-value ranges for the winners or participants in general, and thus highlight the development over time.)
Very interesting work!
According to the German paper, the mean and standard deviation for MMI of "normal" women is 5.0 +- 1.9, and for "normal" men it's 10.6 +- 2.2.
Multiplying that by 20 to get Thessel's FMME:
Normal women: 100 +- 38 Normal men: 212 +- 44
A frequent question on these boards is how a lot of the women here compare in muscularity to men, and this gives you your answer.
Roughly speaking, you could consider an FMME of 100-150 to be a range for "normal" women on the positive side of average. In other words, women who are more muscular than average, but not exceptionally so (roughly speaking, something like 50th-80th percentile).
150-200 could be considered the "gateway" range - fitness models, bikini competitors, athletic women in sports requiring above-average strength, and the like - in the 80th-95th percentile for women, but still below average (although within 1-2 standard deviations) for males of equivalent height. Ashley Kaltwasser (Bikini Olympia) is somewhere in the 180-200 range, per numbers I found online.
200-250 is where women have similar muscularity to the "average" to "slightly fit" man. This is probably your figure and wellness type competitors, more muscular female athletes, and the like. This is also probably the range corresponding to the natural limit for most women not using PEDs, as this is getting into three standard deviations above the mean (i.e. top 0.15%). Cydney Gillon (Figure Olympia) and Isabelle Nunes (Wellness Olympia) are both somewhere around 250.
I suspect the most reasonable "natty or not" cases would be in the 200-250 range, since these are physiques which could be attained naturally for those with favorable genetics, although it's much easier to do so with PEDs (and doubly so if you want to maintain this much muscle at a low bf%!). It's these cases where you need to do a little digging - how quickly did they develop their physique, did it happen gradually or in spurts as you might expect from cycling PEDs, how lean have they been while gaining muscle, etc...
250-300 is where women are more muscular than 60-70% of men. This is where you get into physique territory, where their muscularity is comparable only to reasonably muscular and athletic men. This is almost certainly unattainable without PEDs for the vast majority of women (the exceptions being those with very heavy skeletal frames for their height, and exceptional muscle-building genetics). I'm having a hard time finding stats for current physique competitors, but based on what I can find, Dana Linn Bailey was probably a bit under 250, while Natalia Coelho is a bit above 250. I suspect that number for Natalia is a bit off, though, since I've found other weights listed for her that provide FMME's more like 300 (although these may be at higher bf% values).
Above 300-350 is pretty solidly FBB (as opposed to figure/physique/etc) territory. FMME of 300 is also about 2 sigma above the mean for men, so this is a range occupied by the top 2% of men. In other words, jacked dudes (maybe not quite professional male bodybuilder territory, more "the really jacked guy at my gym" territory, or a competitor at a local male bodybuilding show). Andrea Shaw (Ms. Olympia) was estimated elsewhere in this thread in the 350 range, and Angela Yeo is in the neighborhood of 340.
350-400+ is where you get into seriously massive women... and men. Think Michaela Aycock, Amazonka - I think both were estimated elsewhere in the thread in the high 300's - 400 range. And the sort of men who could rival them in muscle mass. Chris Bumstead is somewhere in the low 400's, for comparison.
I'd guess that somewhere in the low to mid 400's is the limit for women, even on ridiculous amounts of gear, even with god-level genetics, even after years of training.
Males can go a bit higher - Jay Cutler was around 550, and Ronnie Coleman was about 650, at their peaks. Not sure if there's anybody higher than Ronnie, although it wouldn't surprise me if some of the really big strongman competitors were - they may be able to maintain higher muscle mass at a higher bodyfat percentage. I don't think anybody is beating Ronnie by much, though.
Just for poop 'n' giggles, I ran my own stats (69", 175#, 19% bf) through the formula, and came up with an FMME of 244. That puts me 0.7 standard deviations above the mean, and somewhere in the "figure/fitness" territory if I were a woman :-) I was hoping to do a bit better, but I'll take it. I'm a 45-year old man, office worker, slightly overweight but I look reasonably fit since I've been lifting on and off for 25 years. Mostly stepped away from fitness for the past decade due to work/health/personal reasons (hence the excess weight), but started to get more seriously back into training over the last year and gained back a lot of the muscle I had lost.
Thank you, jtrain. Your post not only provides a detailed comparison between muscular women and men ranging from normal to muscular but also touches on another interesting topic: the natural limit for muscle mass in women without PEDs. I’ll try to find some additional information on that later.
From an instagram post by the Japanese athlete Eriko Shimizu (https://www.instagram.com/p/CQ3ey-eBkA9/), I gathered data about her body weight and fat mass between January 2021 and July 2021. Considering her height of 1.58 m, her FMME-value initially dropped slightly from around 190 to 180, before rising to approximately 200 within two months. On 2021-09-11, she competed in her next contest (Nihon Class 2021) – see image. This places her in a similar range of FMME-values as Yôko Shimizu.
I also tried to estimate the Japanese athlete Chie Shikata based on her reported height of 1.67 m and weight of 56 kg (Nishinihon contest 2024, West Japan, 1st image). From the direct comparison (Miss Nihon 2024, 2nd image), I would place her below Yôko Shimizu but above Jessica Preswich (FMME 181, 3rd image). This would roughly put her in the range of 180 to 200, but likely closer to 190 or below.
As promised, I looked into the natural limits of muscle mass in women without PEDs. To get straight to the point: I did not find a definitive answer.
First, the FFMI (fat-free mass index) is commonly used: (Body weight - fat mass) / (height^2) [in kg/m²]. There is also a formula for adjusted or normalized FFMI = FFMI + 6.1 * (1.8 - height).
https://www.burnthefatinnercircle.com/public/... mainly focuses on men. It mentions an average FFMI of 25.4 for 20 Mr. America winners from the pre-steroid era (1939-1959) and suggests a natural maximum of 26-27 for genetic elites. Regarding women, it speculates:
“However, after a little digging, I did locate another older study (Shutz, 2002) which reported that in a large sample of 2649 women, the median FFMI in young females was 15.4. Among this general population (again, not bodybuilders), the high end (95th percentile) topped out at an FFMI of 19. Based on this data, at least one expert has estimated a possible FFMI upper limit of 20 for female natural bodybuilders. This is purely speculation, and may not reflect elite athlete populations, but it is based on the limited data that is available.”
https://martin-fiedler.at/muskelmasse-wie-vie... also primarily focuses on men, calculating a FFMI of 25 for Eugene Sandow and noting that GNBF sets a limit of 26 for men. For women, a natural maximum of 21 is mentioned.
https://www.omnicalculator.com/health/ffmi categorizes normalized FFMI for women as follows: 21.5-25 Suspicion of steroid use; more than 25 Steroid usage likely.
Finally, https://bodyrecomposition.com/women/womens-ma... estimates a maximum of 1.84 lbs lean body mass (= fat-free mass) per inch for women, corresponding to a FFMI of 18 to 21.5 depending on height, or a normalized FFMI of about 18 to 23.
(If we use the MMI difference of 5.6 kg/m^2 between average men and women from Eva Heinen’s study as a basis, the natural FFMI limit for women would be below 27 - 5.6 = 21.4.)
The MMI in kg/m^2 can be calculated from FFMI and body fat percentage (BF%) as follows: MMI = FFMI - 7.6 kg/m² - (FFMI / (1-BF%) * BF% * 0.282). Body fat influences this via the fat-free portion of adipose tissue.
In the following table, I calculated MMI-values for FFMI levels ranging from 16 to 22 and body fat percentages from 5% to 30%. Additionally, I provided normalized FFMI-values for women with heights of 1.65 m and 1.50 m.
By multiplying these FFMI-values by 20, you get the FMME-values. In the thread https://www.girlswithmuscle.com/forum/thread/... ("Your favorite (probably) natural women?"), it was often mentioned that natural women could be either very muscular or very lean, but rarely both. Based on this, I would suggest that women with higher BF% may reach higher maximum FMME-values than those with lower BF%.
A maximum FMME-value of around 200 (or slightly higher) is therefore possible.
Yeah, I was going to write a follow-up post, but life got in the way. The one big thing which the FMME statistic misses is bodyfat percentage. As you said, it's much easier to gain muscle and strength while in a caloric surplus, and that generally means you'll be at a somewhat higher bodyfat percentage.
What people don't completely understand is what steroids do: they convince your body that building and maintaining muscle is the single most important thing. Our genes were shaped over tens of thousands of years, most of which were spent under subsistence agriculture or hunter-gatherer lifestyles. If the animal got away, your family didn't eat that night. If there was a drought or a poor growing season, or the invading bastards trampled your crops again, you might be rationing food for months. Therefore, in a caloric surplus, your tendency is to gain fat so you can live off of it during the lean times. Muscle? Your body puts on as much of that as it needs to get through life, and no more, since any extra muscle is a liability (excess weight to carry around, excess body mass which needs to be perfused, with the extra strength conveying no significant benefit since you already have more than you need).
Lifting weights doesn't cause muscles to grow. It's the recuperation period afterward which does. Your body detects the damage done to the muscles during training, and builds them back to the strength it believes you will need. But if you're in a caloric deficit, you generally won't build more muscle since your genes have greater priorities in keeping your ass alive. So you'll train and train but gains will be slow to nonexistent. Everyone who's lifted for some time has been there; we call them plateaus. It can happen if you're not eating enough. It can happen if you've been doing the same thing for too long, and your body isn't receiving the stimulus it needs to build more muscle than it already has. It can happen if you've reached your natural limit and your body decides there's no point to building any more muscle than you already have. You can lift all you want, but you're going to keep lifting the same every time. Or worse, you'll grind yourself down through overtraining and your strength will actually decrease over time (or an inevitable injury will sideline you).
Steroids turn all that on its head. Now your body revs up to build muscle at every opportunity. Faster recovery enables higher training volume and frequency, which enables faster gains. Your natural genetic limits on muscle growth are raised. And de-prioritizing all that other "useless" stuff (replenishing fat stores, repairing organs, etc) allows your body to do this, even in a caloric deficit with scarily low bodyfat percentages.
That's a bit simplified, but the basic picture.
So yeah, you're likely to find the most amount of muscle - among both natural and enhanced lifters, but particularly the former - in people with higher bodyfat percentages.
It seems reasonable that a FMME of about 200-250 is the natural limit for most women (although it's a lot easier to get there with PEDs).
Using those same numbers (max MMI of ~26), the maximum FMME for natural men in the range of 350.
Another issue that FMME doesn't account for is bone structure. Some people just have more skeletal mass than others, and natural limits on strength are going to depend on that.
For example, my wrist circumference is 6.25", which is pretty low for a man of my height. I have pretty small bone structure. My biceps are a little over 14", which is actually pretty decent for my bone structure. I'm not "huge" but I look pretty fit, comparatively speaking. But it means I'm never going to have a huge MMI, nor am I going to have enormous strength, since I'm limited by my bone structure.
We can't all win the genetic lottery. I don't do too badly, though, since I find it fairly easy to gain muscle mass. I also gain fat very easily. And I have a lot of joint laxity which predisposes me to injuries if I'm not careful.
I'm still trying to figure out how this biases the results for FMME. Somebody with more skeletal mass has a higher overall bodyweight for a given amount of muscle mass and bodyfat compared to a person with less skeletal mass but the same amount of muscle and fat.
Either way, somebody with more skeletal mass can put on more muscle mass (both naturally and enhanced, I suspect), so this is going to play a role in max FMME values.
I was then trying to think of how you could compare two people.
For example, a female bikini competitor with FMME ~ 200 with an "average" man with FMME ~200. Who would win in, say, an armwrestling match?
First up, you have to consider height. FMME is a height-normalized metric. Given a tall person and a short person with the same FMME, the tall person has a lot more muscle mass (roughly proportional to height^2), and likely more strength, than the tall person.
An average-height bikini competitor (say, 5'4") going against an average-height average man (say, 5'9") is going to be at a huge disadvantage. Her muscles might look just as big in comparison on her frame, but her frame is much smaller than the man's. Her arms are also likely shorter, and that puts her at a significant advantage.
On the other hand, this bikini competitor does regular strength training. She knows how to use every ounce of her strength and leverage to her advantage. The average man, not so much. Even leaving aside technique (and a lot of armwrestling is about technique - a competitor with good technique will almost always beat a stronger competitor who doesn't know technique) - the female competitor would be at a significant advantage due to her strength training experience compared to Joe Sedentary.
I'm thinking, for example, of the various Grace Hilbing videos in which she armwrestles regular-looking frat boy types. She wins some, loses some (mostly the former, but there could be selection bias in which videos get posted). She's probably in the ~200 range, FMME wise, as are most of her male opponents, although most of them are taller and have longer arms. She also has a lot of experience and I'm sure has picked up technique along the way, something most of her drunken opponents lack. And that's the other thing - I'm guessing most of her opponents are pretty inebriated, which is going to negatively impact their performance.
So it seems like it could go either way.
Now, take a physique-level competitor in the 250-300 range, and I think she'd put down most men, aside from either very strong and well-trained men (FMME of at least 250-300), those who are experienced armwrestlers with a technique advantage, and some men who aren't as visibly muscular but are much taller so they have a leverage advantage.
Of course, strength comparisons aren't going to be uniform. Even if you have a woman and a man of the same "average" strength, chances are the man will be stronger in upper-body movements, while the woman is stronger in lower-body movements. So if you compare multiple skills, it's likely to be a mixed bag.
Yeah, I was going to write a follow-up post, but life got in the way. The one big thing which the FMME statistic misses is bodyfat percentage.
In my initial post, I mentioned the importance of considering FMME and body fat percentage together. That’s why I proposed creating an FMME/BF map.
It seems reasonable that a FMME of about 200-250 is the natural limit for most women (although it's a lot easier to get there with PEDs).
Using those same numbers (max MMI of ~26), the maximum FMME for natural men in the range of 350.
I also thought about better ways to determine the natural limit of female muscle mass. One approach could be estimating FMME-values for the very early gwm. However, more accurate reference images and values would be needed, especially for their body fat percentages. (like here:
Another option could involve analyzing Japanese bodybuilding/physique competitions, where certain levels were never surpassed — even though some participants were likely not natural. For the relatively most muscular winner, Utako Mizuma, I calculated a potential FMME-value of around 232 for an assumed 8% BF. Even at 7% or 6%, the FMME-value would only rise to 237 or 242. Additionally, the BMI of Japanese athletes has decreased by about 1 kg/m^2 since the 2000s (see: https://www.girlswithmuscle.com/comment/3261333/), which — assuming constant BF% — corresponds to a reduction of 1 kg/m^2 in MMI or 20 in FMME. This would suggest a natural maximum of no more than 220, which aligns with the values for Yôko Shimizu (around 210) and Eriko Shimizu (around 200). However, this does not necessarily mean these Japanese athletes are actually natural. It’s also important to note that these estimates apply specifically to low BF of 10% or less.
I cannot comment on skeletal mass or arm wrestling.
Second overview selected (maximum) FMME-values sorted by categories:
Changelog:
Thanks for pointing out Natasha Broegger's data. I didn't know about the thread. Her FMME value would be 275. If I were to use the original FMME formula, I would have to estimate the weight of the implants. For 1 kg implants I get 289, for 1.5 kg I get 279 and for 2 kg I get 269. So you get similar results in both ways.
Some links to Japanese InBody results (images of the result sheet). Including height, the skeletal muscle mass, the FMME value calculated directly from it (bold) and the value calculated from the FMME formula (italics):
For normal to athletic or overweight women, the results of the FMME values for both types of calculation differ quite widely. For more muscular women, the difference seems to be much smaller. (For Yôko Shimizu, the difference was only about 6%).