Gank Squads vs Protagonist

[RepresentingWrath]

...I'm not sure how exactly you reached all of this, but for me, there's a whole host of issues here.

If you get a fighter from two times higher weight class - I think we can agree that's roughly two times stronger - than their opponents, that guy is going to wipe the floor with them even if there's three at once.

I don't agree that linear and square at the extreme ends of the spectrum. For a succession of duels, even if we assume you can apply this rule (this is going to be difficult because it is designed to work with a singular engagement, not a series of them), you will get a linear law only with massive assumptions - and I can't really call them simplifications because they don't work properly.

If you pit two fighters against each other, one of which is ten times stronger, it should mean, for simplicity and for the sake of the law, that this fighter deals ten times more damage and has the same amount of health. If we assume the damage is dealt continuously, and that it is proportional to remaining health, then the stronger fighter will leave the fight with slightly less than 95% health. In the end, you'll need about ten fighters in succession to bring the strong guy down to zero.

And that seems to work on paper, but I have two main issues with this. One, in reality damage is not dealt continuously. This works for armies because we can approximate them as singular entities with different properties than individual units, but you shouldn't make that simplification in a one-one fight, especially when you have non-linear relationships which arise because of non-linear damage resistances and speed differences.

Two, the assumption that damage is proportional to the remaining health is ridiculous for singular entities. For armies, this makes sense because it's roughly proportional to the number of fighters. For individuals, it just doesn't work like this, even before we include weapons and armor - and if you compound this with the above, you get a relation so drastically different that the law breaks down on a fundamental level.

Another thing, I'm not sure if you skipped over that detail or not, but I don't fully agree with the spear formation. It can be modeled locally with the square law, perhaps, but (with all of the above in mind) only on the assumption you have one-three lines of spearmen. Otherwise, the damage-to-health ratio gets broken and you can't use the square law with any accuracy. The square law works specifically because ALL individuals are engaged in combat at once, and this plainly does not happen in any mundane melee combat with a large number of fighters.

Finally, I can somewhat agree with the last line, but only on the assumption that damage is proportional to health, which, as said above, isn't really realistic. Realistically, the worst case scenario may work this way, but not because of the square law, but primarily because damage is not continuous.

My favorite kind of math.

 

[AnonUnlimited]

Is this due to stamina and endurance?

 

[LilRora]

My favorite kind of math.

You mean differential equations? Or am I missing something?

 

[RepresentingWrath]

You mean differential equations? Or am I missing something?

 

[owotrucked]

If you get a fighter from two times higher weight class - I think we can agree that's roughly two times stronger - than their opponents, that guy is going to wipe the floor with them even if there's three at once.

If you have two times higher weight class, you might win hundreds of successive duels before you run out of hp, so you'll be considered way more than two times stronger. "X times stronger" might be a deceptive wording, so we're not talking about the same measure of "stronger".

One, in reality damage is not dealt continuously.

Of course the model is continuous and we apply it to a discrete case which introduces inaccuracy, but I'm pretty fine tolerating this spread.

You're right when you say that the inaccuracy of continuum defavors the high quality unit and you're in your rights to criticize that the assumptions are mismatched.

As for the other hypothesis, you could also lose attack power continuously with the loss of stamina or even muscle damage. A wound on harmstring, and you suddenly lose the weight behind punches.

Personally? I don't share that opinion at all. I think the assumptions also favors the high quality unit for overkill (no wasted damage overflow). I'll dismiss these as trivial concerns that can be corrected with an offset to favor the higher quality unit.

In addition, a continuous model already implies that we're simplifying a scenario. If you want to consider such things as speed differences and micro management, you obviously need to run a simulation.

only on the assumption you have one-three lines of spearmen

When I say locally, it means that we just consider the fighters engaged at the frontline in reach for the calculation of the outcome/remaining units.

It's true that people at the back and out of reach, who are idling while they slowly get closer to the actions, contribute to make the linear law more accurate to represent the situation.

No one is forcing you to model the overall battle with a single model or equations. In the end, the accurate method to explore intricate scenario will always be a numerical simulation rather than a model fitted on random shit.

I remain on my stance. Writers need to explain properly how MC overcomes number differences like how goblin slayer deal with pesky swarm of goblins. Even if the protag win every single duels in the story, they should get bodied by a zerg rush. If a writer needs real numbers to gauge the situation instead of abstract ideas, they can use the parameters of Lanchester's law to get an idea of the swarms they can deal with

 

[Anonjohn20]

According to Lanchester's square law, if you're outnumbered 1 to 10, you need to be 100 times stronger than the enemy to end a battle on a tie.

I can confirm. I gave my MC a harem that was too large, and he died of dehydration.

 

[Zagaroth]

Does Lanchester's square law consider equipment/skill quality? Like, if i'm wielding excalibur and wearing Space Marine armor and 10 thugs 1/10 of my strength surround me, would it still apply?

Your equipment would be considered part of your strength (barring scenarios where your equipment is ineffective)

 

[Kenjona]

To those discussing size versus numbers. Numbers have a quality of their own and it is generally multiplicative to strength. Check almost any of the how many (Pick an age) year olds could you fight links on the internet. Yes, even three featherweights could indeed take down a super heavyweight in a fight. A lot depends, mainly on how well he keeps tabs on all three and how well they coordinate between each other.

 

[cabbag3]

I can confirm. I gave my MC a harem that was too large, and he died of dehydration.

The best/worse kind of death ?