Mass and Strength Relative to Bodyweight

Training
1

For some people strength relative to their own weight is more important than absolute strength.

The ideal amount of may muscle differ between these two goals. For absolute strength, more muscle mass is always better. For relative strength, there are diminishing returns, and assuming symmetrical gains, perhaps within human reach a critical point at which more muscle is detrimental to performance.

The ideal amount of muscle mass for relative strength is more than zero obviously, and appears to be higher than the amount a beginner carries. It may however be lower than that of e.g. a bodybuilder, who by conventional wisdom is weaker in bodyweight movements such as pull-ups, than a lighter but still muscular person.

At least two important factors are involved:

  1. the less muscle mass you carry, the larger the discrepancy between percentual increase of muscle mass and percentual increase of total body mass (the proportion of your body mass that is muscle increases, as muscle mass increases). This factor causes you to become stronger relative to your bodyweight as muscle mass increases.

  2. power is proportional to the square of the cross-section of muscle, weight is proportional to the cube. This factor causes you to become weaker relative to your bodyweight as muscle mass increases.

At some point, factor 2 will outweigh factor 1 and additional muscle mass will reduce relative strength.

Equivalently,
relative strength (Sr) = absolute strength (Sa) / total mass (mt)
Sa = cross-section radius (r) ^2
mt = r^3 plus non-muscle mass (mn)
Sr = r^2 / (r^3 plus mn), a concave function in [0, inf), Sr reaches its maximum for some finite value of r

A third factor which I excluded is the mechanical disadvantage that may come with large values of r. It will only come to play if Srmax is close to the upper limits of attainable muscle mass.

The optimal r for relative strength will differ between body types and height. Question is, does it fall within the range naturally reachable, or not? I.e. is there is a situation where an athlete would prefer to not gain any more muscle mass, even if it resulted in higher absolute strength? And if so, at what level of muscle mass (perhaps reasonably expressed as FFMI and assuming a fixed body fat percentage) would that most likely happen, for a certain height?

More specifically, did any of you experience an increase of muscle mass, without raising your body fat percentage, which improved your absolute strength but reduced your relative strength, and if so, at what level? Among those you know that are strongest in relation to their bodyweight, what is the typical FFMI?

2

You bring up some interesting points. In professional athletics, I can think of wide receivers and offensive linemen as examples of those that are on opposite ends of the spectrum for body mass and strength. A receiver will not benefit much in gaining muscle as it will hit a point of diminishing returns and thus run slower. Whereas an offensive lineman needs to maximize weight and mass, not regardless of strength gains, but assuming that they will have to sacrifice strength to weight ratios, as weight is as or more important than strength.

From my own life, with one of my hobbies being rock climbing, and the prime movers being the finger flexors of the forearms, any additional mass is detrimental to success. There is no such thing as “popeye arms” where someone has giant forearm muscles, but very small muscles everywhere else.

3

[quote]Ecchastang wrote:
There is no such thing as “popeye arms” where someone has giant forearm muscles, but very small muscles everywhere else. [/quote]

I disagree to this to a certain extent. I was not at your level climbing, but I certainly went through a phase were my forearms were very noticeably more developed then any of the rest of my body. This is when I started to lift to try and compensate for the imbalance.

Going back to the OP though, I think it’s important to quote Dan John “It depends”. The “ideal” balance of muscle and strength depends entirely on the specific goals of the athlete.

4

Dagill2 - Point taken. There is still some limit to growth of certain muscles without attaining overall growth. I have read that it takes about 15 lbs of lean mass gained to add about an inch to one’s arms. Sure climbers have more developed forearms in relation to the rest of their bodies compared to normal folks. But look at sprinters. They really only work their legs, but most have well developed shoulders and arms as well.

Then there’s this guy, real life popeye.

5

[quote]mastero wrote:
Equivalently,
relative strength (Sr) = absolute strength (Sa) / total mass (mt)
Sa = cross-section radius (r) ^2
mt = r^3 plus non-muscle mass (mn)
Sr = r^2 / (r^3 plus mn), a concave function in [0, inf), Sr reaches its maximum for some finite value of r[/quote]
Can I just say that ^^^ that is the kind of complication that is entirely unnecessary and absolutely counterproductive to efficient, effective training. Strength training does not need to involve algebraic equations.

For sure. Most obvious is weight class athletes - competitive powerlifters, Olympic lifters, fighters, etc. When you have to compete at or below a specific bodyweight, there is definitely such thing as “too muscular”, even if it comes hand in hand with increased strength.

Why without raising bodyfat? Plenty of experienced strength athletes actually rely on a certain amount of bodyfat as a means to increase bodyweight, leverages, and performance. It could be argued that intentionally trying to limit bodyfat gains while trying to increase muscle mass and strength will yield poorer results than accepting some increased bodyfat as part of the building process.

However, at 6 feet and 155 pounds, I have to ask what your particular goals are with your own training? It’s sounding like you’re looking for an excuse to not gain weight. If that’s your thing, that’s fine, just be clear and direct about what you want. You don’t have to “math” your way around basic training.

6

[quote]mastero wrote:
The optimal r for relative strength will differ between body types and height. Question is, does it fall within the range naturally reachable, or not? I.e. is there is a situation where an athlete would prefer to not gain any more muscle mass, even if it resulted in higher absolute strength? And if so, at what level of muscle mass (perhaps reasonably expressed as FFMI and assuming a fixed body fat percentage) would that most likely happen, for a certain height?

More specifically, did any of you experience an increase of muscle mass, without raising your body fat percentage, which improved your absolute strength but reduced your relative strength, and if so, at what level? Among those you know that are strongest in relation to their bodyweight, what is the typical FFMI?[/quote]

I’ll give some of these questions my best shot.

For one thing, I’m assuming by ‘naturally reachable’, you’re referring to the use of performance enhancers, most likely steroids. I think it’s important to note that not all steroids are used simply to build mass, or absolute strength. There are many that are better suited for those trying to gain strength while maintaining, or even decreasing bodyweight. Masteron is a good example of this.

That’s why Anderson Silva was taking it (and I suspect many fighters use it). What I’m saying is that there are steroids (and other drugs) that can increase one’s relative strength substantially. I think this more or less addresses your first question. And obviously work capacity can be increased through drug use (think EPO or GW50156).

The answer to your next question is entirely dependent on the competition the athlete is competing in. Is the athlete a marathon runner? A sumo wrestler? A gymnast?

Now for the questions in the second paragraph. I don’t have an answer to the first question, but I can address the second question. The best strength to weight ratio is found in the 123lbs weight class for most lifting world records. As bodyweight goes up, even though athletes stay very lean up to about the 220 category, strength to weight ratios decrease substantially. No idea what the actual FFMI would be. I don’t see how answering this question is particularly useful for real-world applications.

7

[quote]Ecchastang wrote:
Dagill2 - Point taken. There is still some limit to growth of certain muscles without attaining overall growth. I have read that it takes about 15 lbs of lean mass gained to add about an inch to one’s arms. Sure climbers have more developed forearms in relation to the rest of their bodies compared to normal folks.
[/quote]

Absolutely agree, In my particular case it was more a case of serious underdevelopment elsewhere than overdeveloped forearms. They would still have been tiny compared to, well, yours.

[quote]But look at sprinters. They really only work their legs, but most have well developed shoulders and arms as well.
[/quote]

I’m lead to believe (I don’t claim to be an expert), that sprinters train upper body fairly heavily as they feel it helps them to develop power.

8

[quote]dagill2 wrote:

I’m lead to believe (I don’t claim to be an expert), that sprinters train upper body fairly heavily as they feel it helps them to develop power.[/quote]

This is correct. They’re not the smartest folk in the weight room, but they certainly do train the upper body. The sprinters I know all do power cleans. I know 1 sprinter who qualified for the Olympics a few years ago, and another who was just below that level as a hurdler.

9

Chris,

Sorry if the math scares you, its purpose is to show you that the function is concave. If the written text illustrated that point well enough, ignore the math.

I’ll remind you that the original post is about the relative strength of an athlete, i.e. for a certain height, at what point of muscle mass will your relative strength decrease from additional mass? It’s not about making a weight class, that’s a different question.

For example, I’m a runner. Obviously additional muscle mass is detrimental to my performance. That’s not the question. The question is, would my strength relative to my bodyweight increase if my muscle mass increased?

I’m not sure why you’re interested in my personal motives for asking the question, perhaps it’s your way to try to attain value (by ad hominem attacks against the posts of others), but I have nothing against telling you. It goes something like:

  1. General theoretical interest into the workings of nature
  2. I saw a tall and heavy guy do loads of pull-ups and questioned conventional wisdom that there is a great advantage being short and light for bodyweight movements
  3. I like gymnastics and bodyweight movements such as pull-ups

Do you have any observations to add to the discussion? E.g. answers (in context) to questions in my OP.

10

Thanks for your input flipcollar,

Naturally the ideal body composition is different between types of athletes. I’m referring specifically to athletes that would be interested in a high 1RM strength in lifts compared to their bodyweight. For example, in my country “fitness” competitions are common, part of which is bodyweight max repetitions for different exercises.

I think your answer about which weight classes have the best results relative bodyweight may hold the answer. One would just need the corresponding height of the top athletes in each weight class as well.

I agree in that the answer is most likely not particularly useful for practical purposes. It’s more of a general understanding about what body types are optimal for what purposes, similar to the often asked question of how a bodybuilder would compare to a powerlifter in strength aspects.

11

The reason, Chris, that the question referred to an increase of muscle mass with comparable amounts of fat, is that otherwise your results would say much about whether additional muscle mass increases relative power or not. Of course you can gain muscle mass and decrease relative strength by adding 1 kg of muscle and 100 kg of fat. That’s not the question. How can this not be clear to you?

12

The weight of a muscle is not proportional to the cube of its cross-sectional radius. The third dimension you’re looking for is length, which does not change.

So to sorta answer your question, shorter people with smaller frames will have better relative strength than taller people with larger frames, assuming “muscularity” (IE muscle cross section) is constant.

13

[quote]mastero wrote:
i.e. for a certain height, at what point of muscle mass will your relative strength decrease from additional mass? It’s not about making a weight class, that’s a different question.
[/quote]
Your assumption here being that strength increases predictably with muscle cross section? This is obviously false as a look at any top bodybuilders and powerlifters will show you.

I think the key word there is obvious. Pick almost any athletic discipline and it should be pretty obvious whether being a) bigger b) stronger c) leaner will have a negative or positive impact on their performance. In most cases, this isn’t rocket science.

Again, we’re back to the faulty assumption that strength increases linearly with muscle mass. Obviously false.

I hope your questioning didn’t take too much of your time. It shouldn’t take any formulas or complicated maths to see that in a movement where the load is your bodyweight, a lighter guy will have an advantage. This is not rocket science.

14

Steel Nation, you’re right, thanks.

15

dagill, I’ll have to disagree with your last statement. It’s true that a person with a smaller frame will have an advantage, but it appears most people will improve their performance in bodyweight movements by increasing their muscle mass (and becoming less “light”), as long as the increase is an effect of training for strength.

16

[quote]mastero wrote:
as long as the increase is an effect of training for strength.[/quote]

Please explain.

17

[quote]mastero wrote:
dagill, I’ll have to disagree with your last statement. It’s true that a person with a smaller frame will have an advantage, but it appears most people will improve their performance in bodyweight movements by increasing their muscle mass (and becoming less “light”), as long as the increase is an effect of training for strength. [/quote]

Really? Hence all those 250lb gymnasts, yes?

18

[quote]mastero wrote:
Thanks for your input flipcollar,

Naturally the ideal body composition is different between types of athletes. I’m referring specifically to athletes that would be interested in a high 1RM strength in lifts compared to their bodyweight. For example, in my country “fitness” competitions are common, part of which is bodyweight max repetitions for different exercises.

[/quote]

Just a couple things:

A high 1rm max does not necessarily correspond particularly closely with the ability to perform max reps on various exercises, even when bodyweight and height are similar. You’re good at what you practice. I’ll give you an example. There’s a guy on here who goes by CSulli who is very close to the same height and weight as me.

He also has similar 1rm’s to me in squat, deadlift, bench press, and weighted pull up. Yet he’s capable of doing 100 pull ups a day with relative ease, and I’ve never done more than 50 in a day. And I can only do that a couple times a week. Hell, my 1rm’s in the big 3 are comparable to many of the top Crossfit athletes, and yet those guys can absolutely destroy me in anything done for high reps.

19

[quote]dt79 wrote:

[quote]mastero wrote:
as long as the increase is an effect of training for strength.[/quote]

Please explain.[/quote]

1st scenario you hit a max for an exercise, stop using heavy weights and work in 12-15 reps range with assistance exercises for 3 months, you might increase your muscle mass but reduce your specialization for the exercise you measured your strength by

2nd scenario you keep hitting heavy weights regularly and as an effect get more muscle mass, you’ve kept your specialization and will have increased strength compared to your body mass, measured by that exercise

20

[quote]flipcollar wrote:

[quote]mastero wrote:
Thanks for your input flipcollar,

Naturally the ideal body composition is different between types of athletes. I’m referring specifically to athletes that would be interested in a high 1RM strength in lifts compared to their bodyweight. For example, in my country “fitness” competitions are common, part of which is bodyweight max repetitions for different exercises.

[/quote]

Just a couple things:

A high 1rm max does not necessarily correspond particularly closely with the ability to perform max reps on various exercises, even when bodyweight and height are similar. You’re good at what you practice. I’ll give you an example. There’s a guy on here who goes by CSulli who is very close to the same height and weight as me.

He also has similar 1rm’s to me in squat, deadlift, bench press, and weighted pull up. Yet he’s capable of doing 100 pull ups a day with relative ease, and I’ve never done more than 50 in a day. And I can only do that a couple times a week. Hell, my 1rm’s in the big 3 are comparable to many of the top Crossfit athletes, and yet those guys can absolutely destroy me in anything done for high reps.

[/quote]

Agreed, I do think it corresponds to potential of doing max reps, however, with a small amount of adaptation. While I’ve seen plenty of people with high 1RM that can’t do lots of reps, I haven’t seen one that can do lots of reps but doesn’t have a high 1RM. Working capacity for stuff like pull-ups comes quickly, which is why people see some success with programs like GTG / Armstrong.