Help damage calculation when def down / damage increase for enemies

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%) :thinking:
27.3% of 34% = 80.3% = approx. 4/5 or approx, (1 - 20%) :thinking:

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? :thinking:

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! :+1:

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?)

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