# How are AOE Special Skills damage numbers calculated?

Hello all
Since i started to look in the Forum most of my Questions i had about this Game are being answered, however i couldn´t find a Topic that relates to this particular one.
As i played through the Game i was always wondering why AOE (Area of Effect) Damage Skills are slightly different with each Hit.
For example when i use a Heros Special Skill that effects multiple Enemys such as Grimm, Colen, Justizia and so on the Damage Numbers on each Hit are sligthly different, e.g. dealing 245 Damage to the most left Target, but 290 Damage to the most right.
Shouldn´t every Enemy take the same amount of Damage?
Allthough i thought that Defence stats don´t matter when it comes to Special Skills, this would be an explanation of why the damage Numbers are different, maybe someone can clarify that for me as well.
However this Problem occures not only in Arena, Wars etc, but on the normal Map as well.
I tried to replay some Stages where three to four Enemys of the same Type are present, meaning they all have the same Stats and same Colour, but the damage Number of my AOE Skills are still not even.
As if it stands for now i couldn´t find a possible Solution why this is happening, so i´m seeking for some explanations from this awesome Community.

If you see this thread it will explain it for you. There is a random factor included in the calculation which along with slight differences in stats of the heroes attacked should account for the difference.

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No, because…

…they do.

Defense stats affect damage taken from direct-damage Special Skills (though not DoT).

And in addition to that, as @Kilted noted, there’s a random component to damage, even apart from the Attack and Defense stats at play, which is the θ in this equation:

As you can see in that formula, damage is a function of the ratio of Attack and Defense, so it’s going to be different for each enemy, based on their Defense amount, including application of Troops and status effects.

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First, thanks for the Link @Kilted

Thanks for that, i mixed that up my bad.

I mean i hardly understand how you get to this Number at all, also a variation of 1,043 seems quiet a lot.

Well yes, but this only works if the Enemy has different Heros/Troops equal different Sats on Att/Deff, still doesn´t answer my Question of:

So if i face off three Opponents which all have the same amount of Defence, they are the same Colour, basicly everyone has the same Stats, how does θ is a random parameter between exp(-.5)=0.606 and exp(.5)=1.649 come in hand here?
The only explanation i can find is that the System calculates the Damage output for every single Enemy, let´s say first it calculates it for the most left, then for the middle one, then the most right, therefore the random Factor would apply and it will show slightly different Numbers in the outcome.
But on the other Hand since the Heros Special clearly says: deal xxx% Damage to all enemies, that means to me that it should only be calculated once, therefore the outcome should be the same.

That’s not really how it works, though.

That just determines what the Attack amount will be in the damage formula.

It’s just xxx% * Attack stat * Troop modifier * status effect modifier = attack amount used in formula.

The variability between hits against the same targets with identical stats is entirely because of the θ random parameter.

And yes, it can lead to pretty massive differences.

Compare these values, using my Little John and Level 17 Mana Troop for example:

185% damage
891 Attack
22% Troop bonus

1.85 * 891 * 1.22 = 2011 total attack

Here’s how that plays out against some different Defense amounts:

Enemy Defense Low Dmg (θ = 0.606) Average Dmg (θ = 1) High Dmg (θ = 1.649)
500 333 655 1,286
600 260 512 1,005
700 211 416 817
800 177 347 682
900 151 296 582
1000 131 257 504
1100 115 226 444
1200 102 201 394
1300 92 180 354

The range between low and high possible values is fairly massive, and you can see the exponential nature of the damage calculation formula in action, given the flyaway amounts when an enemy’s Defense is proportionally low.

That’s why strong Heroes completely obliterate weak enemies in early PVE Stages, while doing little damage against comparably strong enemies, for example.

As a side note, barring a Special Skill saying otherwise, or an Elemental Defense buff/debuff having been applied, color relationships don’t affect Special Skill damage amounts, only tiles.

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I think I remember seeing a spreadsheet someone created where you can plug in your heroes details and the defence stat of your opponent and it gives the damage spread.

Cant for the life of me remember who made it now though, or find the thread so it may have been an individual post somewhere or just me imagining things

Was it one of these, or something like it?

I also just made a quick one myself to post above, that looks like this:

The math is simple, so it’s not particularly hard to make something like that.

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Yeah, think it was the bottom one of @Guvnor 's.

My mind is so loopy from staring at spreadsheets in work all day I can never remember anymore if it’s something I imagined or not

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Well if that is how it works, that explains everything for me; thanks @zephyr1 for the explanation and the detailed example; also thanks to all for these spreadsheed links, they are realy intresting.
You can close this Thread now if you want.
Have a nice one

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