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Mining for Bits

How is damage calculated?

Rating: 11 votes, 5.00 average.
Damage.

damage for this card = [servantAtk * npDamageMultiplier * (firstCardBonus + (cardDamageValue * (1 + cardMod))) * classAtkBonus * triangleModifier * attributeModifier * randomModifier * 0.23 * (1 + atkMod - defMod) * criticalModifier * extraCardModifier * (1 - specialDefMod) * {1 + powerMod + selfDamageMod + (critDamageMod * isCrit) + (npDamageMod * isNP)} * {1 + ((superEffectiveModifier - 1) * isSuperEffective)}] + dmgPlusAdd + selfDmgCutAdd + (servantAtk * busterChainMod)

FROM YOUR SERVANT
* servantAtk = {Your servant's current Atk value}
* classAtkBonus = {class bonus}
* triangleModifier = {triangle bonus}
* attributeModifier = {attribute bonus}

FROM CARDS
* firstCardBonus = {0.5 if first card is a Buster card, 0 otherwise. No bonus to NPs}
* cardDamageValue
First Second Third
Arts 100% 120% 140%
Buster 150% 180% 210%
Quick 80% 96% 112%
** cardDamageValue for Extra card is 1
** NP cards act as a First card of the appropriate type.
* busterChainMod = {0.2 if it's a Buster card in a Buster Chain, 0 otherwise}
* extraCardModifier = {2 if Extra card in a Brave Chain, 3.5 if Extra card in a Buster/Quick/Arts Brave Chain, 1 if neither}

FROM RNG
* randomModifier = {random from 0.9 to 1.1}
* criticalModifier = {2 if crit, 1 if not}

FROM NP PROPERTIES
* npDamageMultiplier = {NP's damage multiplier (or 1 if it's not an NP)}
* superEffectiveModifier = {NP super effective modifier}
* isSuperEffective = {1 if the enemy qualifies (via trait or status), 0 otherwise}

FROM BUFFS
For those dumbasses that can't use basic logic, you add up all buffs of a given type before including the term. This obviously means they'll stack additively.
* cardMod = {X% [Card] Power Up/Down}
* atkMod = {X% Attack Up/Down}
* defMod = {X% Defense Up/Down), Def Up (but not Def Down) is skipped if the NP ignores defense}
* specialDefMod = Given to some enemies like Quetz's in Babylon or Gawain in Camelot. Defense Ignore NPs do not bypass this value.
* powerMod = {X% Power Up/Down}
* selfDamageMod = {No buff currently uses this. It's like Power Up but on the enemy's side.}

* isCrit = {1 if crit, 0 otherwise}
* critDamageMod = {X% Critical Damage Up/Down}

* isNP = {1 if NP attack, 0 otherwise}
* npDamageMod = {X% NP Power Up/Down}

* dmgPlusAdd = {X Damage Plus/Minus} // Note the lack of %. Divinity and Waver's 3rd skill, for example.
* selfDmgCutAdd = {X Damage Up/Cut} // Also a straight number. Waver's 2nd skill and Mashu's first, for example.

Remember, 10% = 0.1.
* You'll note Attack and Defense buffs are direct and opposite buffs. +10% attack is straight +10% damage and +10% def is -10% damage.
* [Anti-X] buffs will obviously only count if they match you/the enemy. So Power Up [Anti-Dragon] only works if you're hitting an enemy with the Dragon trait and so on.
* Minimum damage is 1 lol. (But only if Atk > Def)

Updated October 17th, 2017 at 04:17 PM by Kyte

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  1. Aedra's Avatar
    Quote Originally Posted by epherion
    What about divinity? I've seen the % on the japanese wiki, but how does it actually affect my damage?
    According to Kyte, it is raw value base, not % base. Though I feel the value is so low that I can ignore for NP dmg for the time being. As kyte has yet to publish the value of each servant skills, I'll wait and see first.

    Back to the NP dmg, for cardDamageValue

    I've tested with 3 more servants here's the result from calculating (unbuff, only CE and passive, ignoring all the NP trait in calculating)

    Though, I'm still waiting for more value from my friends..

    test result
    Updated August 29th, 2015 at 06:25 PM by Aedra
  2. Kyte's Avatar
    It's 8% for Herk's ME and 200 for Divinity, yes.

    Your results are kinda weird, though. Not sure why.

    Here's a test. While I split it into two parts, the game treats cardDamageValue as one single value (adjustAtk keyed to id (card type) and num (card position)).
    Test if the same NP does different damage if it's first, second or third. That should make it quite clear whether or not cardDamageValue is being used.
    Updated August 29th, 2015 at 07:50 PM by Kyte
  3. Aedra's Avatar
    I splitted

    For [card type]

    In my previous post is to determine the [card type] being use in cardDamageValue or not..
    per testing result (though, only 4 so far), yes it is being use (1 for Art, 0.8 for Quick and 1.5 for Buster)

    For [card position]
    It's next to impossible to test w/o a collective of data due to random modifier unless I false proof it (Base on random modifier range limit from 0.9 to 1.1).

    Which I did back then at Heracles testing ( ATK = 7281, no CE, attack wyvern, ignore {1 + (traitModifier * hasSuperEffectiveTrait) + (statusTraitModifier * hasSuperEffectiveStatus)} )
    From calculating NP 1st position,
    - random modifier = 1 : damage = 24,372 lower limit (0.9) = 21,955 , upper limit (1.1) = 26,789
    Real NP damage on 1st positions varies from 22,268 to 26,305 which fall within calculating range.

    Assumption: If [card position] is being used
    NP damage 2nd position would be lower limit = 26,306 and upper limit = 32,107
    NP damage 3rd position would be lower limit = 30,657 and upper limit = 37,425

    Though, the NP damage for 2nd and 3rd positions are all in range of 1st hit. Thus, I false proof the assumption and conclude that [card position] is not being used in cardDmgValue.

    Assumption cardDamageValue (testing in progress..)



    while it's true that data from 1 testing is not enough, I'll keep getting more test data first for both testing until I can finally sure.
    Updated August 29th, 2015 at 08:56 PM by Aedra
  4. PhantasyMind's Avatar
    My test also indicate that Aedra is right.
    Using Vlad III, the damage of third position can become a lot lower then the lower limit of 1.4*1st position lower limit , its still in 1st position's lower range (random modifier 0.9 to 1.0).

    And using my Heracles, the damage output is so much more then Vlad III. Yup, in range of 1.5x vlad III's NP dmg. (The difference between their ATK is calculated, I'm not an idiot LOL)
    Since they have the same npDamageMultiplier (before Vlad III upgraded his NP), I believe [card type] is involved in the NP dmg.
    Updated August 30th, 2015 at 03:51 AM by PhantasyMind
  5. Aedra's Avatar
    They are patching tonight... don't know if they gonna fix/change to anything here or not.. :<

    Guess have to test again later when I have time ugh..
  6. PhantasyMind's Avatar
    Also we can use the data from Lu Bu Feng Xian's test.


    Assume green number 25183 is the lower limit of 3rd position dmg
    25183*1.2/ 1.4 = 21585 (2nd position lower limit)

    21585*1.1/0.9=26381(2nd position upper limit)
    Since Lu Bu has 28241 dmg at the 2nd position, proved [card position] is not involved.
    Updated August 30th, 2015 at 04:03 AM by PhantasyMind
  7. Kyte's Avatar
    Now new APK means no significant changes to the calculations.
  8. PhantasyMind's Avatar
    I got an idea about the [card position] problem ,

    Hypothesis : NP card and Normal card count as 2 type of card, you can only put NP card before another NP card to give one of them the [card position bonus]

    Is this possible? I will test it once I get enough AP
  9. Kyte's Avatar
    No it doesn't work like that. Like I said, there's no card type / card position split in the game. That was simply so I could type a bit less. cardDamageValue is either both or neither.
    Updated August 31st, 2015 at 11:15 PM by Kyte
  10. Kotonoha's Avatar
    I don't understand Aedra's points but at least the colours are pretty!
  11. Aedra's Avatar
    Quote Originally Posted by Kyte
    No it doesn't work like that. Like I said, there's no card type / card position split in the game. That was simply so I could type a bit less. cardDamageValue is either both or neither.
    From the testing I posted before, one thing I'm sure is that cardDamageValue is being used... (though, we might need to call it something else so we are not confusing with normal card values) (aka unknownvalue)

    it should simplify to:
    damage for this card = [servantAtk * npDamageMultiplier * (1 + cardMod) * classAtkBonus * triangleModifier * attributeModifier * randomModifier * 0.23 * (1 + atkMod - defMod) * {1 + powerMod + selfDamageMod + npDamageMod} * {1 + (traitModifier * hasSuperEffectiveTrait) + (statusTraitModifier * hasSuperEffectiveStatus)}] + dmgPlusAdd + selfDmgCutAdd
    The reason is..., if we follow this simplified formula, aka cardDamageValue in original (firstCardBonus + (cardDamageValue * (1 + cardMod))) = ( 0 + ( 1 * (1 + cardMod)) = 1, the range for damage is far off the lower/upper limit (random 0.9 to 1.1) from the real damage.

    That's why I re-calculating with the 2nd table, changing cardDamageValue (aka unknownvalue) to 1 / 0.8 / 1.5 and the data make more sense...


    I'm not saying that this cardDamageValue aka unknownvalue is equal to 1 / 0.8 / 1.5 yet since only few servants have been tested. (I've tested aroun 7 servants only).

    Right now I still need to get more testing result first (which from my testing it seems sometimes Siegfried's damage is still falling off the limit if use x1.5)
    Updated September 1st, 2015 at 01:02 AM by Aedra
  12. PhantasyMind's Avatar
    Quote Originally Posted by Kyte
    No it doesn't work like that. Like I said, there's no card type / card position split in the game. That was simply so I could type a bit less. cardDamageValue is either both or neither.
    That is so strange, because the dmg of red NP is so much more then blue NP , well...

    BTW , my test is showing that my hypothesis is not correct , but I will try to collect more data.
  13. Kyte's Avatar
    Quote Originally Posted by Aedra
    cardDamageValue (aka unknownvalue)
    Why are you conflating the two.
  14. lokilin's Avatar
    I am pretty sure 1 / 0.8 / 1.5 for card type is effect on NPs but position not.
    From my play experience.

    And that is why Quick NPs multiply is so high and buster NPs multiply is low.
    Updated September 2nd, 2015 at 07:01 AM by lokilin
  15. wkdtn201's Avatar
    how about damage per hit? not damage per card
  16. Kyte's Avatar
    Depends on the attack and it's a % of the total damage. Since it always adds up to 100% I saw it pointless to list.
  17. PhantasyMind's Avatar
    * atkMod = {+-X% Attack (Attack Up)}
    * powerMod = {+-X% Power (Power Up, Power Up [Anti-X])}

    Oh, what is the different between power up and attack up? What will be counted as a normal power up? I can't find any on my own ORZ
  18. Kyte's Avatar
    Power Up alone I don't recall being used for any (player-accessible) skills. Power Up [Anti-X] includes dragon killer, beast killer, executioner, boudica's skill and whatever else I forget.
    Attack Up is p common.
  19. Skittles's Avatar
    Did some testing, can someone double check my calculations?
    Conditions: NP first card in chain, no buffs/debuffs, lvl 40 Robin with lvl 20 Kaleidoscope, lvl 40 Cu with lvl 20 Kaleidoscope (Both around 5.1k atk, difference of 14atk). VS caster demon in 40AP master exp daily
    Robin, lvl 3 Arts NP: 1350% modifier, 0.95x Class modifier, 0.9x attribute modifier
    Cu, lvl 2 Quick NP: 1600% modifier, 1.05 Class modifier, 1.0x attribute modifier, 0.8x card multiplier?
    If Quick NP is modified by 0.8x, I expect Cu to do about 16% more damage than Robin. If it isn't, I expect Cu to do about 46% more than Robin.
    Robin averaged 13575 damage across 8 tries.
    Cu averaged 15678 damage across 11 tries (I subtracted 175 from his damage to account for his Divinity B)
    Comes out to Cu doing about 15.5% more than Robin.
    So, I'm inclined to believe card type does somehow affect NP damage
    Thoughts?
  20. PhantasyMind's Avatar
    Quote Originally Posted by Skittles
    Did some testing, can someone double check my calculations?
    Conditions: NP first card in chain, no buffs/debuffs, lvl 40 Robin with lvl 20 Kaleidoscope, lvl 40 Cu with lvl 20 Kaleidoscope (Both around 5.1k atk, difference of 14atk). VS caster demon in 40AP master exp daily
    Robin, lvl 3 Arts NP: 1350% modifier, 0.95x Class modifier, 0.9x attribute modifier
    Cu, lvl 2 Quick NP: 1600% modifier, 1.05 Class modifier, 1.0x attribute modifier, 0.8x card multiplier?
    If Quick NP is modified by 0.8x, I expect Cu to do about 16% more damage than Robin. If it isn't, I expect Cu to do about 46% more than Robin.
    Robin averaged 13575 damage across 8 tries.
    Cu averaged 15678 damage across 11 tries (I subtracted 175 from his damage to account for his Divinity B)
    Comes out to Cu doing about 15.5% more than Robin.
    So, I'm inclined to believe card type does somehow affect NP damage
    Thoughts?

    damage for this NP= [servantAtk * npDamageMultiplier * (CardTypeValue*(1 + cardMod) )* classAtkBonus * triangleModifier * attributeModifier * randomModifier * 0.23 * (1 + atkMod - defMod) * {1 + powerMod + selfDamageMod + npDamageMod} * {1 + (traitModifier * hasSuperEffectiveTrait) + (statusTraitModifier * hasSuperEffectiveStatus)}] + dmgPlusAdd + selfDmgCutAdd

    I keep using this formula since the last comment, and it IS correct until now, I believe it is the case.
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