Help damage calculation when def down / damage increase for enemies

[Godon7137]

Hi everyone.

Does someone can help to understand in which order it makes more sense to activate the heroes?

Example: we have a Franz with Atk 598 (making 215 % damage for all and increase damage enemies reeceive by 50 %), a Green Knight with Atk 1067 (making -24 % def down and 265 % damage to all enemies) and and let´s say a Xiamara with Atk 1354 making 300 % damage to all.

What makes more sense when all 3 are ready to fire?

Franz, Green Knight, Xiamara or
Franz, Xiamara, Green Knight

Does anyone has the correct forumulas and can show me how to calculate correctly?

Thanks in advance.

[Ufeel]

@Zack has the empirical well-test formula

[Zack]

@Ufeel

@Zack has the empirical well-test formula

Haha, thanks! The formula works very well for tile and slash damage, and is also quite good for special damage, so far.

@Godon7137

Does anyone has the correct forumulas and can show me how to calculate correctly?

Well, to the best of my knowledge the calculation goes as follows:
First you need to get (1) the hero card values for attack (of the attacking hero), defense (of the target), (2) all currently applicable permanent modifiers for this battle for those and (3) all currently applicable buffs and debuffs that change those.

• Permanent modifiers are stat changes from troops and probably also from the goblin skills. They apply directly to the attack and defense values.
• Attack buffs are added together, then applied as a factor = (special skill% + buff1 + buff2 + buff3 + …).
  Important to note: Wu’s attack buff and the special skill % are treated like an attack buff.
• Defense buffs are added together, then applied as a factor = (1 + buff1 + buff2 + buff3 + …).
• Debuffs are also added together and then applied as a separate factor = (1 + debuff1 + debuff2 + …)
  edit2: except for the defense debuffs, as we found that defense debuffs get multiplied as follows:
  Example case with -20%, -34% and -65% defense debuffs: the resulting defense is Defense x (1 - 20%) x (1 - 34%) x (1 - 65%) (edit2 end)
  There seem to be limits, for example, the defense value cannot go below a minimum (exact value is currently unknown, maybe 30% of the original value?)

Then the formula is
damage = (base_damage + increased_damage) x team_modifier x damage_modifier ±5%

• The base_damage is linear and only depends on the attack/defense ratio.
• The increased_damage is also linear, but here the defense is being subtracted from the attack. It applies when the attack value is approx. 93% of the defense value or larger.
• The team_modifier is a factor that balances the odds: attacking team gets = 3 x 11/12, while the defending team gets = 3 x 11/10 (Note1: that means that the defenders get +20% damage for specials)(Note2: the factor “3” is there because the initial formula was derived from tile damage)
• The damage_modifier is just a factor for multiplication.
• Very important to note: until here the result of this damage calculation gives the average damage and the game then slaps a ±5% variance on it, with a minimum variance of 1.

damage ≈ (25.5 x attack/defense + IDF x 0.0385 x (attack – 0.93 x defense)) x 3 x 11/12 x damage_modifier ±5%

(The exact values should be close to these.)
IDF = Increased Damage Factor = 0 for attack < 0.93 x defense; 1 for attack ≥ 0.93 x defense

Now for some actual calculation:
First we have to chose a defense value for the target. Let’s assume 1000 defense on the hero card.
Second we have to chose the troops. Let’s assume mana troops level 29 for everybody involved, i.e. +26% attack and +18% defense.

Franz’ attack = 598 x 1.26 = 753
Green Knight’s attack = 1067 x 1.26 = 1344
Xiamara’s attack= 1354 x 1.26 = 1706
Target’s defense = 1000 x 1.18 = 1180

1. Franz’ special damage = [(25.5 x 753x215%/1180) + 0.0385 x (753x215% - 0.93 x 1180)] x 3 x 11/12 ±5% = 151 / 143 / 158 (avg / min / max)
2. Green Knight’s special damage = [(25.5 x 1344x265%/(1180x(1 - 0.24))) + 0.0385 x (1344x265% - 0.93 x (1180x(1 - 0.24)))] x (1 + 50%) x 3 x 11/12 ±5% = 850 / 807 / 892 (avg / min / max)
3. Xiamara’s special damage = [(25.5 x 1706x300%/(1180 x (1 - 0.24))) + 0.0385 x (1706x300% - 0.93 x (1180 x (1 - 0.24)))] x (1 + 50%) x 3 x 11/12 ±5% = 1280 / 1216 / 1344 (avg / min / max)
   The expected average total damage for the target would then be = 151 + 850 + 1280 = 2281

Now the other scenario

1. Franz’ special damage = [(25.5 x 753x215%/1180) + 0.0385 x (753x215% - 0.93 x 1180)] x 3 x 11/12 ±5% = 151 / 143 / 158 (avg / min / max)
2. Xiamara’s special damage = [(25.5 x 1706x300%/1180) + 0.0385 x (1706x300% - 0.93 x 1180)] x (1 + 50%) x 3 x 11/12 ±5% = 1094 / 1039 / 1148 (avg / min / max)
3. Green Knight’s special damage = [(25.5 x 1344x265%/(1180x(1 - 0.24))) + 0.0385 x (1344x265% - 0.93 x (1180x(1 - 0.24)))] x (1 + 50%) x 3 x 11/12 ±5% = 850 / 807 / 892 (avg / min / max)
   The expected average total damage for the target would then be = 151 + 1094 + 850 = 2095

Hope this helps.

edit: corrected a typo for Green Knights damage, where I had typed 1144 instead of 1344.
edit2: corrected the defense debuff statement for our new finding on how they are multiplied

[Godon7137]

Wow. Thanks a lot. I try to understand everything. I think I need some quiet minutes.

Do you ever thought of creating some sort of Excel sheet where you can put all these data and you get the output of the damage or something like that.

Maybe I will try; implying I comprehend everything you wrote. I try me best.

Thanks again!

[Ruskin505]

1 amazing explanation by @Zack

2 I’m intrigued at the way the question was asked. Xiamara does straight damage with no increase for her allies. So why put her anywhere but last? I’m more surprised the question isn’t green knight or franz first since they each add a damage modifier.

I’m curious why OP was thinking to fire Xiamara second but no other alternate order.

[Godon7137]

Because in my eyes it is clear that the damage output is much higher when starting with Franz and GK afterwards instead of starting with GK instead of Franz. Franz ATK stats are sooooo low. Franz is a key factor in firing first due to his damage increase the enemies get.

[Ufeel]

@Zack Thank you very much again for your gentle explanation!!

Honestly, the original thread is super detailed (just to anybody who haven’t seen @Zack and @u2371 formula discussion and tests : it should be more than several hundreds threads),

and I already spent some hours studying it and not really sure if I got it right, so the summarized explanation here is very highly appreciate!!

[Ufeel]

@Zack

Important to note: Wu’s attack buff and the special skill % are treated like an attack buff.

Could you explain more? Do you just mean we add special% to his +185% ?

@Zack

Debuffs are also added together and then applied as a separate factor = (1 + debuff1 + debuff2 + …)
There seem to be limits, for example, the defense value cannot go below a minimum (exact value is currently unknown, maybe 30% of the original value?)

I think def-debuff limit around 68% or 70% makes sense!!
I have C.Perceus who can do 68% EDD, and when I applied Grimm DD, I rarely see any differences. And 68% seems to be a solid constant used to limit Kornel, CBrienne, etc.

---

Also from the formula, it seems like the damage modifier heroes like Franz, Buster make more impact than the “attack buff” heroes with the same buff percentage

E.g. compare Franz +50% to CGrimm +50%

[Zack]

@Godon7137

Do you ever thought of creating some sort of Excel sheet where you can put all these data and you get the output of the damage or something like that.

Unfortunately not. I only have some simple table for throwing in some numbers for tile damage and for special damage, where I can check the expected damage. When needed I quickly change the formula to enemy special damage and slash damage.

No idea yet for a good setup that allows you to see all possibilities for damage during a battle.

@Godon7137

Maybe I will try; implying I comprehend everything you wrote. I try me best.

Try it! It sounds more complicated than it actually is.
You can then adapt it to a table that perfectly matches with your needs.

With the information above you can calculate special damage and enemy special damage.

If you want to extend the calculation for tile and slash damage, please take into consideration

• for tile damage the team_modifier = 1
• for tile and slash damage the “special skill%” in the attack buff calculation can be taken as 100%
• for tile damage the total attack value is the sum of the buffed/debuffed attack values for each hero with the concerned tile colour
• for slash damage the team_modifier = 3 x 11/10

@Elioty33 It looks to me like we could reduce the damage formula for tile damage, slash damage, special skill damage and maybe also for minion damage (and fiend damage?) to one formula like the one above.
Do you know, if the exact values for the damage formula have been found somewhere already?

[Zack]

@Ufeel

@Zack

Important to note: Wu’s attack buff and the special skill % are treated like an attack buff.

Could you explain more? Do you just mean we add special% to his +185% ?

Correct! The 185% from Wu are added to the special skill% like any other attack buff.

For example, if you have Magni with 793 attack with an +48% attack buff from Boldtusk and Wu’s 185% attack buff, this gets added as follows:
attack = 793 x (420% + 48% + 185%) = 5178

@Ufeel

I think def-debuff limit around 68% or 70% makes sense!!
I have C.Perceus who can do 68% EDD, and when I applied Grimm DD, I rarely see any differences. And 68% seems to be a solid constant used to limit Kornel, CBrienne, etc.

Yes, there is a point where the actual damage is lower than what you expect fro the defense down debuffs.
I think there was even a test by @JekylandHyde with El Duque’s -90% defense down stack and elemental defense down against a titan and the tile damage was nowhere near the expected values.

The main problem for finding the exact limit value is that the testing involves large damage numbers and therefore needs lots and lots of tests to cover the complete ±5% variance.

@Ufeel

Also from the formula, it seems like the damage modifier heroes like Franz, Buster make more impact than the “attack buff” heroes with the same buff percentage

E.g. compare Franz +50% to CGrimm +50%

That is correct for special damage, because +50% damage increase the damage_modifier from 100% to 50%, whereas the +50% attack increase the attack value only from, for example, 420% to 470%.

In case of tile damage the damage modifier will have less impact, if the tiles crit and/or have the strong colour bonus. The +50% damage then increase the 200% to 250% damage or the 300% to 350%, whereas the +50% attack increase the attack from 100% to 150%, which may then push you into the increased_damage area

[Godon7137]

I tried to convert your formula to Excel (Green Knight 1st scenario):

=((25,513442,65/(1180*(1-0,24)))+0,0385*(11442,65-0,93(1180*(1-0,24))))*(1+0,5)30,9166 with the result of 766,69

Somehow the copy paste from Google sheets is not working so I add a screenshot:

Your formular is: = [(25.5 x 1344x265%/(1180x(1 - 0.24))) + 0.0385 x (1144x265% - 0.93 x (1180x(1 - 0.24)))] x (1 + 50%) x 3 x 11/12 (letting out ± 5%) with the result of 850

Where did I make the mistake @Zack ?

[Zack]

@Godon7137

=((25,513442,65/(1180*(1-0,24)))+0,0385*(11442,65-0,93(1180*(1-0,24))))*(1+0,5)30,9166 with the result of 766,69

Somehow the copy paste from Google sheets is not working so I add a screenshot:

There is an attack value of 1144 instead of 1344 in the part for the increased damage, right after the 0.0385 factor.

I see that I did this typo there, so this error is mine.
The actual calculation uses 1344 and results in 850 damage as the average value.
=> I’ll immediately correct my typo

[Godon7137]

Allow me one more and last question, @Zack.

How would you expand/change the formula, if you want to add now of, let´s say: -58 % def down against green and +30% increased damage from special skill (we stay at GK 1.version):

Thanks in advance.

[Zack]

@Godon7137

How would you expand/change the formula, if you want to add now of, let´s say: -58 % def down against green and +30% increased damage from special skill (we stay at GK 1.version):

The situation for the +30% special damage (from the 2lb) is clear, because buffs are confirmed to simply get added together. The special skill % value would simply increase by +30%, just like it would increase with a +30% attack buff from Kiril:
attack = 1344 x (2.65 + 0.3) = 3964

The situation for the -58% defense down against nature should also be very clear, but due to the funny behaviour of defense down combinations, it is not that certain and I didn’t finish my testing on these situations until now (too much work in RL at that time and then kind of lost interest).

Found the formula with the bonus testing below. The following is just the path my investigation took - kept it for whoever may find this interesting to read

I expect that the debuffs are simply added together, because the summation of buffs has been verified and the summation of debuffs has been verified for mana generation debuffs (magic2 has a -22% and average tide speed has a -25% mana generation debuff, and additional mana debuffs from specials are simply added to that).

The defense would then become
defense = 1180 x (1 - 0.24 - 0.58)
which would give -82%, but we know from tests that the actual damage for such situations is much lower than what we expect for such a large defense reduction.

It may very well be that there is a limit to the total defense down, for example 30% of the original defense value.
Just like there are official limits on how much you can reduce the max HP (30% of the original max), or the attack and defense values via the goblin specials (30% of their original value).
In season 4 the fungal cave biome (e.g. in province 10) gives -90% mana generation for fire heroes, which is probably a limit value too, because even tiles from combo10 onwards still give -90% (= 8 mana points) of the initial combo1 tile mana of 75 mana points.

With an assumed defense reduction limit of 70% the corresponding defense value for your case with -24% defense down and -58% defense down against nature would become
defense = 1180 x (1 - 0.70) = 354

Bonus:
I just went ahead and did a test on season 3 9-8. I combined the -34% defense from Morel with the -20% from the blue runic rock to see, if the defense reduction is indicated.
Two Wilderfrost Warriors were hit with this combination and showed the following defense reduction:
Warrior 1 defense = 713
Warrior 1 defense debuffs: -20% and -34%
Warrior 1 defense reduction = -337
Warrior 2 defense = 708
Warrior 2 defense debuffs: -20% and -34%
Warrior 2 defense reduction = -335

Overall that is a -47.3% defense reduction (= -337/713 or = -335/708).
As a debuff alone the -34% are indicated and work as a -34% debuff. Same for the -20% defense as a single debuff.
=> in this combination the -20% debuff gets somehow reduced to -13.3%
=> or the 20% remain and the -34% get reduced to -27.3%

13.3% of 20% = 66.5% = approx. 2/3 or approx. (1 - 34%)
27.3% of 34% = 80.3% = approx. 4/5 or approx, (1 - 20%)

Let’s see:
If we now adapt the additional -20% by also reducing it by the -34%, we get

• for Warrior 1: 713 x [ -34% + -20% x (1 + -34%)] = -336.536 = -337 (rounded)
• for Warrior 2: 708 x [ -34% + -20% x (1 + -34%)] = -334.176 = -335 (rounded up)

If we switch the order of the debuffs we get

• for Warrior 1: 713 x [ -20% + -34% x (1 + -20%)] = -336.536 = -337 (rounded)
• for Warrior 2: 708 x [ -20% + -34% x (1 + -20%)] = -334.176 = -335 (rounded up)

Is it a coincidence that this formula fits so well with the reduction values indicated during battle?

Let’s do 2 more tests for verification with a weaker and a stronger monster and a higher defense debuff, for example in season 3 1-1.

Draugr defense = 550
Draugr defense debuff = -20%
Draugr defense reduction = -110
550 x -20% = -110
=> ok

Next with additional defense debuff from Wilbur:
Draugr defense = 550
Draugr defense debuff = -20% and -44%
Draugr defense reduction = -304
=> This is a reduction by -55.2% (= -304/550)

Same formula for the defense reduction, but now with -44% and -20%:

• for Draugr: 550 x [ -44% + -20% x (1 + -44%)] = -303.6 = -304 (rounded)

=> bingo!

Next test against the boss of that mission S3 1-1:
Ancient Moose defense = 811
Ancient Moose defense debuff = -20%
Ancient Moose defense reduction = -163
811 x -20% = -162.2 = -163 (rounded up)
=> ok

Next with additional defense debuff from Wilbur:
Ancient Moose defense = 811
Ancient Moose defense debuff = -44% and -20%
Ancient Moose defense reduction = -448

Formula says:

• for Ancient Moose: 811 x [ -44% + -20% x (1 + -44%)] = -447.672 = -448 (rounded)

=> bingo again!
=> I’m highly certain that this also explains the funny behaviour for the combinations of defense down and elemental defense down!

Now back to your scenario with -24% and -58%.

We now get
defense reduction = 1180 x [ -58% + -24% x (1 + -58%)] = -803.344 = -804 (rounded)
defense reduction = 1180 x [ -24% + -58% x (1 + -24%)] = -803.344 = -804 (rounded)
This is a reduction by -68.08%, so it is probably fine and not subject to a limit value.

Green Knight’s expected special damage = [(25.5 x 1344x(265%+30%)/(1180x(1 - 0.24 - 0.58x(1 - 0.24)))) + 0.0385 x (1344x(265%+30%) - 0.93 x (1180x(1 - 0.24 - 0.58x(1 - 0.24))))] x (1 + 50%) x 3 x 11/12 ±5% = 1682 / 1597 / 1766 (avg / min / max)

Thanks a lot man!
Your question resulted in us finding out how the combined defense debuffs work!

Combined defense debuff formula:
defense x [defense_debuff_1 + defense_debuff_2 x (1 + defense_debuff_1)]

example:
defense = 550
defense debuff = -20% and -44%
defense reduction = -304

calculation:
550 x [ -44% + -20% x (1 + -44%)] = -303.6 = -304 (round up)

There should still be a limit value for the minimum defense (30% of the original value?)

[Godon7137]

@Zack

Thanks a lot man!
Your question resulted in us finding out how the combined defense debuffs work!

Oh no, the credit goes definitely to you. I will try to build a formular with some variables. Let´s see if I will be able!

THANKS AGAIN!

[Ufeel]

@Zack

Then the formula is
damage = (base_damage + increased_damage) x team_modifier x damage_modifier ±5%

@Zack From your formula, do “normal attack buff” (Ithar) and “special skill attack buff” (Grimm C2) have equal effect ? It seems to me that GrimmC2’s buff has considerably more impact (?)

I tested the following scenarios 3 times each (it may not big number, but quite consistent results)

Scenario1: Grimm C2 +19% Special Skill attack to Junaid, and Junaid is able to deal 1813, 1827, 1854

Scenario2: Ithar +30% normal attack to Junaid, and Junaid is able to deal 1734, 1756, 1712

For reference, Bane has defence 275 and without at attack buff, Junaid would do around 1600s

[Zack]

Thank you for those tests.

For the normal situation the formula indicates 1620/1706/1791 (min/avg/max)
For the +19% special skill attack from C2 Grimm it gives 1698/1788/1877
For the +30% regular attack buff it says 1744/1836/1927

Your 1813, 1827 and 1854 from +19% fit with this.
The 1600s without attack buff also fit.
The 1734, 1756, 1712 for the +30% are a bit lower than the 1744-1927 range.

You probably got the lower end of the range for the +30%.
I think we need more data to be sure about each complete ±5% range.

[Ufeel]

Thanks Zack, looking more closely, the mean damage of the two are pretty close in this case : 1788 vs. 1836
(Because Bane def stat is too low i guess)

I did try to test 8 more time, 4 for each, and see Grimm special causes slightly higher damages and still this can happen because of 5% noise. It is difficult to test since only 5 friendly matches are allowed per day

(Some of my tests also have bugs as Junaid LB2 +30% ss is on for 6 turns so i have to remove them)

Maybe i should have test on the other stronger stage enemies

[Zack]

@Ufeel

I did try to test 8 more time, 4 for each, and see Grimm special causes slightly higher damages and still this can happen because of 5% noise

(Some of my tests also have bugs as Junaid LB2 +30% ss is on for 6 turns)

So the situation remains that C2-Grimm’s buff seems to increase the damage more than the +30% attack buff.

Hmm, I’ve “only” tested with regular attack buff and Wu’s attack buff and verified that they get simply added to the special skill %.

Special skill % are always indicated as “deals X% damage”.
The wording for C2-Grimm’s buff on his hero card is “Special Skills deal an additional +19% damage”. In your screenshot it is indicates with “+19% additional power for Special Skill attack” That’s why I think that the +19% are added there as well just like any other attack buff.

But okay, maybe this is my misunderstanding, and it is actually a damage buff, not an attack buff?

Now I really want to test this myself to clarify the issue

[u2371]

@Zack

I think there was even a test by @JekylandHyde with El Duque’s -90% defense down stack and elemental defense down against a titan and the tile damage was nowhere near the expected values.

Yes, it is here

TESTING: El Duque on Daily Titan—Empires and Puzzles Books

@Zack

There should still be a limit value for the minimum defense (30% of the original value?)

The limit have to be somewhere. It is easiest way to prevent divide by 0 situation .

I think the limit is same for both Atk down and Def down.

I wonder if the limit apply to both Goblin’s stat down and normal Atk/Def down. Something like the Atk/Def will never go below -70% of original value by anyway.

For example, let say the limit is max -70% reduction, target with 500 Def get -250Def from Goblin’s Def down and -60% Def down will have actual def at 150 Def but will show in game as 250-150 Def.

Take about Goblin, I have a questions as well.

Does Goblin’s stat modified affect minion/fiend’s attack if minion/fiend summoner get stat modified ?