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In my game you can be minuscule or gigantic, everything has its pros and cons

Outside of obvious things like weight, I've seen that the tallest people tend to be anorexic at absurdly high weights like a 200kg guy with 300cm in height would be almost just bones and skin.

If I can ask everything here, what are the formulas to calculate the strength/power/agility/intelligence of a human based on SCALE

If I can't ask all of them at once, let's go with strength.

scale: assume the person is scaled up or down proportionally so no dwarfism or gigantism, just a straight-up gal or guy scaled up or down.

Definitions:

Strength: muscular capacity to hold weight regardless of leverages, so like how long and how much weight can the muscle hold in a straight line before losing contraction

Agility: reaction time and change of direction, if I'm running and someone is throwing snowballs at me, agility determines how fast I can switch direction to dodge the snowballs and how easily and fast I can process the thought of deciding where to dodge after perceiving the incoming snowballs

power: muscular capacity to contract fully from a full stretch at maximum speed with the maximum weight, a high amount of power will contract incredibly fast when there is little weight resistance and will contract very slowly when the weight resistance is the maximum bearable

intelligence: capacity to imagine consciously, like playing chess by imagining your adversary moves in your head and planning your possible counter moves or if you are more primitive, imagining how your prey might react if you attack at a certain angle and miss their throat and thus planning how to secure the meal.

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  • $\begingroup$ While all the musculature measures - strength, agility and power - are interrelated, strongly suggest that you remove intelligence from this question and look at previously asked questions about minimum brain size for human-like intelligence. Also specify the environment, especially gravity - a human body 10 m tall simply won't work in 1 G due to the squared-cubed law, but might be feasible (albeit disproportionately physically weak) in zero-G. $\endgroup$ Jan 2 at 22:08
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    $\begingroup$ There is no such formula. One of the strongest men in the world is Darren Sadler clocking in a 5' 8" tall. In my youth I was 5' 10" tall and he would have kicked my furry white butt in an embarrassing handful of seconds. Strongman competitors range in height from 5' 8" to 6' 9". Just to add insult to injury, I wrestled a 4' 10" classmate in high school. He was on the wrestling team and I wasn't. I lost with prejudice. And while I'd never ... (*Continued*) $\endgroup$
    – JBH
    Jan 3 at 0:15
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    $\begingroup$ ... claim that the shortest man in the world could take on the tallest man in the world, I wonder if I in my 50s I might not have a shot... if I can get past his reach. My point? Training has more to do with strength than height. $\endgroup$
    – JBH
    Jan 3 at 0:22
  • $\begingroup$ Size certainly has nothing to do with intelligence. Humans are smaller than some species and larger than many, many, many species and yet are more intelligent than any others. $\endgroup$
    – KEY_ABRADE
    Jan 3 at 16:48
  • $\begingroup$ @JBH There certainly is a formula that's why every sport breeds mutats that all look alike, all swimmers look like penguins, all strongmen look like fantasy dwarves, all sprinters look the same, all marathon runners look the same. matter of fact I've never seen an olympic sprinter with short legs or a swimmer with long legs $\endgroup$
    – Xenophile
    Jan 3 at 18:36

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When it comes to making animals bigger there are two rules of thumb you have to remember.

  1. Surface Area to Volume Ratio - Take a single, 1 inch square. It will have a volume of 1 cubic inch, and it will have a surface area of 1X1X6, or six square inches. So it has more surface area than it does volume. Try that with a block of 1000 squares though. Such a block would have a volume of 1000 cubic inches, but it's surface area would be 10X10X6, or 600 square inches. At this point, volume exceeds surface area by quite a bit. As that relative surface area goes down, it's going to be harder for cold blooded organisms to warm up or cool down and harder for warm blooded organisms to dissipate heat. This is why there are no rat sized marine animals and why big animals that live in hot places either have clever surface area hacks like an elephant's ears or spend a lot of time in the water like a hippo. Anything big is going to have to deal with the heat they produce. If they live in the freezing ocean, this is fine. If they live in a sunny grassland, it's more of an issue.
  2. Cross Sectional Area - The amount of weight your legs can hold up are determined by their cross sectional area, not their total bulk. This means that a thicker leg can hold up more, but as with the surface area to volume ratio, weight is cubic while cross sectional area is square, which means that weight will go up faster, and so, the larger an animal gets, the larger it's cross sections have to be by comparison. This means that if you just blew a human up to 100 ft tall, their legs would break under their own weight. Notice how elephants have giant tree trunk legs? Anything that heavy needs structures like that. As something gets bigger, all the structures that hold it up need to get thicker, and the thickness needs to grow faster than the weight in order to keep up. A giant humanoid would probably be built more like a dwarf than a human, needing a thick torso and thick, stubby little legs in order to be able to hold itself upright.

For these reasons, just straight up scaling a human up and down just wouldn't work. You wouldn't get them that much bigger or smaller until physical realities would make them non-viable. A human sized grasshopper or elephant sized human would collapse under its own weight and likely suffocate unless their body form was changed to accommodate their new size in ways that would make them look radically different.

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