Basic DPS Formula

*Tested for PVP, may work for PVE too, just change PVP to PVE stats
**Formulas can be not 100% accurate, but they are as close to reality, as possible

Abbriviations:

DO - Damage Output (final damage that you deal)
BD - Base Damage (hidden, taken from Combat Power stat)
SP - Skill Percent Damage
CM - Common Modifier (all class-wide modifiers)
UM - Unique Modifier from Special Class (Sage 15%/Mystic 35%/Hashashin PVP etc.)
EP - Element Percent Boost
PVPAA - PVP Attack bonus of Attacker (You)
PVPDD - PVP Defence bonus of Defender (Enemy)
FIX - FIX Damage from Skill Glyphs (Burn/Poison etc.)

DO = BD x SP x CM x (1+EP) x (1+PVPAA) / (1+PVPDD) x UM + FIX

All values in this formula are known values from profile info/skill page except for CM and BD

CM can be CRIT/AHIB/AAL/CRIT+AAL

CC - Critical Chance
CP - Critical Power
EC - Chance for Element to be Applied
EB - Elemental Bonus

Math Equation for Labreve
CM = CC x CP + EC x EB + (1 - CC - EC)
EC = 10% EB = CP
Normally it can be CC x CP or EC x CP or 1

Math Equation for Ahib
CM = CC x CP + EC x EB + (1 - CC - EC)
EC = 10% EB = 2
Normally it can be CC x CP or EC x EB or 1

Math Equation for Aal
CM = (CC x CP + (1 - CC)) x EC x EB
EC = 100% EB = 1.1
Normally it can be (CC x CP) x EB or EB

BD can be calculated from Combat Power difference of Attacker (You) and Defender (Enemy). Combat Power itself means nothing, but Attacker Attack and Defenders Defence stat will take main part in BD calculation.

AA - Attacker Attack
AD - Defender Defence

BD consists of Four Parts

BDMin - area, where AA < 5000, BD = 0.01 x AA (if You attack high CP player, ***PVP between two players under 10000 CP is way too complicated and useless to calculate, sorry)
BDFlat - also known as Flat damage, when AA - DD < 150 and AA > 5000, BD = 50 (if You are 300 Combat Power over the opponent or less - you do Flat damage)
BDGrow - strong DPS boost for not alot of Combat Power 150 < AA - DD < 300, BD = 0,25 х (AA - DD) + 2 (if You are stronger than opponent for 300 - 600 CP)
BDMax - uncapped common DPS boost per Combat Power AA - DD > 300, BD = 0,0575 х (AA - DD) + 60 (if You are stronger than opponent for 600 CP or more)

****Slimplified BDMin Depends only from Attackers Attack, so on this Plot crossing with BDFlat can be closer/further to AA-DD = 0

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According to Formula lets discuss Elements in this game

Elemental boost consists of 2 parts - Elemental Percent (EP) and Elemental Modifier (EM)
EP - can take values from 0 to 40 or even more with runes/progression bonuses and EP impact works totally the same for all the Elements.
While EM is more complicated. For two Elements Ahib and Labreve it depends on Crit Power and Crit Chance. Serett and Aal are independant.

Aal - gives 10% bonus damage for all you Damage Output 
Ahib - makes 10% of all you hits do double damage (cant double Crit hits, with Crit Chance 35%: 35% Crit hits, 10% Ahib hits, 55 Normal hits)
Labreve - makes 10% of all you hits do Crit damage (cant perform Crit-Crit hits, with Crit Chance 35%: 45% Crit hits, 55 Normal hits)
Serett - adds one more target for your skill (mostly from 5 base to 6 with Serett)

Aal Table with Different Crit Chance and Crit Power values:

Ahib Table with Different Crit Chance and Crit Power values:

Labreve Table with Different Crit Chance and Crit Power values:

Serett Table with Different Crit Chance and Crit Power values:

Final Table with Crit Chance = 35% and Different Crit Power values:

*Serett here was taken with 25% probability of being in situation when you have more than 5 enemies in Skill Damage Area

Aal now is the most impactful Element for PVP and Boss fights, then Labreve, then Ahib. For Super Mass PVP or Farm PVE, espeshially for Farm PVE Serett can become the top Element cause potentially can have up to 20% total Damage Output Boost.

**Addidtional notes about Labreve. Some structures in Ramoness or PVP events can be invulnerable for Crits, making Labreve the worst Element

***Acknowledgements to Smithy for our recent discussion about Aal Element

One of the most popular Questions about DPS is: Sushi stone or PVP Stone (Sushi stone or Boss/Monster stone in PVE)

*less than 10000 CP equation is not taken

So according to well known formula and parameters below we get this graph:

Tested for +10 Sushi Stone, +7 PVP Stone and t7 Max stat Pets. Changes for +8 Sushi, +5 PVP or t6 Pets are not so significant.

Higher - better. **Look at the red and blue vertical lines. If the difference between Attacker Attack (You) and Defender Defence (Enemy) is 100 which is approximately 200 CP (red line) - any changes from Basic setup will boost your Damage output, while if the difference between Attacker Attack (You) and Defender Defence (Enemy) is 500, approximately 1000 CP (blue line) - only changing Combat Powerpets to PVP pets will boost your Damage output.

Damage dealt is just one side of PVP process, the second part is Damage recieved, and here one of the best ways to combine those two processes is Damage dealt per 1HP lost during non-stop fight.

And here we will again take +10 Sushi Stone, +7 PVP Stone and t7 Max stat Pets for both participants. Our opponent is always in Max Combat Power (Basic) setup.

Higher - better. Sushi Stone and 3PVP pets is the best option for most PVP cases. Only around the difference between Attacker Attack (You) and Defender Defence (Enemy) = 150 (red vertical line ~300 Combat Power) Full PVP setup will shine or around the difference between Attacker Attack (You) and Defender Defence (Enemy) = 300 (blue vertical line ~600Combat Power) Max Combat Power setup will give you the most Damage dealt per 1HP lost

*That may be not true for Combat Power equalized or compensaded events

The second question will be answered here: What is the best Balance Stats, Max Attack or Max Defence

The answer here is quite simple. The more powerful you are against your enemies - the better Max Attack will be, besides while most of your enemies are much stronger than you are - the is close to zero difference how to balance stats. Cause Damage Output is linear and Damage Recieved is rational - we get quite short range of enemies where Max Defence will overperform Max Attack or Balanced

Higher - better. Only around the difference between Attacker Attack (You) and Defender Defence (Enemy) -400 which is approximately -800 CP (red line) - Max Defence will be really helpful, at the difference between Attacker Attack (You) and Defender Defence (Enemy) = 150, approximately 300 CP (blue line) even Balanced overperforms Max Defence. So try to always Max Attack stat.

*That may be not true for Combat Power equalized or compensaded events

With a small modification of calculation we can answer the question about pforitability of Maxing HP instead of Combat Power

After Awakening Patch more than a year ago we got Max Hp increased so high, that Combat Power got inevitable priority. And even still, formulas got changed, Compat Power multiplied, but HP is not worth to max. Now Combat Power crystals are one grade higher than HP, so if you are between two red crystals - they are approximately same, if you want to incrustate Pink Combat Power or Red HP - take Pink Combat Power.

Higher - better. Changes in Damage dealt per full HP while we change just Sushi Crit to Sushi HP or Change all pets to HP pets is so low, that we cant find the real difference, except small area of Combat Power equality.
Full Red HP Crystals are better if you are #1 Whale and have 5000 Combat Power higher than anyone else.

*That may be not true for Combat Power equalized or compensaded events