# Damage Calculation

Well, maybe there is no third linear.

I found a topic about +%attack vs -%attack

It turn out that -%attack affect after +%attack regardless the order of skill casting. I think this test will give helpful information for ±%attack and ±%defense test in the future.

new Data on 146 DEF:
730/145-155 (9 data points - 147, 150, 155, 154, 154, 147, 154, 155, 145)
4041/804-882 (only 11 data points - 852, 809, 871, 878, 815, 882 879, 831, 804, 861, 819)

Although this is not enough data for a precise description of these points yet, it already confirms the prediction as per the linear formula. I would also say that it refutes my Gompertz formula as it cannot deal with this.

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Attack buff:
Today I tested with Boldtusk’s +48% ATK, then added CRigard’s +48% as well. My small and tiny heroes die a bit too fast too get data from every battle, so here is what I have so far:

C-Brienne3-50+8% ATK gives 503 ATK. With a +48% ATK boost this becomes 744 ATK (=503 x [1 + 48%]), so the expectation is tile damage according to 744 ATK, i.e. 26-28.
This is exactly the damage that I get: 12 data points - 26, 27, 27, 27, 28, 28, 28, 27, 28, 27, 26, 28

My tiny CoD1-1+16% ATK dies too quickly. I only got three data points so far: 17, 18, 17
CoD1-1+16ATK has 338 ATK. With +48%ATK this becomes 500 ATK.
At 500 ATK the tile damage should be 16-18. Looks very good so far.

I have included a Gobbler 4-70+11%ATK in my team for 711 ATK, which will become 1052 ATK with the +48%ATK boost. No data for him yet, though.

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@Zack I actually think that you is still test neutral tile attack at high ADR. I know it is little bit boring because it need a lot of data.

Yes, the next test is ±%attack and ±%defense test. But you can test if a bit if you are bored from testing neutral tile attack at high ADR. It look like there is no different between ATK from buff and base ATK in tile damage (In skill damage, it might not same). Anyway, we still need some damage at high ADR to conclude as well I think you should test big attack booster (Tarlak, Miki, Wu Kong/Ranvir, Guardian Gazelle). I’m not sure if there is something different from normal attack boost or not.

I think we need some test to find titan defense as well.

Overall, I think tile damage formula is

tile damage = (total tile damage) ± (variance)
(variance) will be calculate from (total tile damage) with 1 at minimum
(total tile damage) = Floor[ (main damage) + (bonus damage) ) x (1 + (cri Bonus) + (element bonus) ]
(main damage) = a x ATK / DEF
(bonus damage) = 0 , if ATK <= k x DEF
_____________ = b x (ATK - k x DEF) , if ATK > k x DEF
(cri Bonus) = 1 , if cri active
_________ = 0 , if cri not active
(element bonus) = 1 , for strong element
_____________ = -0.5 , for weak element
_____________ = 0 , for otherwise

The idea of (bonus damage) is that if you make ATK exceed k x DEF, you will get additional damage for every ATK that exceed k x DEF. I think this is what the developer’s idea is.

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First, I got more data on the +48% attack buff against 744DEF:
My CoD1-1+16%ATK +48%ATK for 500ATK now has 9 data points - 17, 18, 17, 16, 18, 18, 16, 16, 17
=> 500/16-18 confirmed

Gobbler4-70+11%ATK for 711 ATK. With +48%ATK this becomes 1052.
Expectation is 1052/47-51
Result is 1052/47-51 with 14 data points - 48, 47, 49, 48, 51, 49, 48, 48, 51, 49, 51, 47, 49, 50

My Boldtusk+20 with troop bonus has 735 ATK. With +48ATK this becomes 1087ATK
1087/50-54 with 8 data points - 51, 52, 54, 54, 54, 50, 52, 52

=> Seems enough to confirm that attack buffs are added multiplicatively to the ATK value, just as assumed/tested before.

unbuffed attack for 744DEF
My Boldtusk+20 with troop bonus has 735 ATK
735/25-27 with 10 data points - 26, 25, 26, 26, 27, 25, 27, 27, 26, 25

CoD with his 338 ATK
338/10-12 with 7 data points - 10, 11, 11, 10, 11, 11, 12

data for 146DEF:
Sorry, I messed up and went with the wrong team today for adding to the combined 4041ATK.

I went with Mono instead for a combined ATK of 4929ATK (= 923+998+1018+1070+920)
4929/985-1079 with meager 7 data points - 1050, 1034, 991, 985, 1066, 1074, 1079

It is definitely not very exciting but interesting enough to keep going.

Some of those will be difficult. The 744DEF team is fixed and has no hero that reduced attack or defense. I guess I’ll have to keep bugging my other alliance member…

Wu is all I got from those. So far my previous tests strongly point to Wu (and Ranvir, Tarlak and Miki) boosting damage, not attack. But let’s take a closer look step by step.
I expect Gazelle to “simply” boost ATK, just like Black Knight.

Yes, I did very little testing on titans recently. For a 10* Emperor Dragon with 3168000 HP it looked like he had something like 2500ATK and 560DEF. The normal attack always crits, but doesn’t show as a critical hit.

We will have to check the damage formula for the defender first. That curve looks significantly different. That’s why I haven’t posted my diagram for slash attacks yet - I had no luck so far to align the slash damage curve with the tile damage curve…

With this linear type of formula it might be as simple as a +20% higher “a” value, though.

Agreed. Tiebreaker bonus can be added at some point. It seems to increase damage multiplicatively. But I have very little data on that one.

Yes, and this also means that stacking colour is very effective because you push beyond that point and get the additional bonus damage

edit: corrected a typo for the damage range of the unbuffed CoD with 338ATK