runners, lifters, scientists, engineers, geeks, gamers, casuals.

I am asking the following: "Do muscles atrophy and grow linearly, exponentially or depreciatively or possibly like a bell curve? Also same question but for fitness.", because I would love to know more about the metrics behind the human body and it's relationships with maths. This will truely help me better setup my training programs (for myself and hopefully one day others).

So far I do not have enough data to have a conclusion on this. I do theorize that it behaves as a bell curve though. Here is why I believe that. When you exercise in the begining you start getting small improvements, after a while they increase and increase at the rate of which they improve, it peaks, and then you start to have deminishing returns on your efforts. (Eg. Weight lifting, spriting 100m)

I really want to know that if you relatively increased the difficulty of each exercise as you got relatively stronger at what rate would you develope?

Eg. If you increased the difficulty by 5% each time, and managed to keep up pace, then you would have an exponential increase in performance. Though if you start to no longer manage the 5% increase and instead it slows down to a 4,3,2,1% increase over time then it's more like a bell curve.

Please let me know, or direct me to where I can learn, as much as possible about this. Thank you for your time. =)

  • Muscular growth is just an increase in volume...there's no reason for it to behave in a bell curve...if you add water to a balloon it grows until it explodes. Same with muscles, they grow until they reach a structural limit, what however has a bell curve is strength.... Strength is not linear because of hormonal reasons.
    – user33488
    Commented Jun 26, 2020 at 13:08
  • And since muscular growth is linked to progression in strength, if strength fluctuates then so will muscle growth.
    – user33488
    Commented Jun 26, 2020 at 13:09
  • Please try to limit queries to one per question. You may ask as many questions as you would like, but having a single question that is actually 5 questions goes against Stackexchange format. Commented Jun 26, 2020 at 13:23

2 Answers 2


(In this answer I am only addressing muscle growth.)

Muscle growth occurs on a per need basis within certain genetic and environmental parameters. Presenting a challenge to the muscles (typically by training) creates a stimulus for growth. Environmental factors (relative to the muscle tissue) such as stress and nutrition can promote or discourage additional muscle growth.

How fast can muscle growth occur then? In an optimal scenario, researchers Lyle McDonald and Alan Aragon have weighed in on this. Lyle's model sees individuals gaining 12-24 pounds of muscle in the first year each subsequent year is capable of half of its predecessor with women's rates typically being half of what men can do. Alan's model suggests a percentage based model where beginners gain 1.0-1.5% of their total body weight per month, intermediates see 0.5-1.0%, and advanced individuals see 0.25-0.5% per month.

But what about genetic parameters? This determines how far an individual could potentially go with regards to muscle growth. And distance from genetic potential determines speed of growth with faster rates occurring the further one is from that potential.

So the ideal rates look something like this, enter image description here

However, professional bodybuilder and coach Greg Doucette suggests that realistic models are much more modest. With such rates looking more like this.

enter image description here

Each category represents a "tier" of genetic predisposition for muscle growth. With women seeing half of these numbers.

  • High-High totals at 48 lbs of muscle in 10 years.
  • Med-High totals at 31.5 lbs of muscle in 10 years.
  • Low-Med totals at 21.5 lbs of muscle in 10 years.
  • Low-Low totals at 16 lbs of muscle in 10 years.

"Strength" or what others consider strength comes in waves, a continous up and down.

To make an example: you are incredibly weak, getting your first push ups is an uphill work, it's hard. After you learned how to do push ups, getting from your very first repetition to doing 30 in a row is downhill in terms of effort.

Then if you wanted to do them with weights or doing one arm push ups, you are going uphill again and everything slows down once more. This because we already have the strength to do those movements, but we do not know how to active the strength. Once we learned then it's easier to progress from there, but learning a new level of strength takes further work. Strength is a skill. Muscle is not the cause of strength but the adaptation to strength.

Growing muscle is like growing calluses, it makes you better at resisting damage.

This graph Shows how the difficulty in increasing strength works.

enter image description here

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