Unit power rate

[AOEisLOVE_AOEisLIFE]

i like this new and constructive criticism kaiser... oh wait.

Yep it's constructive, I explain why his formula is not relevant. If you want I can even write the real algorithm to compare units fighting each other, much more accurately, even though it's ofc not perfect.

^he just says that because he can't calculate the power rate of his mass vs enemy mass in real time ingame in his head. what a newb.

[bwinner]

So can you explain what this formula does and how you came up with it?
P(a, h, p) = ah/p^2. Are you saying that unit X beats unit Y <=> P(a_X, h_X, p_X) > P(a_Y, h_Y, p_Y)? (assuming no micro and units are standing next to each other)

When you have a system like : if u (x,y) ->(-k1*y,-k2*x) and then with X=(x,y) solve the equation X'=u(X), you can prove that the solution which respect a such equality (with x,y number of each unit and k1, k2 coefficients that represent the number of y(resp x) that x (resp y) kill per second). I won't give more détails, but it's Something like that.
However, overkill is really important in real fight, that's why kaiser sais that you should rather use an algorithms, btw the idea to program it isn't bad, because I think it could be a usefool tool for the eso-assistant

[tedere12]

nerds trying to correlate aoe with maths

[Dsy]

Btw this formula nothing to do with beating some1. It just shows unit combat efficiency for its price.
If you go back when i calculated it for musket type units, you can see rusket is the best musk type unit for its price. Tt means if you make 1600vs sepoys versus 1600vs ruskets, ruskets will win. -> because rusket is the most cost effective according to the formula.

[Jaeger]

I didn't understand. Can you reply? I wrote my comments below in bold:

When you have a system like : if u (x,y) ->(-k1*y,-k2*x)
What does this mean? Is u a bijective function u:R^2 -> R^2, where u(x, y) = (-k1*y,-k2*x) ? The function DSY made is P(a, h, p)=ah/p^2, a surjective function P: R^3 -> Q^+. I don't see what this has to do with anything. Also, why did you put negatives in front of k_1 and k_2?


and then with X=(x,y) solve the equation X'=u(X)
As I understand your notation, X is just a member of R^2, what does X' mean?

you can prove that the solution which respect a such equality (with x,y number of each unit and k1, k2 coefficients that represent the number of y(resp x) that x (resp y) kill per second).
What is y(resp x) and x (resp y)?

Also, I don't understand what you say that you can prove. You say "You can probe that the solution which respect such equaloty (...)", which is not a complete sentence.

[bwinner]

I didn't understand. Can you reply? I wrote my comments below in bold:

When you have a system like : if u (x,y) ->(-k1*y,-k2*x)
What does this mean? Is u a bijective function u:R^2 -> R^2, where u(x, y) = (-k1*y,-k2*x) ? The function DSY made is P(a, h, p)=ah/p^2, a surjective function P: R^3 -> Q^+. I don't see what this has to do with anything. Also, why did you put negatives in front of k_1 and k_2?


and then with X=(x,y) solve the equation X'=u(X)
As I understand your notation, X is just a member of R^2, what does X' mean?

you can prove that the solution which respect a such equality (with x,y number of each unit and k1, k2 coefficients that represent the number of y(resp x) that x (resp y) kill per second).
What is y(resp x) and x (resp y)?

Also, I don't understand what you say that you can prove. You say "You can probe that the solution which respect such equaloty (...)", which is not a complete sentence.

Actually, I would have prefere to whrite it with matrix, but I didn't want to use Latex...
-U is a linear fonction yes.
-X is actually X(t) : R->R^2
-coeff are negativ because they reprensent the amount of loss (killed by others)
-solving the equations for equality mean X (t)-->(0,0) when t-->+infiny

I will whrite more later when I have time.

[fei123456]

There used to be a formula:

HP*attack*number^2

It's just the same with yours. Good math.
muitiplier can be considered in this too. Skirm has 15 attack, but when you're fighting with musk, they can be considered to have 30 atk.

[Kaiserklein]

When you have a system like : if u (x,y) ->(-k1*y,-k2*x) and then with X=(x,y) solve the equation X'=u(X), you can prove that the solution which respect a such equality (with x,y number of each unit and k1, k2 coefficients that represent the number of y(resp x) that x (resp y) kill per second). I won't give more détails, but it's Something like that.
However, overkill is really important in real fight, that's why kaiser sais that you should rather use an algorithms, btw the idea to program it isn't bad, because I think it could be a usefool tool for the eso-assistant

I actually already have an program for this. Basically you make your units fight in "rounds", and at each round you remove the dead units and move to next round, so it takes drop-off into account. And you also split perfectly the hits from your units so that there is no overkill, which ofc never happens in game, but is still the most accurate way to theoretically try how well units perform against each other.
When one side has no units left, you just check how many units are left on the other side, and can easily calculate the % of units left compared to what you initially had.

For example, with this program, you can see that in a theoretical fight of 6 uhlans vs 5 huss (it's kinda fair in term of VS) on the previous EP (180 hp uhlans), all uhlans died and there was 1 full hp huss left. On the current EP, for the same fights, you will have all huss dead and 1 full hp uhlan left. So we can see the performance difference is pretty big here, even though the hp difference is only 5 hp (could actually even be 1 hp, which is approx 0.5% of the total hp of an uhlan, and the result would be the same).
Another example is sepoys vs musks. According to that formula, musks>sepoys. But in fact in a 5 sepoys vs 6 musks fight (exactly the same investment on both sides), 1 sepoy is left with full hp, so sepoys are clearly better.

Said in another way, it shows that the formula in the OP is really not accurate.

[Dsy]

Sepoys wins only cause it has 25 damage and simple musks has 150 health means they maximize their damage output on them...
You cant calculate every side effects in any formula. Thats just simple impossible. If you check science even on high levels lot of side effects simple ignored cause its impossible or not worthy to calculate with.

[Kaiserklein]

But you can try sepoys against cav, against skirms, against anything, they will do better than musks...

[Panmaster]

The resource cost of units is the most reliable indicator of it's class rating.
Units stats are very simple in AOE3: cost, attack, armour, speed, range, ROF, obstruction radius, area of effect, damage cap

[macacoalbino]

Sometimes I stop to think how much time we spend theorizing about best units, unit composition best BOs and then Aiz comes and recks us with Lancer+Halbs timing or something weird like that

[Dsy]

In melee vs cav sepoy has different score.
15*3*190/157^2 = 346,87
13*3*150/131^2 = 340,88

Sepoy score is increased to 365,12 calculate with the melee resistance. Means they are 7% more cost effective vs cav than muskets.
All it means its not a surprise they do better vs cav than muskets.

[Kaiserklein]

They do better vs everything lol...

[Dsy]

If you do 6 musks vs 5 sepoy enable hp card in scenario means muskets will have 172 hp means 1 more hit for the sepoy. Muskets wins every time.

[Dsy]

If i calculate the old version of sepoy but now with 207 hp cause musks deals 23*9 damage on them to kill (which is 207)
Sepoy has 209,94 score

Its simply shows the scenario results. Totally in range.

[pecelot]

Such test don't really prove much — it was discussed before already

[Dsy]

hp*damage = power
If you dividing power/cost you will get: What power you get for your payed cost. If you dividing it again (with same cost) you get what power you get for 1 of your cost. Means it shows all power you get for 1 villsec (if you calcualting with villsec). Its not so hard.

[Dsy]

Lets in depth calculation why halberdiers sucks...

Vet Musk vs vet halb

Musk vs halbs again in melee vs nocav: villsec 131,176 calculate with mele resistance(mr)
180/0,8*15/131^2 = 0,196666 * 1000 = 196,666
200/0.9*25/176^2 = 0,179350 * 1000 = 179,350

Conclusion: Vet musk is better choice vs meele noncav opponents.

Lets see vs cav with mr: Same calculation as above just multiple their damage with their cav multi
Musk got score(*1000) = 590
Halb got score(*1000) = 358,7

Conclusion: Musk seems a "bit" more powerful vs cav than halbs

So question what halbs are good for?
(you can see counter scores are easy to calculate after you have the base)
(in the future i calculate every units on 1,5 attack speed means i will divide 3 rof units damage with /2)

[Dsy]

Lets calculate:
Cav archer vs dragoon

First i of all i declare that i will calculate ranged resistance only for dragoon, and dont calcualte mr for archer.

Lets see villsecs: 219,257
cav archer: 265*13/219^2(*1000)=71,829 (x3 vs cav)
dragoon: 200/0.7*11/257^2(*1000)=47,583 (x3 vs cav)
dragoon: ep200/0,8*11/257^2(*1000)=41,635 (x3 vs cav)

Conclusion: archer is more cost effective though it lacks of good hit and run micro

[Dsy]

So make

Musk vs cav archer and goon (in ranged)
All we need is musk ranged rate:
150*11,5/131^2 (*1000) = 100,51

We can compare now them to dragoons and cav archers which had the scores of in the last post:
cav archer: 71,829 (x3 vs cav)
dragoon: 47,583 (x3 vs cav)
dragoon (ep): 41,635 (x3 vs cav)

[Dsy]

Realized calculation way which can be handy:
We need to calculate only no melee and no ranged resistance score cause in the end we can divide the index:
Dragoon base score fo example: 33,308
If you dide it with 0,7 you get Re ranged resistance power index: 33,308/0,7=47,583
On EP ranged res: 33,308/0,8=41,635

Cool.

[Aizamk]

Lets in depth calculation why halberdiers sucks...

no u

But on a more serious note, when you are comparing how good unit A is compared to unit B vs another unit C, if you want to do things purely mathematically, then you have to consider that unit C is also doing damage, and that A might fare better DPS wise, but might die faster, meaning that in large scale battles, assuming perfect micro, the total DPS will drop exponentially over time.

Anyway, don't apply maths to aoe3 units, you'll inevitably end up with stupid results like "rajput are bad" or "halbs are bad" which clearly isn't the case. Always need to apply a sense test.

[deleted_user0]

elifents are bad. @Aizamk @aizmak

[Dsy]

I think you mean vet musk and vet halb vs cav comaprison (in melee)
That poin we dont really care about the cav. We just wanted to know musk or the halbs are more cost effective vs cav. And we got the numbers. This formula contains which die faster cause it contains hp and attack in the same proportion.