Damage

Players deal damage when they attack monsters or other players. There are many factors which affect how much damage is dealt by the various attacks available to players.

Damage Range
Most attacks in the game do not deal simple fixed values but can deal damage over a range of values that comes from the base damage range. The formulas on this page can be applied to the average damage of the range to find an average result or it can be applied individually to both the minimum and maximum damage values to find the true range of the damage. The average damage is more meaningful when looking at the average DPS (damage per second) but having a high maximum damage can be desirable in PvP situations where high spike damage is difficult to defend against.

Actual damage will be a value randomly picked between the minimum value and the maximum value of the damage range. This applies to the physical damage range for physical attacks or the magical damage range for magical attacks. The only equipment that contributes a range of damage is the weapon which has a base range and equipment with the stats "Maximum Physical Attack" or "Maximum Magical Attack" which only add to the maximum of their respective ranges.

Base Damage
Base damage is the physical and magical attack shown in the character info in game. For physical attacks, the base damage is equal to the damage you deal with a normal attack of your weapon.


 * base damage = attack multiplier * weapon attack

Weapon Attack
Weapon attack in general is how much your weapon contributes to your damage. This is basically the sum of all the physical and magical attack attribute on the player's gear and level.


 * weapon attack = attack from weapon + attack from shards in weapon + attack from rings and other equipment + character level

Don't forget about the +attack or +max attack stats on the weapon.

Weapon attack can also be gained from attack charms. Ammo contributes to the weapon attack for ranged weapons. Other than character level, all other factors of weapon attack are found from equipment. Weapon attack can be increased by refining or sharding with a damage shard (garnet or sapphire) to weapons.

Attack Multiplier
The attack multiplier comes from how your stats, masteries and buffs contribute to your base damage.

Daggers and ranged weapons:
 * attack multiplier = 1 + ( Dex / 150 ) + weapon mastery + physical attack buffs

Melee weapons:
 * attack multiplier = 1 + ( Str / 150 ) + weapon mastery + physical attack buffs

Magic weapons:
 * attack multiplier = 1 + ( Mag / 100 ) + magical attack buffs

Where ( Dex / 150 ) and ( Str / 150 ) are rounded to 2 decimal places. ( Ex. 1 + ( 100 / 150 ) + 0 + 0 = 1.67 )

Example: For an archer with 450 Dex and level 10 bow mastery attack multiplier = 1 + ( 450 / 150 ) + 0.6 = 4.6

This means his base damage is 4.6 times his weapon attack.

Comparison of sources of physical attack multiplier:
 * Level 10 bow mastery adds 60% (+0.6 to attack multiplier) weapon attack
 * Level 10 Strength of Titans attack buff adds 30% (+0.3 to attack multiplier) weapon attack
 * Level 10 take aim adds 300% (+3.0 to attack multiplier) weapon attack
 * Level 3 True Form removes 50% (-0.5 to attack multiplier) weapon attack
 * 150 Str or Dex adds 100% weapon attack
 * Spark Eruption adds 150% weapon attack
 * Advanced Spark Eruption adds 300% - 400% attack
 * Demon / Sage Spark Eruption adds 500% attack
 * Gloom weapon proc adds 100% attack as does Unrelenting

Elemental damage from a buffed skill (Frostblade, Blazing Arrow, Poison Fang, Condensed Thorn) or from elemental damage shards on weapon does not get multiplied by attack multiplier.

Attacks Per Second
Attacks per second (APS) is a measure of your attack rate when using normal attacks and depends largely on your weapon and gear. In many ways it is easier to consider the attack interval instead which is the inverse of your attack rate.
 * APS = 1 / attack interval
 * attack interval = 1 / APS

Attack intervals are always multiples of 0.05 seconds as that is the smallest unit of time the game uses. An assassin's dagger normally has a rate of 1.25 attacks per second, meaning that each attack is .8 seconds long, or that it has an interval of .8 seconds. There are two ways that we can increase this attack rate: -interval gear, and skills to increase your attack rate by a percentage.

In the case of gear, once we have determined the attack interval, we simply subtract the gear value from it.
 * base attack interval = base attack interval for weapon type - attack interval from gear

Going back to assassin's daggers, the Twilight Temple Hook and Thorns have the interval -.05 stat on them, meaning that their interval is .75 instead of .8. This gives them an attack rate of:
 * 1 / .75 = 1.33

The second way to increase your attack rate is through the use of skill such as Demonic Eruption or Heaven's Wrath. In this case, we need to multiply the interval we have by the new percentage of the attack rate:
 * new attack interval = base attack interval * ( 1 - attack speed increase % )

If our Hook and Thorn wielding sin used Demon Spark (25% increase), his new attack interval would be:
 * .75 * ( 1 - .25 ) = .5625

Since the new attack interval is not evenly divisible by .05, we need to round down to the nearest interval. In this case, we get .55.

Translating this back to attack rate, we get:
 * 1 / .55 = 1.82 attacks/second

Skill Damage
Most skills are of the form:
 * skill damage = base damage + skill weapon attack multiplier * weapon attack + constant damage

You can simplify this to:
 * skill damage = ( ( base weapon attack multiplier + skill weapon attack multiplier ) * weapon attack ) + constant damage

Amplifying Damage
There are several skills that can amplify the damage you do as well as magical mastery. Sources of damage amplification are multiplied together.


 * skill damage dealt = skill damage * product( 1 + amplification from each debuff )

"Product", meaning the all 1+amplifications in the parentheses multiplied together. For example, a 30% amplification from sage Amplify Damage when combined with a 20% amplification from Extreme Poison will give 56% total amplification since (1.3) * (1.2) = 1.56 (which is the product, in this case).

Comparison of sources of amplify damage:
 * 20% more damage from Extreme Poison
 * 100% more damage from Heaven's Flame
 * 20% more damage from level 10 veno Amplify Damage
 * 20% from level 10 magic masteries

Skill Damage Amplification
There are some sources that amplify damage done by skills. This damage amplification does not apply to normal auto attacks. These stack additively with each other. They multiply with the other more general damage amplifications above.

Sources of Skill Damage Amplification
 * 20% more skill damage from level 10 Endless Breeze Primal passive skill
 * 20% more skill damage from mystic Invigorate buff (PvE Only)
 * 15% more skill damage from duskblade Moon Chant level 10 buff (PvE Only)
 * 400% more skill damage from Blessing of the Gods Faction Base buff (PvE Only)

A player with level 10 Endless Breeze, Invigorate, and level 10 Moon Chant will do +55% more damage from their skills in PVE. The PvE buffs above all disappear when changing maps.

Critical Hit
A crit is an attack that does more damage than a normal attack. This damage is given as the rage damage multiplier in your character info and is 200% for all classes but assassins that have a skill to get 230% rage damage. Your chance to crit is given in your character sheet and comes from equipment, crit buffs, the Rainbow Blessing (cleric-only genie skill) buff, and Dex.


 * chance to crit = 1 + ( Dex / 20 ) + crit from equipment + crit from buffs

Where ( Dex / 20 ) is rounded down.


 * crit damage = rage damage * damage inflicted

Damage Reductions
There are several sources of damage reductions.

PvP Damage Reduction
In PvP all damage is reduced by 75% (corresponding to a damage multiplier of 25%). This does not apply to some attacks from venomancer pets.

Terrain-Based Damage Reduction
In PWI combat can occur on land, in water, and in the air. If both the attacker and target are in the same terrain then the target will take full damage. If they are on different terrain then there may be a 50% damage reduction. This damage reduction applies to both melee and ranged attacks but does not apply to monsters, venomancer pets, mystic summons, or damage over time (DOT) effects.

Level Difference Damage Reduction
If the target is a higher level than the attacker then a level difference damage reduction may apply. This damage reduction is ignored by venomancer pets and mystic summons which makes those particularly effective fighting against ?-level mobs (which count as level 150).

Skill-Based Damage Reduction
A number of skills provide the Bless buff and similar buffs which reduce damage. These skills do not apply to damage done from damage over time (DOT) effects.

Some examples of skill-based damage reduction:
 * Cleric's Regeneration Aura (50% reduction)
 * Cleric's Guardian light (60% reduction)
 * Barbarian's Invoke the Spirit (90% reduction)
 * Venomancer's Bramble Hood (75% reduction)
 * Archer's Wings of Grace (30% reduction)
 * Celestial Eruption (25% reduction)

High APS Damage Reduction
When the attack rate of your character is either 4.0 or 5.0 attacks per second, damage done by normal attacks is reduced by 5%. This damage reduction was added in the PWI Descent expansion and does not otherwise show up in your character info window. There is also an unconfirmed 20% loss of accuracy with 4.0 and 5.0 attack rates.

Resistance
Physical Resistance is based on your Str, Vit, and equipment defense (the sum of the Physical Defense found on all of your equipment). Similarly Magical Resistances are based on your Mag, Vit, and equipment Magical Resistances. Magical Resistances should be calculated separately for each of the 5 magical elements, but most equipment has the same resistance across all the elements.


 * physical defense = Round{ ( Vit + Str - 2 ) / 4 } + Round{ Def * ( 1 + Round{ ( ( 2 * Vit ) + ( 3 * Str ) ) / 25 } / 100 ) } + 1
 * magic resistance = Round{ ( Vit + Mag - 2 ) / 4 } + Round{ Res * ( 1 + Round{ ( ( 2 * Vit ) + ( 3 * Mag ) ) / 25 } / 100 ) }

Defense and resistance work by lowering damage according to the following formula. The actual defense amount is the value from the character sheet but lowered by the attacker's penetration. (Values within "Round{ x }" are rounded to the nearest integer.)

"Attacker level" in this formula can be modified by the "Highest Level" attribute found exclusively on Moonlight Crystals.


 * physical reduction% = physical defense / ( ( 40 * attacker level ) + physical defense - 25 )
 * magical reduction% = magic resistance / ( ( 40 * attacker level ) + magical resistance - 25 )

The damage reduction from defense cannot be larger than 95%.


 * physical reduction% = min(95%, physical reduction%)
 * magical reduction% = min(95%, magical reduction%)

The reduction is rounded down to two decimal places.


 * damage delivered = damage dealt * ( 1 - reduction% ) 

The above reduction percentages are shown in the character sheet when hovering over the stat. If equipment adds a physical damage reduction stat it does not contribute to this reduction %. This is a separate reduction that applies in a different step from the above.


 * physical damage delivered = damage dealt * ( 1 - defense reduction% ) * ( 1 - total physical damage reduction from equipment% )

Penetration
Physical Penetration and Magical Penetration are new stats added in the Riptide content update. These stats are similar to defense debuffs in that they lower the defense of the target by a percentage. Unlike debuffs though there is no status applied to the target as the lowered defense only applies to the attacker's damage. Furthermore, with penetration the defense is lowered as a percentage of the opponents total defense after all buffs and debuffs while traditional defense debuffs are a percentage of equipment defense, which is typically much lower.


 * penetration percentage = penetration / (10000 + penetration)

With greater penetration, the penetration percentage gets closer to 100% but it will never reach it. At 10000 penetration the penetration percentage is 50% so it would be as if opponents had half as much defense or resistance as they would normally have.


 * final target defense = target defense * ( 1 - penetration / (10000 + penetration))
 * final target defense = target defense * ( 10000 / (10000 + penetration))

Attack and Defense Levels
Attack and defense levels come from various skills, bless boxes, grade 12 gems, and powerful equipment. The damage depends on the attacker's attack level and the target's defense Level. For PVE, all monsterss have a base of 0 attack level and 0 defense level but these can be modified with buffs and debuffs. Before the PWI Sirens of War expansion, attack and defense levels did not apply to damage over time (DOT) effects but now they do.

if ( attack level > defense level ) then:


 * damage taken = damage delivered * ( 1 + ( attack level - defense level ) / 100 )

if ( attack level < defense level ) then:


 * damage taken = damage delivered / ( 1 + ( 1.2 * ( defense level - attack level ) / 100 ) )

Damage results are rounded down. For example, a damage result of 367.9 becomes 367.

Slaying Levels and Warding Levels
Slaying and warding levels come from Morai and Quicksand Maze. They are similar to attack levels and defense levels but only apply to PvE damage dealt and received.

Slaying levels are a PvE-only damage amplification that only applies to damage dealt to monsters. It applies to normal attacks, skills, and genie skills. At near 0 slaying level, every additional slaying level adds about 1% more damage but slaying levels suffer some from diminishing returns. At 60 slaying level (as found on G15 Morai weapons) you only have +50% damage amplification.


 * Slaying Damage Amplification = 3 * Slaying Level / ( 300 + Slaying Level )
 * damage dealt = raw damage dealt * ( 1 + Slaying Damage Amplification )

Warding levels are a PvE damage reduction that only applies to damage players take from monsters. The effectiveness of warding level damage reduction depends on the level of the monster.


 * Warding Damage Reduction = Warding Level / ( Enemy Level + Warding Level )
 * damage received = raw damage received * ( 1 - Warding Damage Reduction )

These are totally separate forms of amplification and reduction that multiply with all other forms of amplification and reduction. For example if you get +40% damage from slaying level and +30% damage from attack level, in total you will have a combined effect of +82% damage since 1.4*1.3 = 1.82.

Spirit
Spirit is a new stat introduced in the PWI New Horizons expansion. It is similar to both attack levels and defense levels, but is more effective in PvP than in PvE. Spirit can be obtained from Soulprime and Lifeprime War Avatar Cards, Soulprime and Lifeprime nuema levels, and from increasing your boundary level.

In PvP roughly 10 spirit is 1% more damage and 1% less damage taken.


 * PvP Spirit Damage = (1,000 + Attacker Spirit) / (1,000 + Target Spirit)
 * damage dealt = raw damage dealt * (PVP Spirit Damage Amplification)

In PvE spirit is 4 times less effective so 40 spirit is 1% more damage and 1% less damage taken. All monsters have 0 spirit.


 * PvE Spirit Damage Amplification = (4,000 + Spirit) / 4,000
 * PvE Spirit Damage Reduction = 4,000 / (4,000 + Spirit)


 * damage dealt = raw damage dealt * (PVE Spirit Damage Amplification)
 * damage taken = raw damage taken * (PVE Spirit Damage Reduction)

These are totally separate forms of amplification and reduction that multiply with all other forms of amplification and reduction.

Evasion and Accuracy
Most physical attacks can be evaded, in which case they do 0 damage. Magic attacks never miss but can be interrupted during channeling time.


 * evade% = ( target evasion - 1 ) / ( ( 2 * attacker accuracy ) + ( target evasion - 1 ) )


 * hit% = 1 - evade%

The evade equation is rounded up to the nearest 2 decimal places (remember 0.67 = 67%). Thus, you can only get a 100% hit% if the target's evasion = 1.

Bramble Damage
The Physical Reflect buff, better known as being "brambled", is normally endowed by the venomancer skill Bramble Guard. It may also be given by the genie skill Alpha Male, the demon version of the barbarian skill Roar, or some monsters will buff themselves with it.

Attacking a brambled target with a melee physical attack causes the attacker to take bramble damage. Bramble damage is a percentage of raw physical damage and can be thought of as a physical attack from the target to attacker.

To calculate bramble damage you start with the physical attack of the attacker before factoring in crits, attack levels, or any kind of damage reduction. For a simple unarmed punch, this attack is equal to the base damage in the character sheet. Using just this damage, a new attack is generated from the target back at the attacker based as a percentage of that damage. For instance a physical attack of 1000 (before crit or any kind of damage reduction) will be reflected back as 600 physical damage by level 10 Bramble Guard (60% reflect damage).

This attack is a physical attack which is treated as if it originated from the brambled target, thus increasing aggro. Like any attack from the brambled target, it uses the brambled target's Attack Level and is mitigated by the original attacker's Defense Level and physical defense using the above equations. This brambled attack has a chance to crit according to the brambled target's crit rate and not the original attacker's. The original attacker's Attack Level and chance to crit as well as the brambled target's Defense Level and physical defense has no effect on the reflected bramble damage.

Heals
In some ways heals can be thought of as an attack that does negative damage, but there are significant differences. Heals never appear in the damage log and never have a chance to critical hit. The amount of healing done does not depend at all on attack level, defense level, defense, resistance, slaying level, or warding level. Most healing skills found on caster classes depend only on base magic attack. This means that the best magic weapon to use for heals is one that gives high attack. Physical classes tend to have healing skills that either heal a fixed amount or heal as a percentage of their maximum HP. The only kind of heal that you can directly see is the healing done by the Bloodpaint buff, which is a percentage of melee damage dealt.

Effective Health
The amount of damage you must deliver to kill something or that something needs to kill you, winds up being health divided by the damage delivered percentage. This simplifies to:
 * health / ( 1 - ( defense / ( ( 40 * attacker level ) + defense ) ) ) )

You should probably be thinking about what this number will be for you in various plausible situations when choosing between defense and health (for example, when comparing between two different shards that cost the same amount, or when choosing between two different belts).

To choose between Vit, citrine, and garnet shards you will have to make two calculations for every stat/shard combination:


 * effective health against physical damage = HP / ( 1 - physical reduction ) / ( 1 - bonus physical reduction from equipment )


 * effective health against magical damage = HP / ( 1 - magical reduction )

'Physical reduction' and 'magical reduction' is physical and magical resistance in decimal form. To calculate effective health for enemies with different levels, put ' physical defense / ( ( 40 * attacker level ) + physical defense ) ' in place of 'physical reduction' and ' magical defense / ( ( 40 * attacker level ) + magical defense ) ' in place of 'magical reduction' in the above formulas.

To calculate effective health with consideration of attack and defense levels use one of the two following equation sets.

If enemy's Attack Level is higher than your Defense Level:


 * effective health against physical damage = HP / ( 1 - physical reduction ) / ( 1 - bonus physical reduction ) / ( 1 + ( attack level - defense level ) / 100 )


 * effective health against magical damage = HP / ( 1 - magical reduction ) / ( 1 + ( attack level - defense level ) / 100 )

If enemy's Attack Level is lower than your Defense Level (and for PvE where the enemy's Attack Level = 0):


 * effective health against physical damage = HP * ( 1 + ( 1.2 * ( defense level - attack level ) / 100 ) ) / ( 1 - physical reduction ) / ( 1 - bonus physical reduction )


 * effective health against magical damage = HP * ( 1 + ( 1.2 * ( defense level - attack level ) / 100 ) ) / ( 1 - magical reduction )