Gank Squads vs Protagonist

[owotrucked]

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. This is usually appliable in open terrain where the gank squad can fully use all their forces to flank.

With this equation, even if a solo OP protagonist is strong enough to win 10 successive duels in a row, he would lose to a gank of 4 simultaneous enemies.

This is assuming there's no AOE, no crowdcontrol, no outplaying using enemy as shield. It also assumes that there's no overkill (overflowing damage is applied to the next enemy), and that damage dealt is proportional to remaining health (like get an arm injured will weaken the guys).

Conclusion:
- an OP protagonist could be the martial tournament winner and lose to a random group of thugs with 1/10th of his power
- if your protagonist is too stronk, adding more enemies square the difficulty
- if you don't like your protagonist getting zergrushed, give him crowdcontrol and AOE options

Also, swinging a weapon in a wide arc doesn't really count as AOE, because most of the kinetic energy would be spent on the first target hit and leaves no juice for the next target.

 

[Masked_writer]

What if your mc is just a giant (like the species), would number trick still apply ? Or do i have to buff the grunt attacking my mc

 

[Deleted member 84247]

Thanks for the Ted Talk. Obama approves of this message.

 

[Seaspecter]

Question, does this apply to tentacle monster protagonists?

 

[BigBadBoi]

Yeah we all played jrpgs before where you got hit by a surprise attack ambush by trash mobs and got your ass beaten

 

[owotrucked]

What if your mc is just a giant (like the species), would number trick still apply ? Or do i have to buff the grunt attacking my mc

Lanchester's law was for big armies.

If your giant doesn't lose attack power in proportion to lost hp, it'll be a lot more favorable to him so you'll need to add even more enemies

 

[RepresentingWrath]

Oh, it's time! It's time, IT'S TIME, IT'S WELL ACKHCHUALLY TIME!

 

[LilRora]

Lanchester's square law was designed specifically for modern armies with long-range weapons. You should have specified that. That law also specifically applies to idealized cases when the only thing that matters is the rate of killing the opponents - I wouldn't call that strength, at least not without an explanation.

There's also Lanchester's linear law for ancient armies (with medieval combat, I believe, falling somewhere in between), then there's also a number of different laws with specific modifications that account for various factors other than army sizes and individual strength.

If you attempt to apply Lanchester's square law to a general scenario, and especially to fantasy, you run into so many issues it's difficult to list them all out. Different body types, various skills, abilities, equipment, counters, compatibility, and more I haven't thought about.

When you have a very limited framework, such as in games, then both linear and square laws can work very well depending on the game, but in general they are practically useless without a high number or restrictions and caveats.

For your conclusions, too, the first one isn't true. For that, Lanchester's linear law would work much better, but even that isn't really accurate.

 

[Corty]

That is why my MCs always have a group with them. Solo leveling is cringe.

 

[owotrucked]

Nah the first conclusion is valid, a thug grabs the protag and then they beat him up. The protag gotta have way higher stats. The quantification of the disparity of stats should be actually simulated than modeled with an equation. RTS games can help with that

Linear and square are both extreme end of the spectrum, with linear being a succession of duels, and square being a gankfest.

Individuals in a spear formation can cover their comrades and could locally be modeled with square law.

The square law is enough to paint a broad stroke about the worst case scenario for your OP MC

 

[RepresentingWrath]

RTS games can help with that

It's not a reply to your comment but a separate thought. This piece right here made me think of Total War Warhammer, where you can make a one man doomstack. If you level up your lord correctly and use proper items you can solo multiple armies at the same time.

 

[beast_regards]

Question, does this apply to tentacle monster protagonists?

If attacked by 10 Magical Girls?

My bets are on tentacle monsters.

Magical Girls are conceptually weak against tentacle monsters.

 

[Seaspecter]

If attacked by 10 Magical Girls?

My bets are on tentacle monsters.

Magical Girls are conceptually weak against tentacle monsters.

That is true.

 

[Biggest-Kusa-Out-There]

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. This is usually appliable in open terrain where the gank squad can fully use all their forces to flank.

With this equation, even if a solo OP protagonist is strong enough to win 10 successive duels in a row, he would lose to a gank of 4 simultaneous enemies.

This is assuming there's no AOE, no crowdcontrol, no outplaying using enemy as shield. It also assumes that there's no overkill (overflowing damage is applied to the next enemy), and that damage dealt is proportional to remaining health (like get an arm injured will weaken the guys).

Conclusion:
- an OP protagonist could be the martial tournament winner and lose to a random group of thugs with 1/10th of his power
- if your protagonist is too stronk, adding more enemies square the difficulty
- if you don't like your protagonist getting zergrushed, give him crowdcontrol and AOE options

Also, swinging a weapon in a wide arc doesn't really count as AOE, because most of the kinetic energy would be spent on the first target hit and leaves no juice for the next target.

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?

 

[Kenjona]

Lanchester's square law was designed specifically for modern armies with long-range weapons. You should have specified that. That law also specifically applies to idealized cases when the only thing that matters is the rate of killing the opponents - I wouldn't call that strength, at least not without an explanation.

There's also Lanchester's linear law for ancient armies (with medieval combat, I believe, falling somewhere in between), then there's also a number of different laws with specific modifications that account for various factors other than army sizes and individual strength.

If you attempt to apply Lanchester's square law to a general scenario, and especially to fantasy, you run into so many issues it's difficult to list them all out. Different body types, various skills, abilities, equipment, counters, compatibility, and more I haven't thought about.

When you have a very limited framework, such as in games, then both linear and square laws can work very well depending on the game, but in general they are practically useless without a high number or restrictions and caveats.

For your conclusions, too, the first one isn't true. For that, Lanchester's linear law would work much better, but even that isn't really accurate.

Lanchester's law is like the Physics joke. It works, but....
"Milk production at a dairy farm was low, so the farmer wrote to the local university, asking for help from academia. A multidisciplinary team of professors was assembled, headed by a theoretical physicist, and two weeks of intensive on-site investigation took place. The scholars then returned to the university, notebooks crammed with data, where the task of writing the report was left to the team leader. Shortly thereafter the physicist returned to the farm, saying to the farmer, "I have the solution, but it works only in the case of spherical cows in a vacuum"."

So in a game universe run by a computer: Absolutely Lanchester's law is king if you make sure to include modifications subject to the computer programs changes to physics in that scenario.
Even the US military (and other militaries) who use it as a basis for certain types of training, tweak it with parameters based around the scenario being looked at or trained for.
That said Lanchester's laws can take in a Fantasy worlds issues as long as they are known for.

TL/DR: The law is not immutable and can be affected by other circumstances that are outsider its programmed calculations, but if known and included, does indeed allow for it.

Now the Square cube law on the other hand may take exception to your run of the mill fantasy giant.

 

[Snake99]

Who wins a fight is defined by many factors, both psychological and mechanical, that formula is good to use as a guide but I don't think it is good to rely completely on it.

 

[Kenjona]

What if your mc is just a giant (like the species), would number trick still apply ? Or do i have to buff the grunt attacking my mc

Men used to hunt mammoths and win. Mostly from ambush, by entrapping and/or wearing them down. So it depends.

 

[owotrucked]

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?

It's a simplified model where the relative strength of the units is only represented by "how many duels a unit can win in a row" so the equipment/skill quality is lumped/hidden in that number. If you don't want to lump everything in that number, you have to make a real numerical simulation I guess

Outside of memeing about battle outcome, the law can help estimate how many hp or units are left (if it's a landslide or tight victory) depending on a scenario (open ambush or chokepoint defense)

if your guy is alone with the front, rear, sides open, you can use square law. If your guy can kite and use walls and corners to cover themselves, you can use linear.

 

[LilRora]

Nah the first conclusion is valid, a thug grabs the protag and then they beat him up. The protag gotta have way higher stats. The quantification of the disparity of stats should be actually simulated than modeled with an equation. RTS games can help with that

Linear and square are both extreme end of the spectrum, with linear being a succession of duels, and square being a gankfest.

Individuals in a spear formation can cover their comrades and could locally be modeled with square law.

The square law is enough to paint a broad stroke about the worst case scenario for your OP MC

...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.

 

[Hans.Trondheim]

I always fight against groups of people in my workplace, like 44, 52, 60 peeps every hour, and I always WIN.

How?

"Sir Hans, why are you single?"

"Alright, entire class gets a failing grade from me today."

Disclaimer: for those who fail to get it, this is just a joke, and my students know it.