Damage Calculation

[ApollosEmpire]

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

[khonghjinh]

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

[Aviendha]

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.

[Kerridoc]

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

[ChuckyF]

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)(θatt/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.

[Argon]

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.

[AHgpIOLLIa13]

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=25attack/defense

[AHgpIOLLIa13]

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

[Garanwyn]

Based on what data? There was extensive testing of the damage formula presented in this thread when it was created.

[AHgpIOLLIa13]

Consequently, you have your own data to check. It’s just my humble opinion.

[Rockabillysav]

Can we somehow calculate the damage made from a single tile (3 opposite strong colours).? Thanks in advance and perfect work by the way.

[Argon]

Roughly: 2 x 100 / 3 x ((attack1 + attack2 + attack3) / defense) ^ 1.35

[Gryphonknight]

I have always wondered if the number of stars ( 1- 14 ) your opponent has influences the damage calculation and any possible soft cap. Personally, it is how I would have coded it.

Looking at the 1* Titan discussion, it is looking possible, but an equally strong candidate is simply using the raw defense stat number for generating a soft cap break point.

[Outlaw_Hawk]

Everyone has contributed a lot to this thread. SO MUCH information, numbers and statistics. I’m lucky I can smell the color 9 right now.

[yelnats_24]

I’m a little bit confused regarding the effect of ramming pulverizer -34% defense, shouldn’t it result in:
(1/(1-0.34)^1.35 = 1.752x damage or 75% increase?

After some discussion in Anzgogh thread, I collect small data while farming. I compare Scarlett 4/50 skill damage against boss of S1:5-4 (the left one) with or without -34 def down:

#	Normal	34% def debuff
Average	748	1085
1	742	1115
2	754	1054
3		1086

Actual increase = 45%
It’s closer to calculation without exponents which have 52% increase

I know that the sample size is too small, but it seems some other have also experienced that:

@Dandaniel1234

Unfortunately in reality Wilbur and Falcon won’t increase the damage Anzogh does by 6 times.
Nothing wrong with your math, but when I use them all three, the damage is only
doubled. Wilbur, Falcon and Anzogh (other fire heroes give same results, e.g. Scarlett) are 8/8 special. With Wilbur, Falcon and Wu it gets to 4 times, but only when it hits

@yelnats_24

I do find it a bit off when I experimented with level 1 Frida and Valen in my alt account.

I was using this formula:

@SolemnWolf

Damage ≈ 100 x ( θ x Att / Def ) ^ 1.35

In that formula, -40% in defense from Frida will result in:
100 x ( θ x Att / (1-40%) Def ) ^ 1.35
= ((1 / 0.6) ^ 1.35) x 100 x ( θ x Att / Def ) ^ 1.35
= 1.993 x (100 x ( θ x Att / Def ) ^ 1.35)
= 1.993 Damage

However when I try it with Ragnhild, it only increase it from 39 to 65 (1.667 times damage)

It is as if there is no ^1.35
1/(1-40%) = 1/0.6 = 1.667

This is also the case when I combined Frida, Valen, and Ragnhild.

If there is ^1.35
The result should have been:
1/(1-0.4)^1.35 = 1.993x damage (from Frida -40% ice defense)
1/(1-0.2)^1.35 = 1.352 damage (from Valen -20% defense)
1.993 x 1.352 = 2.694x damage

However my Ragnhild damage was only increased from 39 to 78 (2x) as if there is no ^1.35:
1/(1-40%) = 1/0.6 = 1.667
1/(1-20%) = 1/0.8 = 1.25
1.667 x 1.25 = 2

@Dandaniel1234

Nothing wrong with your math, but when I use them all three, the damage is only
doubled.

As I have mentioned above, my Ragnhild damage was doubled with -40% elemental defense debuff and -20 defense debuff. Therefore, I believe that with Falcon -54% elemental defense debuff and Wilbur -44% debuff, the result should have been more than doubled.

Suppose we ignore the ^1.35, it will be:
1/(1-54%) = 1/0.46 = 2.174
1/(1-44%) = 1/0.56 = 1.786
2.174 x 1.786 = 3.882x damage

If there is indeed ^1.35, it should be:
1/(1-54%)^1.35 = 1/0.46^1.35 = 2.853
1/(1-44%)^1.3/= 1/0.56^1.35 = 2.187
2.853 x 2.187 = 6.241x damage

Can you post a comparative screenshoot?

@Kerridoc is more familiar with damage formula, I hope he can point out why Wilbur + Falcon only result in doubling the damage from Anzogh. Maybe he can also check my math whether it’s correct or not.

N.B.: I only did it one time so it doesnt’ take into account random parameter.

@Dandaniel1234

@yelnats_24

As I have mentioned above, my Ragnhild damage was doubled with -40% elemental defense debuff and -20 defense debuff. Therefore, I believe that with Falcon -54% elemental defense debuff and Wilbur -44% debuff, the result should have been more than doubled.

My results are more consistent with this math:
when it states the defense is reduced by x% the damage is increased by
(1+(x/100))^1.35 so for example for:

-Falcon the damage is increased 1.54^1.35=1.791 (79% increase)
-Wilbur the damage is increased 1.44^1.35=1.636 (64% increase)
-Gormek (or Valen or many others) 1.34^1.35=1.484

The relationship between debuffs seems additive rather than multiplicative and
for targets debuffed by both Wilbur and Falcon the damage Anzogh (or other reds)
would do is 1+0.791+0.636=2.427
I know it’s more than doubled, but it’s not even close to 6 times or even triple

@Argon

Nicely caught. It seems there indeed isn’t ^1.35 in damage formula for elementally debuffed enemies. I’m happy I managed this little test on my first try

Attacking hero:

First case:

Without exponent: 100×(4,62×938÷(1,2x811×0,46)) = 968 ([587…1595] with random parameter), damage done: 1142, with exponent: 2142.

Second case:

Without exponent: 100×(4,62×938÷(1,2×(962−328)×0,46)) = 1238 ([751…2041] with random parameter), damage done: 1182, with exponent: 2987

Edit: Added 1.2 multiplier for 20% defense bonus for defense team.

@Garanwyn

@Kerridoc may well have better information on some of this than I. But here’s my understanding:

@Solemnwolf didn’t talk about elemental debuffs because they didn’t exist yet when he made the damage equation.

But it appears that all elemental effects, such as buffs and debuffs, happen outside the exponential. Strong and weak tiles, which have a factor of 2x and 0.5x respectively, are known to apply outside the exponential. And I believe that this is how elemental buffs and debuffs work.

[Garanwyn]

You can’t pull individual buffs and debuffs out in isolation like that, because they sum before the exponent is applied. You have to account for troop buffs and the defender buff before exponentiating.

[yelnats_24]

Did you refer to Scarlett-Grimm experiment? They are against monster not other hero so no troop buff or defender buff.

All other variables are unchanged, only with or without -34% defense from Grimm.

Without -34% defense, the formula is:
Damage = 100 x ( θ x Att / Def ) ^ 1.35

If -34% defense debuff is calculated before exponentiating:
Damage = 100 x ( θ x Att / (Def × (1-0.34) ) ^ 1.35
= 100 x ( θ x Att / (Def x 0.66 ) ^ 1.35
= (1 / 0.66) ^ 1.35 x 100 x ( θ x Att / Def ) ^ 1.35
= 1.752 x 100 x ( θ x Att / Def ) ^ 1.35
= 1.752 x [damage without -34% defense debuff]

@SolemnWolf

Att +30% = Damage +42.5%
Def -30% = Damage +60%

Att +30%: (1 + 0.3) ^ 1.35 = 1.425
1.425 - 1 = 42.5%

Def +30%: (1 / (1 - 0.3) ^ 1.35 = 1.619
1.619 - 1 = 61.9%

I use the same principle as the OP.

[Keith1234]

If a hero hits for 380 x 275% does he hit for 138 or 1045?

[zephyr1]

@Keith1234 I moved your post to a thread that can help answer it.

The Damage Calculation formula is a bit more involved than your question implies, but effectively a Special Skill percentage is a multiplier of the hero’s Attack stat.

If you look at the top post of this thread, you can see how that comes into play in the larger calculation of damage — and why the non-linear nature of damage calculation can make the Special Skill percentages quite misleading.

[KLinMayhem]

Seems like gm should take more dmg than he does compared to MN from panther and mok arr. both had kunchen debuff as well. gm had elemental buff, but that’s only a 5% increase.