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(Redirected from Armor Penetration)

Stats Damage Spell Restoration Luck
Enchantments Health Impact Power Footstep Sound
Healing Action/Interaction/Cast Speed Silence
Shield Looted Handled Supplied Experience
Spells

Damage Formula

(
  (
    (
        + (Base Damage + Buff Weapon Damage) * Combo Multiplier * Impact Zone Multiplier
        + Gear Weapon Damage|Magical Damage
        + Divine Strike Damage
    )
    * (1 + Power Bonus)
    + Additional Damage
  )
  * (1 + Hit Location Bonus)
  * (1 + Race Damage Bonus)
  * (1 - Race Damage Reduction)
  * (1 - Damage Reduction * (1 + Damage Reduction Mod) * (1 - Penetration))
  * (1 - Projectile Reduction)
)
* Projectile Falloff
+ True Damage

Base Damage

Buff Weapon Damage

Buff Magical Damage

Magical counterpart to Buff Weapon Damage. Functions the same except it is a Magical stat and as such will be affected by Magical modifiers and not Physical modifiers.

Only affects Magic Weapon Damage and not other sources of Magical Damage.

Sources include:

Gear Weapon Damage

  • The damage added by the "Additional Weapon Damage" affix on gear (formally "Physical Weapon Damage Add"). This stat benefits from Power Bonus. This stat will only apply to direct attacks from weaponry, and will not apply to skills such as Rupture, Caltrops, Achilles Strike, and so on. This is a Physical stat, and so will not add to sources of Magical Damage. This stat is different from "Buff" Weapon Damage, in that it will not be multiplied by your Impact Zone Multiplier or your Combo Multiplier. It is unknown if this is affected by Scaling as no weapon-sourced damage has less than 100% Scaling.

Gear Magical Damage

  • The damage added by the "Magical Damage" stat on the Magic Staff, Spellbook, and Crystal Ball. This damage benefits from Power Bonus. This damage will apply to all sources of Magical Damage, and will do so multiple times per spell, if the spell has multiple damage sources. Examples include each hit of Magic Missile, or Zap's direct hit and DoT portions. This is a Magical stat, and so will not add to sources of Physical Damage. This stat is influenced by Scaling.

Divine Strike Damage

  • The damage added by the Cleric buff "Divine Strike". This stat benefits from Power Bonus. Unlike Weapon Damage, this stat will apply to both weapon attacks, and indirect sources of Physical Damage, such as Rupture, Caltrops, and Achilles Strike. This is a Physical stat, and so will not add to sources of Magical Damage. This stat is influenced by Scaling.

Impact Zone Multiplier

  • A multiplier enforced when hitting with the "sour spots" of certain weapons. See Weapons for each weapon's exact multipliers.

Combo Multiplier

  • A multiplier enforced when hitting with the latter hits of certain weapons' combos. See Weapons for each weapon's exact multipliers.

Power Bonus

  • A multiplier that affects all damage types listed so far. This can be of the Physical or Magical variety, and each will only apply to its respective damage type (Physical Power Bonus will not apply to Zap, for example). This value can be positive or negative, and is influenced by gear or by the player's Attributes. This stat is influenced by Scaling. Physical Damage Bonus is included (modifies Physical Power stat).

Additional Damage

  • The damage added by specific Perks or by the "Additional Physical/Magical Damage" affix on gear. This can be of the Physical or Magical variety, and each will only apply to its respective damage type (Additional Physical Damage will not apply to Zap, for example). This stat does not benefit from Power Bonus. This stat will apply to any instance of its respective type of damage, and will do so multiple times per skill if applicable. Examples include Achilles Strike's individual movement damage ticks (Physical), or each hit of Magic Missile (Magical). This stat is influenced by Scaling.

Hit Location Bonus

Also referred to as Hit Location Multiplier, Limb Modifier, or Headshots

A multiplier enforced when hitting the head or the limbs with certain attacks. The multipliers:

  • Head: +50% (1.5x)
  • Body: +0% (1.0x)
  • Arms: -20% (0.8x)
  • Legs: -40% (0.6x)
  • Feet/Hand: -50% (0.5x)

Area of Effect and Damage over Time sources are not affected by this multiplier.

For on-hit damaging effects there are some exceptions. These exceptions are also mentioned on their respective class description:

  • Warlock's Blow of Corruption does benefit
  • Wizard's Ignite and the Ignite's burn does benefit, even though the burn is a status/debuff

Some other on-hits that correctly don't benefit, listed for the sake of making it extra clear:

  • Cleric's Smite does NOT benefit
  • Barbarian's Achilles Strike does NOT benefit as it doesn't hit any part of the body
  • Rogue's Poisoned Weapon does NOT benefit as it is a status/debuff

Headshot Damage Reduction

Comes from implicit rolls on equipment like the Hounskull.

This reduces Hit Location Bonus if the target hitbox is a head, while Ranger's Sharpshooter increases it. For example, targeting the head with the Sharpshooter perk against a player with 20% Headshot reduction results in
1.5 + .15 - .2 = 1.45x headshot multiplier

Headshot Penetration

Applies to Headshot Damage Reduction in the exact same way that Penetration applies to Damage Reduction. For example, 50% Headshot Penetration converts 20% Headshot Damage Reduction into just 10%.

Race Damage Bonus

A more recently researched multiplier that is currently only utilized by Race specific damage increases.

Race damage bonus applies to both Physical and Magical base damages, and is not restricted to Weapon damage, such as Undead Race Damage Bonus from Cleric's Undead Slaying perk.

Race Damage Reduction

A more recently researched multiplier that is currently only utilized by Race specific damage reductions, like Undead Race Damage Reduction from Warlock's Infernal Pledge perk.

It is assumed to be like Race Damage Bonus in that this applies to both Physical and Magical base damages, but needs confirmation.

It is currently impossible for a player to be damaged with Race Damage Reduction active against a target that also has Race Damage Bonus, meaning it is unknown if this adds or multiplies with Race Damage Bonus.

Damage Reduction

  • A defensive multiplier based on the opponent's Damage Reduction stat. Physical Damage Reduction applies to Physical Damage sources, such as weapon hits, Rupture, Achilles Strike, and so on. Magical Damage Reduction applies to Magical Damage sources, such as Zap, Explosive Bottles, Poison Weapon, and so on.

Damage Reduction Mod

A multiplier to Damage Reduction recently added that modifies the base Damage Reduction. When active, it can even be seen modifying Physical/Magical Damage Reduction in the in game Character stat sheet.

Penetration

  • A multiplier to Damage Reduction after Damage Reduction Mod that can be acquired from certain weapons, or from the "Armor Penetration" and "Magical Penetration" affixes on gear. This stat multiplies with their Damage Reduction %, not their Armor Rating/Magic Resist Rating.

% Damage Reduced = Target's Damage Reduction (after Mod) * (1 - Attacker's Pen)

This then multiplies the damage an enemy takes with this new reduction by (1 - Target's Modified Damage Reduction) Or, combined Damage Multiplier = 1 - Target's Damage Reduction (after Mod) * (1 - Attacker's Pen)

  • This modifier cannot bring Damage Reduction below 0% meaning there is no functional benefit to exceeding 100% Penetration
  • This modifier also does nothing if the target's Damage Reduction % is 0% or less.
  • Using these limitations, the above formula can be expanded to the following: (note that for brevity, Damage Reduction is written as DR and Penetration is written as Pen.

Damage Multiplier = max((1-DR*(1-min(Pen,1))),1-DR)

Projectile Damage Reduction

  • A defensive multiplier that can be acquired from Plate Armor, or the Projectile Resistance Perk for Fighter. This influences damage done by Projectiles, including but not limited to Arrows, Bolts, Throwables. Some magic are also projectiles and are specified on class pages, like Warlock's Bolt of Darkness

Projectile Falloff


True Damage

  • The damage added by the "True Physical Damage" or "True Magical Damage" affixes on gear. Each will only apply to its respective damage type (True Magical Damage will not apply to an Arming Sword, for example). This damage is mostly unaffected by any other multipliers, and is added at the end of all calculations. This stat is influenced by Scaling.
  • Cleric's Perseverance Perk is effectively "negative True Damage", however it seems to not reduce damage if that damage would be reduced below 1. For example, 1 stack of Rogue's Poison Weapon tends to deal less than 1 damage per second, and so Perseverance will not reduce it.

True Base Damage

Created instances of Base Damage that are True, meaning they are functionally identical to the above mentioned True Damage, except that they create a new damage instance rather than adding to it.

Absolute Reduction

Reduces the final damage dealt flat after all other modifiers, to a minimum of 1 damage per instance, including each tick of Damage over Times such as Rogue's Poisoned Weapon.

Does not affect the Dark Swarm damage nor negative amounts of Percent Max Health Healing.

Cleric's Perk Persevereance has 2 Physical Absolute Reduction that reduces all incoming magic and physical damage by 2 per instance.

Golem appears to have 300 Physical Absolute Reduction, but after extensive testing it is nearly confirmed that Physical Absolute Reduction is either bugged for PVE enemies or is not being applied to Golem in any capacity.

Damage/Healing over Time

Damage or Healing that is dealt over a period of time, in the form of a Status.

  • Rather than calculating the value per hit, they calculate the total damage/healing, and then divide by the number of damaging/healing ticks, which is usually the same as the number of seconds.
  • Additionally, nearly all Damage over times have 50% Attribute Bonus Ratio rather than 100%, making damage increases only half as effective
  • Example: Rogue's Rupture skill does 20 physical damage over 5 seconds, or 4 damage a second. If they attain +5 additional physical damage this becomes 22.5 damage over 5 seconds, or 4.5 a second.
  • The number of damaging ticks is affected by the receiving player's Buff/Debuff Duration, and is rounded down to the nearest integer. This strictly affects how long the DoT lasts, and not the damage per tick of the DoT
  • Sources like Ray of Darkness, Din of Darkness, Torture Mastery, and movement based abilities like Achilles Strike and Earthquake are not Damage/Heal over times, rather, bonuses apply per-hit to these like normal.
  • Sources like Locusts' Swarm and Explosive lanterns fire only deal damage while inside the area and are also not damage over times

Formulas

Note, "Value" refers to either Damage or Healing

Base # of Ticks = Base duration/Interval length

Total duration = Base # of Ticks * (1 + Debuff Duration%)

Total ticks = floor(Total duration)

Total Value = Base Value/Base Ticks * Total ticks

Value per interval = Total value / Base Ticks

Value per second = Value per interval / Interval length


Since nearly all Damage/Healing over times have an Interval length of 1 second, these can be simplified to:

Total Duration = Base Duration * (1 + Debuff Duration)

Total Value = Base Value / Base Duration * floor(Total Duration)

Value per second = Total Value / Base Duration

Examples

Example 1: Rogue's Rupture

  • Rogue's Rupture which normally does 20 damage, with -17% Physical Power Bonus% and +10 additional physical damage will instead deal 23.3 damage due to having a 50% Attribute Bonus Ratio.

Total damage (before debuff duration) = 20 * (1-.17 * .5)+10 * .5 = 23.3

  • Rupture lasts 5s and deals damage in 1s intervals, so against a Bard with 25% longer Debuff duration, it will instead deal 27.96 damage

Base ticks = 5/1  = 5 ticks

Total duration = 5 * (1 + .25) = 6.25s

Total Damage = 23.3/5 * floor(6.25) = 27.96 damage

Damage per second = 27.96/5 = 5.592 damage per second

Example 2: Wizard's Zap's Burn

  • Zap's Burn deals damage with a 1s interval and lasts only 1s total, meaning any negative debuff duration, even -1%, will make it have 0 ticks and deal 0 damage due to rounding.
  • On the contrary, it would require at least 100% debuff duration% on the target to get an extra tick from Zap.

Example 3: Potion of Healing

Shapeshift

Shapeshifts base damage (and Healing) works slightly different to other damage/healing. Instead of having a base amount decided from an equipped weapon/spell/skill/etc, the base amount is some multiple of a primitive attribute, such as Strength for the Bear.

The typical base damage section-
( 

         (Base Damage + "Buff" Weapon Damage) * Combo Multiplier * Impact Zone Multiplier
       + Gear "+N Weapon Damage"|"N Magical Damage"
       + Divine Strike Damage

)

is replaced by

( 

         Primitive Stat * Primitive Multiplier
       + Primitive Add
       + Divine Strike Damage

)

Note the removal of Gear and Buff weapon damage, as well as Combo and Impact multipliers. Please note that Divine Strike Damage has not been confidently confirmed to work yet with Shapeshift damage.


All following parts of the formula can apply so long as they are applied to the Shapeshift.

Primitive Stat

Primitive refers to the 7 core Stats; Strength, Vigor, Agility, Dexterity, Will, Knowledge, and Resourcefulness.

Druid's Bear scales off of Strength, Panther off of Agility, Chicken Resourcefulness, and Rat off of none.

Primitive Multiplier

Primitive Multiplier is a multiplier to the primitive stat. Note, for some Shapeshift attacks this is 100%, meaning they effectively do not have a multiplier.

Primitive Add

Primitive Add simply adds to the base damage after the Primitive Multiplier. Note, some Shapeshift attacks this is 0, meaning this can be skipped.

Example

If a given Shapeshift attack is described to deal "Agility * 2.0 + 5 base Physical Damage", then its Primitive Multiplier is 2 (200%), and its Primitive Add is 5. With 30 Agility and 10% Physical Power Bonus, damage dealt would be:

(30 * 2 + 5) * (1 + 0.1) = 71.5

Health Cost

Warlock's spells cost health instead of using the Spell Count mechanic. This loss of health is not affected by any damage modifiers. This means that unlike True Damage, health costs can't be reduced by effects like Cleric's Perseverance perk.

Rounding

  • Damage/Health: All sources of damage/healing can do decimal amounts, and therefore you can have decimal health. Damage text that is displayed when you hit a dummy is always rounded down. Health on players' details page is always rounded up.
  • Details page: Currently all details round up, but some to the nearest integer, and some to the nearest tenth. Wizard's Sage and Warlock's Malice can give decimal knowledge/will, although their displays round up to an integer. Expect all decimal stats to have a margin of error of +/- .1, and integer stats to have a margin of error of +/- 1.
  • Memory Capacity is both rounded up to the nearest integer in the details page and in reality. +1% Memory Capacity will always equate to at least +1 Memory Capacity
  • Buffs/Debuffs: Durations are not rounded and last their exact amount. However, durations that perform an action in intervals, like Damage/Healing over Time, are rounded down to the nearest integer, resulting in thresholds that players may want to take advantage of. In other words, increases must be greater than its interval length, which is usually 1 second.
  • Maximum Health can be decimal with fractional Strength and Vigor scaling, in which case the displayed Maximum Health is rounded up.

Total Ticks = floor(Base Duration * (1 + Bonus Duration))

Examples

  • A 5s buff with 19% bonus duration will have

floor(5 seconds * (1 + .19)) = 5 ticks

  • A 5s buff with 20% bonus duration, however, will have

floor(5 seconds * (1 + .2)) = 6 ticks

  • A 5s buff with -1% bonus duration will have

floor(5 seconds * (1 + -.01)) = 4 ticks

Notes

  • For statuses that can stack their damaging effect several times over, like Rogue's Poisoned Weapon, the stack multiplier is not applied to the base damage in the beginning. Rather, the damage for one stack is calculated first, then that value is multiplied by the number of stacks after. This means that flat bonuses like Additional Physical/Magical Damage will apply once per stack rather than once for the entire stack.
  • Rogue's Weakpoint Attack debuff applies a multiplier to the target's Armor Rating directly. Because Armor Rating to Physical Damage Reduction follows a variable curve, it is very difficult to predict exactly how much this will increase damage to players. Damage to monsters is much easier to predict as all monsters of a given type always have the same, static PDR value, and almost all monster types have the same PDR.

Attribute Bonus Ratio

Also known as "Scaling"

Information moved to Scaling.

Additional vs True

Difference

Using the formula, the difference between Additional Physical/Magical and True Physical/Magical can be summarized as follows:

Additional damage:

  • Scales with Hit Location Bonus which can be both a good and a bad thing
  • Reduced by Damage Reductions
  • Reduced by Projectile Damage Falloff if its a gravity-affected projectile
  • Generally better against enemies with lower damage reduction, and when headshots can be hit easily/consistently.

True damage:

  • Unaffected by Hit Location Bonus which can be both a good and a bad thing
  • Unaffected by Damage Reductions
  • Unaffected by Projectile Damage Falloff
  • Generally better against enemies with higher damage reduction, or when some sources of your damage cannot headshot, or when headshotting is difficult, or when using gravity-affected projectiles


On a particular hit, True damage is always better than Additional damage when it cannot headshot (Damage over Time / Area of Effect).

Additional is substantially better in PvE for physical hits as most Monsters have negative Physical Damage Reduction, and headshots are very consistent.

Note that neither of these benefit from Physical/Magic Power Bonus.

Formula

To determine exactly which is better with your specific stats and by how much, use the following formula: 

(1 - Damage Reduction after Penetration) * (Hit Location Bonus) * (Damage Falloff)

For non-gravity affected projectiles, Damage Falloff can be left out.


If the resulting number is greater than 1, Add is better.

If the resulting number is less than 1, True is better.

Examples

Example 1

Scenario: Headshot against slightly above average damage reduction

For example, against an enemy with 33.33% Damage Reduction (after Penetration) with a headshot (1.5x Hit Location Bonus) (not projectile): 

(1 - .3333) * 1.5 = 1x

In this scenario, True gives exactly the same amount of damage as Additional.


Example 2

Scenario: Low damage reduction with a Damage over Time

Against an enemy with 20% Damage Reduction when using a Damage over Time (1x Hit Location Bonus) (not projectile): 

(1 - .2) * 1 = 0.8x

In this scenario, Additional gives 80% of the damage that True gives. In other words, Additional gives 20% less damage than True does.


Example 3

Scenario: No damage reduction, hitting limb

Against an enemy with 0% Damage Reduction and the damage hits a Hand (0.5x Hit Location Multiplier) (not projectile): 

(1 - 0) * 0.5 = 0.5x

In this scenario, Additional gives 50% of the damage that True gives. In other words, Additional gives 50% less damage than True does.


Example 4

Scenario: PvE with a headshot

Against an enemy with -22% Damage Reduction and the damage hits the head (1.5x Hit Location Bonus) (not projectile): 

(1 - -.22) * 1.5 = 1.83x

In this scenario, Additional gives 183% of the damage that True gives. In other words, Additional gives 83% more damage than True does.


Example 5

Scenario: Gravity-affected Projectile

Against an enemy with 10% Damage Reduction and an *arrow* hits their arm (0.5x Hit Location Bonus) after being in the air for half a second with a Recurve Bow (0.7x Damage Falloff) 

(1 - .1) * 0.5 * 0.7 = 0.315x

In this scenario, Additional gives 31.5% of the damage that True gives. In other words, Additional gives 68.5% less damage than True does.


Example 6

Scenario: Realistic PvP

Lastly, for a more realistic example, you can guess what your average Hit Location Bonus is. If you never hit the head, and sometimes you hit limbs/arms/feet, your average may be 0.9x.

Against an enemy with 20% Damage Reduction: 

(1 - .2) * 0.9 = 0.72x

In this scenario, Additional gives 72% of the damage that True gives. In other words, Additional gives 28% less damage than True does.

Bugs

  • Rogue's Rupture, although Physical damage, does not get increased by the Ambush perk if any Combo Multiplier is present (meaning not 1x). This may have to do with a change to Ambush during the Multiclassing period that made Ambush only buff physical weapon-hits.
  • Drum's, Throwing Knives, and Francisca axes benefit twice from Gear and Buff Weapon Damage, but not Torches. Untested for Arrows/Bolts.
  • While Wizard's Staff Mastery is noted as "Buff Weapon Damage" it actually acts as Base damage because it creates an entirely new damage instance.

Calculators

Open source Damage and health calculator web-app!



Full stat weapon / spell / druid / DPS / Hits-to-kill(PVE) / Hits-To-Die / Healing calculator! (Make a copy to edit values)



Video Guides

Note that Hit Location Bonus is outdated in this video.




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