CA diminishing return

[BadOrc]

Anyone got a chart out the there? I lost mine and can’t find a new one.

 

[Jarvin]

What do you mean CA diminishing return?
If CA diminishes then so does fire/shock damage dealt, morale of armies among many others

there's no point in trying to make any chart for it because it'd provide 0 valuable insight about anything

 

[BadOrc]

Iam not goona get in to a debate why i need it is not the question. i Will make a new one myself when i get back home.

 

[Eruth]

What is CA? The jargon wiki page doesn't list it.

 

[Commonblob]

What is CA? The jargon wiki page doesn't list it.

Combat ability

 

[Eruth]

Combat ability

Thank you.

 

[lambda x.x]

It is diminishing returns in terms of "damage dealt" -- that is, going from X% CA to (X+10)% CA gives you a relative damage increase of 10/X % (where having no CA bonuses would mean X = 100). So if you graph that say using wolfram alpha, you'll see the curve -- as X gets higher, the relative damage increase decreases.
Intuitively, this is because going from 100% -> 110% is a meaningful increase, whereas going from 10000000% -> 10000010% is negligible.

However, it is (counter intuitively) not diminishing in terms of "casualty ratio" in a hypothetical combat scenario. That is, going from say 110->120 yields a better casualty ratio increase (roughly 12^2/11^2, or a 23% increase) than 100->110 (roughly 11^2/10^2, or a 21% increase). This is called Lanchester's square law (and is a reasonable model for eu4 combat since a unit's damage dealt scales with their strength on a per-regiment basis). This can be thought of as the "snowball effect" -- the stronger you are, the more decisively you will win.

So the question is what are you actually looking to perturb as you change combat ability? I made the mistake in the past of caring about "damage dealt," which makes it seem like CA has diminishing returns (just like tax for example), but what we really care about should be casualty ratio in combat, in which case it is not diminishing.

By the way, this does not mean you shouldn't round out your combat modifiers -- all Lanchester's square law says is that casualty ratio is the square of damage dealt, so if there were two hypothetical CA modifiers that are multiplicative with each other (say CA and discipline, while conveniently ignoring the direct defensive implications of discipline), having say 5% of each is still better than having only 10% of one when it comes to optimizing damage dealt (and therefore casualty ratio).

 

[BadOrc]

T

It is diminishing returns in terms of "damage dealt" -- that is, going from X% CA to (X+10)% CA gives you a relative damage increase of 10/X % (where having no CA bonuses would mean X = 100). So if you graph that say using wolfram alpha, you'll see the curve -- as X gets higher, the relative damage increase decreases.
Intuitively, this is because going from 100% -> 110% is a meaningful increase, whereas going from 10000000% -> 10000010% is negligible.

However, it is (counter intuitively) not diminishing in terms of "casualty ratio" in a hypothetical combat scenario. That is, going from say 110->120 yields a better casualty ratio increase (roughly 12^2/11^2, or a 23% increase) than 100->110 (roughly 11^2/10^2, or a 21% increase). This is called Lanchester's square law (and is a reasonable model for eu4 combat since a unit's damage dealt scales with their strength on a per-regiment basis). This can be thought of as the "snowball effect" -- the stronger you are, the more decisively you will win.

So the question is what are you actually looking to perturb as you change combat ability? I made the mistake in the past of caring about "damage dealt," which makes it seem like CA has diminishing returns (just like tax for example), but what we really care about should be casualty ratio in combat, in which case it is not diminishing.

By the way, this does not mean you shouldn't round out your combat modifiers -- all Lanchester's square law says is that casualty ratio is the square of damage dealt, so if there were two hypothetical CA modifiers that are multiplicative with each other (say CA and discipline, while conveniently ignoring the direct defensive implications of discipline), having say 5% of each is still better than having only 10% of one when it comes to optimizing damage dealt (and therefore casualty ratio).

Yes you are correct. However this is not a ”ingame” thing for me. I just thought i could save some time. This is more of a ”sideproject”.