Unit Calculators

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Hungary Dsy
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Unit Calculators

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Post by Dsy »

1. UnitCostEffectivity
It calculates a specific unit cost effectivity.
You can use it to compare 2 specific units cost effectivity. For example: cassador vs skirmisher.

2. UnitPower (fei123456 wrote the math, i just programmed it down)
It calculates x amount of a specific units combat effectivity.
You can use it compare 2 specific armies combat effectivity. For example: 4 hussars vs 6 uhlans.

Its very easy to use. Write the stats which the program asks for and press enter.



Notes:
Use unit attack with multipliers. For example a pike does 8*5 = 40 damage if you compare it to a cavalry unit.
For resistance/food,wood,coin costs you need to enter 0 if the unit hasnt got these.
Unit resistance in percentage but use it without %. For example a unit has 20% resistance you write in the program only 20.
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France louis293
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Re: Unit Calculators

Post by louis293 »

Hi, sorry for the old topic answer,
I am suprised of the results it gives (the first software which calculate the cost effectivity of a unit). Indeed when i multiply the HP or the attack by two, it multiply the value of the unit by 2, but when i divide the cost of the unit by two it multiply the value by four. Does it make sense ? I expected a formula like: HP (corrected with the resistance)*attack(taking into account the rate of fire) / total_cost(in villager second) .

But here it seems to be rather something like HP*attack / (total_cost)² so why using the square in the formula ? (i tried by dividing by 3 the cost and it multiply it by 9 also)

I wanted to use this software to compare the cost effective of a strelet against other ranged infantery (which is good to know in practise as it is often the case in early age 2), i found the strelets to be almost as cost effective as longbow which doesn't seems the case in practise when u engage them. So is there an error or do i understand wrong the way of calculating ?

Thanks in advance,
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Re: Unit Calculators

Post by Darwin_ »

If you look up something called "lanchester's laws," it will answer your questions.
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Re: Unit Calculators

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Post by aligator92 »

louis293 wrote:Hi, sorry for the old topic answer,
I am suprised of the results it gives (the first software which calculate the cost effectivity of a unit). Indeed when i multiply the HP or the attack by two, it multiply the value of the unit by 2, but when i divide the cost of the unit by two it multiply the value by four. Does it make sense ? I expected a formula like: HP (corrected with the resistance)*attack(taking into account the rate of fire) / total_cost(in villager second) .

But here it seems to be rather something like HP*attack / (total_cost)² so why using the square in the formula ? (i tried by dividing by 3 the cost and it multiply it by 9 also)

I wanted to use this software to compare the cost effective of a strelet against other ranged infantery (which is good to know in practise as it is often the case in early age 2), i found the strelets to be almost as cost effective as longbow which doesn't seems the case in practise when u engage them. So is there an error or do i understand wrong the way of calculating ?

Thanks in advance,
The thing is, do not use this tool. It neglects so many things that are relevant that it is essentially useless. I think Strelets are even more cost effective than lb by the way
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Re: Unit Calculators

Post by louis293 »

Thanks, its also i am just interested a bit of the maths behind haha^^, of course hit and run abilities, range and so on are very important but being a modest master sergent level player sometimes it ended just in spaming units without a lot of micro, so i am still curious to know. I always though lb was the most cost effective unit in a figth versus other ranged infantery units. It still can give an idea. Also it can be usefull in early cavalry figths to know if u can trade you hussards versus uhlans or cossacks, i am just curious of the theory, of course in practise in a RTS the micro/macro is much more important to know than thoose theoritical calculations. But i am just curious especially because of the results it gives with thoose (..)² that seems to be in the formula.
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Re: Unit Calculators

Post by [Armag] diarouga »

Don't use that yes.
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Re: Unit Calculators

Post by aligator92 »

as far as I know there is no big math or theory behind it. It is as simple as HP*Att/Cost^2

you are certainly correct in thinking that lb perform well vs other ranged infantery. They have higher damage output to compensate for their lack of multipliers vs heavy infantry. But Strelets are cost efficiency personified so I am not sure about what is more effiecient 1v1. But once the various upgrades come in, Strelets will certainly be more efficient.
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Re: Unit Calculators

Post by [Armag] diarouga »

lb have a shit animation however, they don't attack in big masses, and they miss. And they have no mobility, while strelets are super fast, it's not close honestly.
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Re: Unit Calculators

Post by Kaiserklein »

Lbs are just better than strels in low numbers, assuming you're microing them and you have something to block. Perfectly microed lbs would easily be one of the very best units in this game.

Now in bigger masses they go full retard and aren't as strong. Still a very strong unit in some situations, but with clear weaknesses.
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Re: Unit Calculators

Post by RefluxSemantic »

aligator92 wrote:as far as I know there is no big math or theory behind it. It is as simple as HP*Att/Cost^2

you are certainly correct in thinking that lb perform well vs other ranged infantery. They have higher damage output to compensate for their lack of multipliers vs heavy infantry. But Strelets are cost efficiency personified so I am not sure about what is more effiecient 1v1. But once the various upgrades come in, Strelets will certainly be more efficient.
I honestly don't think HP*Att is really true either.

If I want to compare units in a rough sense, I usually just calculate the hp/villager second and the attack/villager second. This gives at least some estimation of how strong a unit is.
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Re: Unit Calculators

Post by [Armag] diarouga »

RefluxSemantic wrote:
aligator92 wrote:as far as I know there is no big math or theory behind it. It is as simple as HP*Att/Cost^2

you are certainly correct in thinking that lb perform well vs other ranged infantery. They have higher damage output to compensate for their lack of multipliers vs heavy infantry. But Strelets are cost efficiency personified so I am not sure about what is more effiecient 1v1. But once the various upgrades come in, Strelets will certainly be more efficient.
I honestly don't think HP*Att is really true either.

If I want to compare units in a rough sense, I usually just calculate the hp/villager second and the attack/villager second. This gives at least some estimation of how strong a unit is.
Not really because it snowballs.
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Re: Unit Calculators

Post by RefluxSemantic »

It's not exactly true, but it gives a pretty decent approximation. The snowball effect you are referring to is, I assume, the fact that high hp units are generally favorable. This is of course true, but for most comparisons that you will make units are pretty close in how much hp they have, so this effect isn't extremely relevant; Doing a simple hp/cost and attack/cost calculation will give a pretty good approximation for strength when you compare it to similar hp units.

So what I normally end up doing is comparing some units I'm curious about to some benchmark unit, whose strength I know. For example when looking at Yabusame, I'll compare them per cost to dragoons per cost to get some sense of strenght. This definitely has some merits. It's not exact science, but I don't think the exact formula is figured out yet.
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Re: Unit Calculators

Post by louis293 »

RefluxSemantic wrote: I honestly don't think HP*Att is really true either.
It is a good theoretical approximation of the stength of a unit i think , a unit A beats a unit B if it kills it before being killed (obivous i know^^), so if:

(hp_A/dps_B) > ( hp_B/dps_A ) corresponding to "time to kill unit A by unit B" bigger than "time to kill unit B by A"
which is equivalent to:
hp_A*dps_A > hp_B*dps_B

so HP*Att (in fact HP*DPS) seems to be a correct evaluation, now intuitively i would just say ok so the cost effectivity is just HP*Att/(cost_villager-sec) so why does it seems to be /(cost_vilager-sec)² in the software ? where does the square come from ?
Darwin_ wrote:If you look up something called "lanchester's laws," it will answer your questions.
seems to be a good explanation, i read the wikipedia of it and some other articles (explaining it applys for RTS games) here there is a little bit more maths behind, so from what i have understood the previous intuitive reasonning without the square would apply if all soldiers are not figthing at same time but by making two big waiting line, one for each army and a constant 1vs1 battle, if one soldier die, another replaces him to continue until one waiting line is finnished. But according to "lanchester's laws" when all units are figthing at the same time this linear approximation does no longer apply, instead the power of an army evolves with the square of the number of units.

So instead of: number_units*power_individual_units
it is: (number_units)²*power_individual_units

First i though that it doesn't help me to analyze cost effectiveness but if you assume same amount of ressources available and obviuosly that number_units = ressources_available/cost_unit, you ended for a given amount of ressources with the power of an army given by the formula:

(ressources_available)²*HP*damage_per_second/(cost_villager_second)²

and u keep ressources availaible as a constant to compare it to another type of unit.

That being said its just a mathematical model and if enginners or physics students are present here u would agree that as usual it ins't completely true according to real life (usually u don't take the frictions into account :ugly: ) here we don't take into account: the range (obviously if u get some free volleys before opponent it helps), the starting animation time, the dps is not continuous but discrete provoking overkills, the micro (hit and run for example :kinggreen: ), the population effectiveness (nice to produce strelets but if u forget houses... :devil: ) etc and other things i forget.

Now if i have some free time i will try to make big tests of equal cost of army and see if results get closer to the formula with or without the square. All of this will not help me to get 2nd lieutnant haha but its interesting ;).
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Re: Unit Calculators

Post by Kaiserklein »

Darwin_ wrote:If you look up something called "lanchester's laws," it will answer your questions.
Ah yeah, makes sense, we need differential equations to calculate this, because of the drop off effect.

You can't isolate a unit and consider its strength, you have to take into account how fast it's gonna die (and thus how much less dps your side is gonna have). So it's more complex than just multiplying and dividing stats, you need a whole model and equations. And tbh approximating it just doesn't work, it really gives extremely inaccurate results. It's why I'm always pissed at this "calculator", it's just a random formula that gives wrong results.

I remember I coded a small algorithm that makes units fight round by round (a round is basically a volley) with no overkill, so you can estimate how well they perform against each other with perfect micro. But surely with actual maths you can simulate it
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Re: Unit Calculators

Post by Le Hussard sur le toit »

It's pretty hard to get the right model I think because many parameters are difficult to estimates (for example if you want any accuracy you'd want something like a "standard overkill coefficient". Anyway I doubt a mathematical model would do better in this case than actual repeated simulations in a scenario editor.
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Re: Unit Calculators

Post by duckzilla »

A good approach could be a weighted average of:
  • Kaiserklein's algorithm
  • simple scenario with two armies (each 5k worth in resources) clashing without micro
It would give you an expected relative value of the two units, given that you micro a bit but don't have perfect micro.
One significant advantage would be the relative simplicity of this combined approach.
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Re: Unit Calculators

Post by Kaiserklein »

Le Hussard sur le toit wrote:It's pretty hard to get the right model I think because many parameters are difficult to estimates (for example if you want any accuracy you'd want something like a "standard overkill coefficient". Anyway I doubt a mathematical model would do better in this case than actual repeated simulations in a scenario editor.
Well yeah I was assuming perfect micro, no pathing issues etc. Overkill varies too much depending on the situation. Either way it would definitely be more accurate than HP*Att/Cost² or whatever BS
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Re: Unit Calculators

Post by Le Hussard sur le toit »

duckzilla wrote:A good approach could be a weighted average of:
  • Kaiserklein's algorithm
  • simple scenario with two armies (each 5k worth in resources) clashing without micro
It would give you an expected relative value of the two units, given that you micro a bit but don't have perfect micro.
One significant advantage would be the relative simplicity of this combined approach.
How do you define your weights ? I mean besides them being 1-0 for Kaiserklein and 0-1 for me ? Do you make simulations to estimate the weights you will use in your simulation ?
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Re: Unit Calculators

Post by duckzilla »

Le Hussard sur le toit wrote:
duckzilla wrote:A good approach could be a weighted average of:
  • Kaiserklein's algorithm
  • simple scenario with two armies (each 5k worth in resources) clashing without micro
It would give you an expected relative value of the two units, given that you micro a bit but don't have perfect micro.
One significant advantage would be the relative simplicity of this combined approach.
How do you define your weights ? I mean besides them being 1-0 for Kaiserklein and 0-1 for me ? Do you make simulations to estimate the weights you will use in your simulation ?
I would do two different weighting schemes. A general one with .5/.5, which gives an overall rating of a unit without taking a players micro abilities too much into account. And then a player-centric one (e.g. .7/.3 for strong players), which takes the micro skills into account by putting a higher/lower weight on Kaiserklein's algorithm.
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Re: Unit Calculators

Post by louis293 »

Thanks for all answers, i was just curious of the reasonning behind the formula which seemed counter intuitive for me at first, not if it is actually relevant in practise. Will try to do some scenario tests to compare the units i am interested in.
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Re: Unit Calculators

Post by RefluxSemantic »

Tbh I still mostly appreciate stats/cost and then comparing to some benchmark unit whose strength you know. Its going to give some insight most of the time.

After that just skip modelling it and start using scenario editor tests.
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Re: Unit Calculators

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Post by Kaiserklein »

Not really. If you have two units with 100 hp 10 attack costing 100 res vs one unit with 200 hp 20 attack costing 200 res, the big unit wins with 25% hp left. Yet that's equal resources investment on both sides, and according to the "formula" the efficiency is the same for both units.
So it can be wrong by a margin of 25% which basically means it gives zero insight. 25% actual efficiency difference is huge, probs the gap between the best and the worst units in the game.
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Re: Unit Calculators

Post by RefluxSemantic »

Kaiserklein wrote:Not really. If you have two units with 100 hp 10 attack costing 100 res vs one unit with 200 hp 20 attack costing 200 res, the big unit wins with 25% hp left. Yet that's equal resources investment on both sides, and according to the "formula" the efficiency is the same for both units.
So it can be wrong by a margin of 25% which basically means it gives zero insight. 25% is huge, probs the gap between the best and the worst units in the game
Yes, but then you realize that you're usually comparing units who are only at worst ~20% apart in hp. So it's actually pretty reasonable.
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Re: Unit Calculators

Post by [Armag] diarouga »

RefluxSemantic wrote:
Kaiserklein wrote:Not really. If you have two units with 100 hp 10 attack costing 100 res vs one unit with 200 hp 20 attack costing 200 res, the big unit wins with 25% hp left. Yet that's equal resources investment on both sides, and according to the "formula" the efficiency is the same for both units.
So it can be wrong by a margin of 25% which basically means it gives zero insight. 25% is huge, probs the gap between the best and the worst units in the game
Yes, but then you realize that you're usually comparing units who are only at worst ~20% apart in hp. So it's actually pretty reasonable.
If it's only 20% yes, but it's not always true. For instance, you can't compare jans and musks that way. Some goes for huss/coyotes etc
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Re: Unit Calculators

Post by louis293 »

Kaiserklein wrote:Not really. If you have two units with 100 hp 10 attack costing 100 res vs one unit with 200 hp 20 attack costing 200 res, the big unit wins with 25% hp left. Yet that's equal resources investment on both sides, and according to the "formula" the efficiency is the same for both units.
So it can be wrong by a margin of 25% which basically means it gives zero insight. 25% is huge, probs the gap between the best and the worst units in the game
indeed, very good example to show the inaccuracy of the formula

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