# Damage Calculation

Short story: work got overwhelming during the last weeks and it looks like it will continue like this for a while.

In addition, collecting data for special damage is extremely tedious. Instead of matching 3 suitable tiles you need to match at least 9 suitable tiles. If your hero AND the target survive that long, you get one single data point. Getting relatively complete data for a single defense value seems practically impossible, unless it’s from a popular mission like 8-7, which will still take quite a while to collect.

At least I got a little bit of data for comparing special damage from different special %.
First, Vela with 923ATK and 130% special % giving 1199 attack power compared to
Obakan 1-1 with 370ATK +18%ATK for 436ATK and 275% special % giving 1199 attack power.

Same target with 694 DEF. Both give the exact same damage range

DEF Special ATK ATK/DEF avg damage variance current Z-U Z-U variance actual min actual max
694 1199 1,72766570605187 171 8 175 8 163 179

Next is Berden3-50 with 493ATK +5%ATK for 517ATK with 325% special% giving 1680 attack power compared to
C-Wu4-70 with 728ATK +10%ATK for 800 ATK with 210% special% giving 1680 attack power

Same target with 818 DEF. slight difference for the min damage - probably just very unlucky.

DEF Special ATK ATK/DEF avg damage variance current Z-U Z-U variance actual min actual max
816 1680 2,05882352941176 235,5 11,5 237 11 224 247
816 1680 2,05882352941176 235 12 237 11 223 247

I’m willing to accept that this data is sufficient for our purposes.
=> the same attack power gives the same average damage and damage range

The variance of 12 is a surprise though. With 5% and rounding down we would expect a variance of 11.

new data:

Obakan special versus Little John: 694 DEF / 436 ATK x 275% = 1199 ATK - 28 data points - 174, 176, 179, 173, 165, 173, 169, 165, 169, 169, 165, 163, 169, 164, 173, 166, 173, 179, 168, 178, 167, 163, 175, 178, 176, 177, 163, 178

Berden special versus Tiburtus: 818 DEF / 517 ATK x 325% = 1680 ATK - 51 data points - 238, 231, 238, 240, 224, 244, 227, 233, 235, 237, 235, 229, 227, 240, 238, 229, 234, 236, 242, 227, 232, 227, 233, 237, 226, 226, 242, 242, 243, 228, 242, 233, 237, 226, 241, 228, 239, 243, 230, 244, 235, 238, 230, 239, 241, 225, 235, 229, 247, 234, 242

Costume Wu special versus Tiburtus: 818 DEF / 800 ATK x 210% = 1680 ATK - 48 data points - 226, 244, 225, 237, 232, 228, 230, 232, 242, 224, 232, 229, 234, 229, 227, 223, 244, 233, 234, 244, 238, 234, 240, 237, 235, 236, 229, 223, 245, 234, 227, 226, 223, 228, 230, 226, 242, 242, 226, 236, 226, 247, 229, 225, 235, 235, 239, 239

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That’s too much praise for me. It was teamwork with @u2371.
I wouldn’t have found that formula by myself.

Our current Z-U formula is kind of summed up in this post here.
Since then the parameters have been updated and have slightly changed.
We’ve investigated mostly tile damage so far and started to check on special damage.

Shall we make a summary post with the current status of the formula?

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Hi @Zack and @u2371
I’ve been playing a bit around your formula, trying to get something more simple to communicate.
I integrated the c value into the defense, by saying defense is lowered by 5%. Let’s call this lowered defense def*
This way, we have a bonus damage if att>def*, which is 0.04*(att-def*).
I thus integrated this lowered defense into the first part of the formula, which change the value of a from 25.5 to 24.
We get: damage= 24* att / def* + (att>def*) * 0.04*(att - def*)
Now, let’s put 24 in factor of the whole formula, and change b into a denominator.
The denominator is 24/0.04 : precisely 600.

Which gives
damage= 24* ( att / def* + (att > def*) * (att - def*) / 600 ) )

I can definitely see this formula as coded by SG.
They chose a 24* att / def.
Then want a bonus damage for att> def, they code it the same way but don’t want it to depend on defense, so they choose an arbitrary 600 medium defense.
Later they adjust the damage up by lowering the defense by 5%.

Does it sound likely to you ?

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From my understanding, for two of the extreme situations this would then look as follows

att=140 and def=744
damage = 24 x 140 / (0.95 x744) = 4

att=4929 and def=744
damage = 24 x 4929 / (0.95 x744) + 24/600 x (4929 - 0.95 x 744) = 336

It’s close to the actual average damage values that we found (5 and 332) and an interesting and simpler variation of the formula. I like it
Still, SG has added some extras to this.

For improved accuracy, I’m afraid, we need more data for fine-tuning.
(I’m currently not working on this due to RL)

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I was always curious how it works and often found that it doesn’t work as it’s stated in original formula. For example, there are bosses on final stages of S4 map that have 6500+ attack and deal 130% special skill damage. They ought to do more than 1900 skill damage to my hero with 940 defense (troops bonus applied), but they did barely 400. So kudos for correcting it

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Amazing (and overwhelming) work in this thread. I must admit I gave up reading and understanding all of it. I came here to see if there was a simple (does not need to be accurate at all) value between the effectiveness of defence vs health. I see somewhere this is set at defence being 2x as the value of health.

My reason for asking is because I have a hero-overview where I want to make simple calculations of attack effect and damage absorption. This is just to be able to compare heroes vs each other.

For attack I have simply multiplied atk power with special %. I am fine with this not taking into account effectiveness vs different enemies.
For defence my suggestion would be simply def power x2 + health to get total damage absorption value. Any suggestions to this, without complicating the matter?
Remember, this is just to compare hero vs hero

I am bumping this as many have never seen it.

Thanks @SolemnWolf

Can someone confirm for me that special skill defence is not as strong as normal defence up in relation to a special skill attack? So a 50% special skill defence buff is not as strong as a normal 50% defence buff?

Never heard that before and it sound completely nonsensical.

I said I wasn’t sure but I cudve sworn I read somewhere on this forum regarding damage calculation that normal defence down like Frigg is more effective than just special skill defence down like Mists. Something to do with normal defence affects the defence stat whilst
special skill defence affected the special skill only.

Well yeah exactly that´s the difference. The one affects defense in general, while the other only affects defense when damage comes in from a special skill, meaning it will not trigger at all when hit by tiles/slash attacks. That´s in the name.
So yes the regular is “better” because it works also on tiles/slash attacks. But 50% is 50%. The only difference is when they trigger.
And btw if you have 2 heroes that do defense down, it´s better to have one of each kind, because both can be active at the same time, otherwise they will overwrite each other. So in that case skill def down is “better” for the second hero. Same idea as with elemental defense down.

This is an old thought—and heck no, I didn’t read the whole thread. But on account of Quenell’s skill revealing that the hero’s power effects the dmg done…

may I ask is it [power] a variable in your curve-fitting schema?

From what my former analysis has shown me, the formula for special damage is not using „power“ as a variable.

I assume that Quenell’s „+40% power“ simply means that the special damage is calculated with a higher „attack power“ or „% damage“. But I don’t have Quenell, so I can’t really check.

During a raid or war battle tap on Quenell and on her targets to check Quenell’s attack (= QA) and her targets’ defenses (= TD) as the damage is calculated separately for each target.

We haven’t fine-tuned the exact values of the special damage formula’s parameters, but maybe check with the following formula (assuming that QA x 320% ≥ 0.93 x TD):

Expected damage for Quenell on attack team:
[25.5 x QA x 320% / TD + 0.0385 x (QA x 320% – 0.93 x TD)] x 3 x 11/12 ±5%

after 5 turns for the +200% power:
[25.5 x QA x (320% + 5x40%) / TD + 0.0385 x (QA x 520% – 0.93 x TD)] x 3 x 11/12 ±5%

Expected damage for Quenell on defense team:
[25.5 x QA x 320% / TD + 0.0385 x (QA x 320% – 0.93 x TD)] x 3 x 1.1 ±5%

after 5 turns for the +200% power:
[25.5 x QA x 520% / TD + 0.0385 x (QA x 520% – 0.93 x TD)] x 3 x 1.1 ±5%

For example,
Attacker’s Quenell with 971 attack and 26% attack bonus from troops
Target with 1000 defense (troop bonus already included)

Expected damage
[25.5 x 971 x 1.26 x 320% / 1000 + 0.0385 x (971 x 1.26 x 320% – 0.93 x 1000)] x 3 x 11/12 ±5% = 590 (min=560; max=620)

[25.5 x 971 x 1.26 x 520% / 1000 + 0.0385 x (971 x 1.26 x 520% – 0.93 x 1000)] x 3 x 11/12 ±5% = 1020 (min=969; max=1071)

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Sorry been busy with work. Found something more to do with power being a variable in skill damage:

Now you can test?

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What this power increase for SS does is very straight forward (for once ). For example, if Quenell has hit 100% additional power, the damage she puts out is 2 times what the damage would be calculated as without this buff. Glenda has the same type of buff, just at 40% - so the SS’s of those under her buff would deal 1.4 times what the damage would be calculated as prior to the buff. Quenell maxes out at 200% power increase for SS’s, thus that would be 3 times. It is funny and cool to see Quenell hit when she has has the 200% max power increase for SS after EDD & DD have been applied to the targets

Looking at the info under the topic for Glenda here, I believe the wording for her SS needs to be updated, if I’m not mistaken as I don’t actually have her. Her buff is worded now similar to Quenell using the word ‘power’.

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@OAlexisO regarding your most recent post about how Quenell’s power gain effects her skill damage: I tested it with Quenell on the bosses of s1:7-4 (the monster chest stage for s1). Here’s the pix of the dmg:

1. Quenell’s skill damage without a power buff:

1. Quenell’s skill dmg with a +200% power buff:

cc: @Zack above are the first two data points for Quenell’s skill damage with and without power gain buffs (minimum and maximum power gains).

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This additional attack power is added to % attack damage that hero does.

So Quenell normally hits for 320%, with 200% buff she will hit for 520% (320% + 200%). It works the same with all attack up/attack power up buffs.

“Power” stat on card doesn’t matter durning damage calculation.

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@Radar1 I can follow your reasoning so far. I need to be able to link theory to experiment somehow in order to verify that something is true. Do we know how the skill damage varies as a function of the X% dmg on the skill description?

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Very interesting! Is this formula applied to all heroes? Are the 25.5; 0385; 0.93 and the others constant?

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QA=1213 and TD=246

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