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 Battle Arena Damage Formula

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Colaleon
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PostSubject: Battle Arena Damage Formula   Wed Mar 27, 2013 4:57 am

Note: this is the formula to use during Battle Arena events (and Guild Battle events), where you create a team of 7 units (or 10 units) and fight without the aid of your allies. The formula to use during normal Arena events, where you create a team of 5 units and fight with the aid of 2 random allies, is found in a different topic: Arena Damage Formula.

During Battle Arena events, the damage units deal is determined by these factors:

  • RANK - The rank of the unit. In other words, the amount of stars it has. However, RANK kan never be higher than 6! For units with 7 or more stars, use 6 as the value of RANK. For example: Orlando is a 2* unit. His rank is 2. Anton is a 4* unit. His rank is 4. Lilith is a 7* unit. Her rank is 6.
  • LEVEL - The level of the unit. Note: this concerns the unit's current level, not his maximum level.
  • HIGH BASE DMG - The highest number of the unit's 3 attack numbers: land, sea or air. Bonuses, such as skills that increase dmg by a cerain percentage, are not included. In other words, this is the number you see on the card when it's in your unit list, not when it's in battle. For example: at level 80 without any bonuses, Anton has 36528 land damage, 0 air damage and 18586 sea damage. His highest base damage is 36528. At level 100 without any bonuses, Rose has 36250 land damage, 38800 air damage and 35240 sea damage. Her highest base damage is 38800.
  • MID BASE DMG - The second-highest number of the unit's 3 attack numbers: land, sea or air. Bonuses, such as skills that increase dmg by a cerain percentage, are not included. In other words, this is the number you see on the card when it's in your unit list, not when it's in battle. For example: continuing on from the examples of Anton and Rose, Anton's second-highest base damage is 18586 and Rose's second-highest base damage is 36250.


The formula to calculate the damage dealt in a Battle Arena battle is as follows:


Battle Arena Damage = ( 1 - 1.5 * RANK ^ 2 / 100 ) * ( HIGH BASE DMG + MID BASE DMG ) * LEVEL / 100

The final Battle Arena Damage is rounded up or down to an integer number (down if the first decimal is smaller or equal to 4, up if the first decimal is greater or equal to 5).


For example: let's calculate the Battle Arena Damage for a level 80 Anton. Anton has rank 4. His highest base damage is 36528. His second-highest damage is 18586.
Battle Arena Damage = ( 1 - 1.5 * RANK ^ 2 / 100 ) * ...
Battle Arena Damage = ( 1 - 1.5 * 4 ^ 2 / 100) * ...
Battle Arena Damage = ( 1 - 1.5 * 16 / 100) * ...
Battle Arena Damage = ( 1 - 24 / 100) * ...
Battle Arena Damage = ( 1 - 0.24) * ...
Battle Arena Damage = 0.76 * ...
Battle Arena Damage = 0.76 * ( HIGH BASE DMG + MID BASE DMG ) * ...
Battle Arena Damage = 0.76 * ( 36528 + 18586 ) * ...
Battle Arena Damage = 0.76 * 55114 * ...
Battle Arena Damage = 0.76 * 55114 * LEVEL / 100
Battle Arena Damage = 0.76 * 55114 * 80 / 100
Battle Arena Damage = 33509.312
Battle Arena Damage = 33509



If you want to simplify the formula, you could split it into different formula's for each rank:


7* Battle Arena Damage = 0.46 * ( HIGH BASE DMG + MID BASE DMG ) * LEVEL / 100

6* Battle Arena Damage = 0.46 * ( HIGH BASE DMG + MID BASE DMG ) * LEVEL / 100

5* Battle Arena Damage = 0.625 * ( HIGH BASE DMG + MID BASE DMG ) * LEVEL / 100

4* Battle Arena Damage = 0.76 * ( HIGH BASE DMG + MID BASE DMG ) * LEVEL / 100

3* Battle Arena Damage = 0.865 * ( HIGH BASE DMG + MID BASE DMG ) * LEVEL / 100


You could simplify it even further, by assuming maximum level without level breaking:


Level 140 7* Battle Arena Damage = 0.644 * ( HIGH BASE DMG + MID BASE DMG )

Level 120 6* Battle Arena Damage = 0.552 * ( HIGH BASE DMG + MID BASE DMG )

Level 100 5* Battle Arena Damage = 0.625 * ( HIGH BASE DMG + MID BASE DMG )

Level 80 4* Battle Arena Damage = 0.608 * ( HIGH BASE DMG + MID BASE DMG )

Level 60 3* Battle Arena Damage = 0.519 * ( HIGH BASE DMG + MID BASE DMG )


Or if Ambrosia fruits were used to raise their maximum level by 20 levels:


Level 140 7* Battle Arena Damage = 0.736 * ( HIGH BASE DMG + MID BASE DMG )

Level 140 6* Battle Arena Damage = 0.644 * ( HIGH BASE DMG + MID BASE DMG )

Level 120 5* Battle Arena Damage = 0.75 * ( HIGH BASE DMG + MID BASE DMG )

Level 100 4* Battle Arena Damage = 0.76 * ( HIGH BASE DMG + MID BASE DMG )

Level 80 3* Battle Arena Damage = 0.692 * ( HIGH BASE DMG + MID BASE DMG )


For anyone wanting to use this formula in a Spreadsheet where you have the base damage numbers of all characters and you want to assume the character is at its maximum level without using ambrosia, here's how you would rewrite the formula (you would have to replace "RANK", "LAND ATK", "AIR ATK" and "SEA ATK" with the appropiate columns):

=ROUND((1-1.5*MIN(RANK;6)^2/100)*(SUM(LAND ATK;AIR ATK;SEA ATK)-MIN(LAND ATK;AIR ATK;SEA ATK))*20*MIN(RANK;6)/100;0)

Or if you want to assume ambrosia has been used to raise the maximum level by 20 levels:

=ROUND((1-1.5*MIN(RANK;6)^2/100)*(SUM(LAND ATK;AIR ATK;SEA ATK)-MIN(LAND ATK;AIR ATK;SEA ATK))*20*(MIN(RANK;6)+1)/100;0)

In these formula, it is assumed RANK can be higher than 6, so MIN(RANK;6) is used to make sure no value higher than 6 is used there.


Last edited by Colaleon on Wed Aug 21, 2013 7:01 am; edited 3 times in total
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Colaleon
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PostSubject: Re: Battle Arena Damage Formula   Wed Mar 27, 2013 5:09 am

I suspect that this is the part of above post that most people will revisit this topic for to find, so I will repeat it in this post:

Colaleon wrote:
If you want to simplify the formula, you could split it into different formula's for each rank:

7* Battle Arena Damage = 0.46 * ( HIGH BASE DMG + MID BASE DMG ) * LEVEL / 100

6* Battle Arena Damage = 0.46 * ( HIGH BASE DMG + MID BASE DMG ) * LEVEL / 100

5* Battle Arena Damage = 0.625 * ( HIGH BASE DMG + MID BASE DMG ) * LEVEL / 100

4* Battle Arena Damage = 0.76 * ( HIGH BASE DMG + MID BASE DMG ) * LEVEL / 100

3* Battle Arena Damage = 0.865 * ( HIGH BASE DMG + MID BASE DMG ) * LEVEL / 100
Remember the final Battle Arena Damage is rounded up or down to an integer number (down if the first decimal is smaller or equal to 4, up if the first decimal is greater or equal to 5).



A note on damage modifiers
The damage dealt by your units can be modified by skills in the following cases:

  • The Double Attack skill (which is a "Battle Arena only" skill) allows your unit to hit twice. However, each hit will only deal 80% of the damage he would otherwise deal with one hit.
  • The Triple Attack skill (which is a "Battle Arena only" skill) allows your unit to hit thrice. However, this also reduces the damage dealt by each hit. I have not yet been able to confirm by how much it's reduced exactly.
  • The Quadra Attack skill (which is a "Battle Arena only" skill) allows your unit to hit four times. However, each hit will only deal 47% of the damage he would otherwise deal with one hit.  
  • The Area Attack skill allows your unit to hit all enemy units in the first line. However, this also reduces the damage dealt by the attack. I have not yet been able to confirm by how much it's reduced exactly.
  • The Attack Boost skill works somewhat differently in the Battle Arena than it does in the normal Arena. I have confirmed that Camille boosts the attack of all his allies by 17% (so each attack will deal 117% of the damage it would normally deal), but he doesn't boost his own attack. This effect lasts until Camille's next attack (or it simply effects all your units in the queue once, I'm not sure). I suspect other units with Attack Boosts work similarly, but this has not yet been confirmed. It's also unknown if these effects can stack.


A note on Guild Battle events
The damage dealt by your units is modified by the zone you're deployed in:

  • Your units will deal 20% more damage if you're deployed in the ATK zone.
  • Your units will deal 5% more damage if you're deployed in the MID zone.
  • Your units will deal 5% less damage if you're deployed in the DEF zone.


Last edited by Colaleon on Fri Sep 20, 2013 4:52 am; edited 5 times in total
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MythSearcher
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PostSubject: Re: Battle Arena Damage Formula   Thu Apr 04, 2013 3:32 am

The problem now is, how much damage can the units take?

It seems like 5* units can take more than 4*s, and lv is also a factor.
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BkWiz
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PostSubject: Re: Battle Arena Damage Formula   Wed May 08, 2013 8:14 pm

Stats = HP.

How the formula is calculated for health, I don't know.

For starters, Christmas Reamy does less damage and has less health than Petra. How much different, it's hard to quantify.

But it was quite noticable last Battle Arena.
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Colaleon
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PostSubject: Re: Battle Arena Damage Formula   Wed Aug 21, 2013 7:12 am

I've added lines to describe the 7* formulas where they needed to be added, making this topic up to date again. Notice how 7* units use the same formulas as 6* units.

I've also added a note about the Guild Battle event modifiers in the second post.
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sagexsdx
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PostSubject: Re: Battle Arena Damage Formula   Wed Aug 21, 2013 12:13 pm

I'm not getting the right numbers for guild battle dmg. I have a MLB Camille in the mid zone. I used your formula

=ROUND((1-1.5*RANK^2/100) * (MAX(L,A,S)-MIN(L,A,S))*LVL/100, 0)

and then multiplied it by 1.05

the formula comes out to be 56306. In game, it says 66780.

My level 103 Purifica is closer. Formula says 46640. Game says 47937.

Ideas?
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sagexsdx
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PostSubject: Re: Battle Arena Damage Formula   Wed Aug 21, 2013 1:34 pm

sorry i'm dumb. I forgot that damage numbers change per level -_-
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