# Damage Calculation

OK, I think I followed all the various equations/calculations, but suppose I want to compare my 3-70 Lianna with my 4-50 Caedmon - someone please tell me if I’m on the right track, or if I screwed up somewhere.

First, assume I’m planning to choose just one of these to fill a single-target attack role. I don’t need to figure for defense, because we’ll assume they’d be hitting the same targets, so I can directly compare the attack, defense, etc. as shown.

ATTACK: Lianna 613 vs Caedmon 605
It is NOT accurate to simply divide 613/605=1.013 and say that Lianna does 1.3% more tile damage than Caedmon, right?

Instead, I take (613/605)^1.35=1.01789… so call Lianna roughly 1.8% better in that regard, yes?

If I’m on the right track with that, then it should follow…

SPECIAL - ignoring any “small” buffs and just comparing direct %
EDIT: I initially had (1+5.12) in there, assuming 100%+512% but that was wrong.
Lianna is (613x5.12) - call it L
Caedmon is (605x3.45) - call it C
so (L/C)^1.35 --> 1.734, meaning Lianna’s special hits +73.4% harder than Caedmon’s at these stats?

DEFENSE: Lianna 604 def, 1049hp vs Caedmon 607 def, 1075hp
Lianna: 1049*[604^1.35], call it L
Caedmon is 1075*[607^1.35], call it C
so C/L --> 1.0312, meaning Caedmon has about 3.1% edge in defensive terms at these stats?

At least, I think I kind of fudged these numbers together in a way that makes sense to me. The defense calculation I did kind of factors in, with all else being equal, the Caedmon with slightly higher defense and slightly higher HP, can take a little more punishment than Lianna… and tries to quantify it.

So… math nerds, where did I screw up? (I’m kind of a math nerd myself, but sometimes get ideas in my head that don’t make sense, so it helps to have other poke holes in how I’ve conceptualized it. That’s how I learn. :P)

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Nice examples!

You’ve got it all correct except here:

That extra 1 shouldn’t be in the special multiplier. So, for example, Lianna’s special attack power should be 613x5.12.

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Oh, duh… I was thinking “base” was 100% damage, and the special was adding 512% damage. See what I mean about missing something basic? I’ll revise. Thank you!

I just wanted to make sure that as I was looking at the various equations and trying to compare attack, defense, etc. that I wasn’t just making things up that made no sense.

EDIT to add: So… Lianna hits 73% harder than Caedmon? I guess that’s significant, despite the closeness of their numbers otherwise. That 512% is pretty awesome, eh?

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You’re welcome. And you’re definitely not just understanding the equation, but using it smartly. Percentage improvement is an excellent way to look at hero comparisons. Being able to separate out the fully exponentiated difference between heroes makes apples-to-apples comparisons much easier.

And yeah, Lianna is a beast The exponentiation really magnifies the top special percentages.

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I thought the special skills are listed as “512% damage” not 512% attack. So the specials between Lianna & Cademon should be (613/605)^1.3 * (5.12/3.45) = 1.51 --> 51% higher.
This matches what I’ve seen from my raid videos…

[it also took me a while to realize that color bonuses only apply to troop attacks. Does not apply to special skills or any attacks from the enemy…]

It would make sense if they did it the way you’re describing. That’s not actually how they did it though. Take a look at the examples section by Solemnwolf upthread:

https://forum.smallgiantgames.com/t/damage-calculation/29624/13

Example number 2 is specials.

And yeah, slash attacks and specials only appear to have color for the purposes of color debuffs. They don’t behave as strong or weak like tile damage. He’s the thread on elemental damage, which covers the question toward the bottom of the first post:

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Im not sure about the calc on specials, it does not appear to be working that way. The damage done to any opponent on the defense side seems to be centered around what the damage would be vs the strongest opponent on the defense team. I’ve done 5 raids now using one specific attacker and avoiding any buffs or talents, and in each case the damage is +/- a few % of the same number, no matter who I hit.

What you’ll find is subtle variations depending on the heroes starting attributes. I developed a sheet to assess emblem allocation and leveling. It uses the above damage equation and incorporates color stacking, troop boosts, etc. I was amazed to see how much the talents improve your heroes… it is pretty dramatic! I pasted an image below that shows a 2.5 tile increase to kill a Richard tank that is fully ascended/talented with a focus on D and health. The attack team is listed as well and is 4:1 color stack with Kiril, Evelyn, Lianna, Tarlak, and Kadilen

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A lot depends on when and how the % boost is applied. If the defense or health % boost of 3% is only applied to base stats (as indicated by the points listed on the in game talent tree) then it wont make as much of a difference. If however the % is added to the troop stats and boosted after subsequent stat upgrades then it does make a bit more of a difference if you talent with D or health stats. A very subtle difference, but a difference nevertheless. For Richard there are a few factors that come into play. One is his actual talent, which is boosting his D stats by 25% for two turns. The more D, the better the stat boost. Another is that he has low health stats. Again, depending on when and how the % health boost is applied, you can eek out a very slight increase if you add an additional health stat in lieu of a D stat.

1 point of defense = 2 points of health. so how does adding health help more then adding defense?

By and far it doesn’t. Defense seems to be the better stat to max than health. I was just making a point that the percent boosts are stated as points in game. If they are applied as points based on base stats and not a percentage of talented stats then it is pointless to choose health over defense. EDITED HERE - I added a photo above that shows an initial choice of health over D for the first talent stats. It increases the STC-DEAD (strong tiles connected until your hero is dead) stat by 0.01 tiles… Like a said a minimal increase IF they apply the point increase as a percent of your new stats rather than your base stats before you start the talent ascension.

OK I see where you are coming from

This is why defense nerfs are more damaging to the enemy than buffing the attack

thank you for sharing. i know that for some, they dont agree with the opinion or the equation, but there is no perfect or almost always right, so one usable is appreciated

I don’t think it is, but someone would have to do a study of the difference between how much healers heal hero’s total health (the more health you have the more you are healed) vs how much the difference in defense kept your health up.

Some damage bypasses defense—like Proteus and Natalya. Ypu need raw health to survive those specials.

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So today I analyzed a video of my 8* titan hit, calculated the “raw” attack values for each hit with corresponding buffs and debuffs (attbuffs/titan debuffs) and ended up with a polynomial fit -10^(-6)(x^2)+0.0878*x-38.28 when plotting the “True” tiledamage as a function of “raw” attack value due to the limitations of Excel. “Raw” attack value was used because titan defence is at this point unknown. “True” tiledamage is recorded tiledamage divided by multiplier ie. for a strong attack colour hitting the weakspot the multiplier was 3.

Now this is essentially an upside down parabola and will start to yeild smaller tiledamages when the “raw” attack values bypass the peak. But I figured I would find a power for “raw” attack value that follows this curve up to a point and ended up with the power 0.72 which is interestingly quite close to the reciprocal of raid damage power (1.35^(-1)=0.74). From there on I was able to calculate that an 8* titan (green dragon) would have around 160 defence. And titan attack tile damage would follow quite nicely a formula of multiplier*(100/3)att/def)^0.72, where the multiplier is corresponding value for weak/strong/critical attack.

With this formula it is noteworthy that the sample size was quite small with only 11 strong colour attacks landing on titan (thanks Wu) and 18 neutral color (yellow) tiles landing on titan. But I feel I ended up with many diffirent combinations of buffs and debuffs along with combos increasing attack up to 1,5 times the normal damage.

Feel free to comment and use for your own calculations.

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Interesting comment, thanks for sharing. Recently, I tried to roughly calculate defense of a 10* titan from the tile damage I was doing to him and I came to conclusion his defense is close to 500.

to my mind, damage for 1 neutral stone is calculated by this way:
if attack>defense then
dmg=25attack/defense + (attack-defense)/25
else
dmg=25
attack/defense

correct variant:
if attack > defense then
dmg=25 * attack/defense + (attack-defense)/25 +/- [0…~2]
else
dmg=25 * attack/defense +/- [0…~2]

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