Editing Damage calculation

{{DisambigMsg|how damage is calculated|the definition|Damage}}
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[[Category:Game mechanics]]
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==A Simplified Damage Calculation==
''Note: For simplicity, on this page the term '''attack''' describes any attempt to [[damage]] an opponent. However, whenever the word "attack" is used in skill descriptions, it refers to the [[attack]] action.''

There are many different factors to consider while calculating damage.  To avoid confusion, this section presents a simplified damage calculation which only takes into consideration the more common factors.

The Approximate Damage (ApproxD) depends on the Raw Damage (RD) and the Armor Effect (AE).
:'''ApproxD = RD &times; AE;

For damage that ignores armor, AE is set to 1.

A level 20 character will do the damage stated in the skill description to a character with 60 armor.  A level 20 character with 12 in a weapon attribute will do the stated weapon damage to a character with 60 armor.
===Raw Damage===
Skill-based offense (like [[Shock]]) have a specific raw damage (RD) value indicated in the skill description.

Weapons attacks select RD each time uniformly from the damage range of the weapon.  For weapons that have an attribute requirement on their damage range, there is actually another hidden range used for when the attacker does not meet the requirement (see [[Weapon#Linked Attribute|here]] for details).

{{:Damage/Armor effect}}

== Effective Damage ==
The Effective Damage (ED) considers all the Damage Modifiers that were dropped when calculating the Approximate Damage.  The ED depends on the Raw Damage (RD), various Damage Modifiers (D*), and the Armor Effect (AE).

:'''ED = [([RD &times; DScale &times; AE] + DShift) &times; DMult] + DNeg'''

Again, for attacks that ignore armor, AE is set to 1, essentially removing it from the equation.

{{:Damage/Damage Modifiers}}

==Damage Cap and Redirection==
Certain enchantments will restrict the maximum damage the target can receive, or redirect some of the damage away from the target, thus making the received damage less than the Effective Damage.  Redirection is always applied before the cap.

==Notes==
Every 8 ranks in a physical damage attribute thus doubles the net noncaster damage caused; similarly, every 13 character levels doubles caster damage. The accounting per rank or level is as follows: every rank in attack attributes scales the damage by exactly a factor of 2<sup><sup>(1/8)</sup></sup> (roughly 9%), and every character level scales the caster damage by 2<sup>3/40</sup> (roughly 5.33%). Note that the effect of cumulative ranks or levels is ''compounded''; for example, 5 ranks in an attack attribute doesn't increase damage by 45%, but by (1.09<sup><sup>5</sup></sup> - 1) &times; 100 &asymp; 53%.

It is important to keep in mind that certain skills such as [[Greater Conflagration]] and [[Judge's Insight]] change the damage type, and therefore can have an effect on AR bonuses or DR calculation. The articles on these skills explain their damage type changes in more detail. Only in the early [[PvE]] game, advanced PvE areas, or in exceptional situations is the EffectiveAR actually less than the EffectiveDR, so the AE generally always ''reduces'' the effective damage. The philosophy behind the AE scale can be seen as follows: in the prototypical case where the attacker and target are roughly equal [[PvP]] players, the attacker's ranked 12 noncaster attack or normal caster attack at character level 20 will exactly negate the target's EffectiveAR of 60 (standard for all spell caster PvP armor).

The AE equation gives us a handy rule of thumb: every 40 increase (decrease) in EffectiveAR halves (doubles) the amount of normal damage (i.e., damage not caused by armor ignoring attacks). A Warrior with 100 armor against physical damage being whacked by a sword will take half as much damage as any 60 armor Elementalist being whacked by the same sword. Skills such as [[Healing Signet]] temporarily reduce AR by 40, which translates to double damage for normal attacks. An increase of approximately 16 armor would correspond to taking 75% damage. (Many ranger [[insignia]] such as Pyrebound or Frostbound give AR bonuses of +15.)


Consider a Mesmer, an Elementalist, and a Ranger being hit by the same attribute level 16, caster level 20 [[Fireball]]. The Mesmer with only 60 armor takes all 119 damage. The Elementalist has Pyromancer's insignia with 75 armor against fire and takes 92. The Ranger wears Pyrebound insignia for 100 armor against elemental damage so he takes 60 damage.

==Illustrative Examples==

===A Simple Example===

You are a Warrior, with 16 Swordsmanship and wielding a Vampiric Longsword of Fortitude, attacking a Monk, who has 70 armor (either from a Blessed Insignia or Stalwart Insignia), with a normal attack.

====Raw Damage====
The minimum Raw Damage is 15 and the maximum is 22.  (Life steal is not considered damage by the game and doesn't count.)

====Damage Rating====
Using the second formula, 
:'''DR<sub><sub>noncaster</sub></sub> = 5 × Rank''';   if Rank &lt;= Threshold
:'''DR<sub><sub>noncaster</sub></sub> = 5 × Threshold + 2 × (Rank-Threshold)''';   if Rank &gt; Threshold
:'''Threshold<sup>1</sup> = Level /2 + 2'''

Your rank in Sword Mastery exceeds the threshold (which is 12 for a level 20 character), so your Damage Rating is '''DR<sub><sub>noncaster</sub></sub> = 5 × Threshold + 2 × (Rank-Threshold) = 5 × 12 + 2 × 4 = 68'''

====Armor Rating====
The monks BaseAR is 60 - standard caster armor.

She is using Stalwart (or Blessed) Insignia, but she is not using any +armor mods on her weapon, so her ARShift is +10.  You have no armor penetration.


Her Armor Rating is '''EffAR = BaseAR &times; (1 - NAP) + ARShift = 60 + 10 = 70'''

Using the formula for Armor Effect, '''AE = 2<sup><sup>(EffDR - EffAR)/40</sup></sup> = 2<sup><sup>(68 - 70)/40</sup></sup> = 2<sup><sup>(-2)/40</sup></sup>'''


Using a calculator (or the [[Damage Rating progression|chart]]), gives an Armor Effect of 96%.  Which takes us all the way back to the first equation.  Your Approximate Damage is '''(15-22) &times; 96% = (14 - 21)'''.  Not very spectacular, but it's the process that is important.

===An Unnecessarily Complicated Example===

You are a Warrior, with 16 Axe Mastery and 10 Strength this time and wielding a Sundering Chaos Axe of Fortitude, attacking a Monk, who has 70 armor and is under the effect of [[Dark Escape]].  Your first attack is [[Executioner's Strike]], followed by [[Critical Chop]].

:'''ED = [([RD &times; DScale &times; AE] + DShift) &times; DMult] + DNeg'''

====The First Attack (Executioner's Strike)====

=====Armor Effect=====
As before, you have a Damage Rating of 68 (at level 20 and 16 weapon mastery), but the Armor Rating has changed, due to armor penetration.  Your Sundering prefix does not trigger.

The new Armor Rating is '''EffAR = BaseAR &times; (1 - NAP) + ARShift = 60 &times; (1 - 0.10) + 10 = 64'''

Which gives a total Armor Effect of 107%.

=====Damage Scale=====
Your axe does +15% from its inscription and +20% damage from customization, for a total Damage Scale of 38%.

=====Damage Shifter=====
You have no external damage bonus other than your attack skill, like [[Strength of Honor]] or [[Order of Pain]], so the Damage Shifter is +42 (level 16 on Executioner's Strike).

=====Damage Multiplier=====
[[Dark Escape]] gives the monk a Damage Multiplier of 1/2.

=====Damage Negator=====
None

=====Effective Damage=====
The new raw damage for your axe is 6-28, giving a final formula of '''ED = [([RD &times; DScale &times; AE] + DShift) &times; DMult] + DNeg'''


The minimum damage is '''ED = [([6 &times; (1.20 &times; 1.15) &times; 1.07] + 42) &times; 0.5] + 0 = 25'''

The maximum damage is '''ED = [([28 &times; (1.20 &times; 1.15) &times; 1.07] + 42) &times; 0.5] + 0 = 41'''

====The Second Attack (Critical Chop)====

=====Armor Effect=====
As before, you have a Damage rating of 68, and the Monk's Armor Level is still the same. But this time, the Sundering Prefix triggers.
So we have a new Armor Rating: '''EffAR = BaseAR &times; (1 - NAP) + ARShift = 60 &times; (1 - 0.30) + 10 = 52'''

This gives a total Armor Effect of 132%. To avoid any inaccuracies we will use the exact term: 2<sup>0.4</sup>

=====Damage Scale=====
Your axe does +15% from its inscription and +20% damage from customisation, for a total Damage Scale of 38%.

=====Damage Shifter=====
You have no external damage bonus other than your attack skill, like Strength of Honor or Order of Pain, so the Damage Shifter is +21 (level 16 on Critical Chop).

=====Damage Multiplier=====
[[Dark Escape]] gives the monk a Damage Multiplier of 1/2.

=====Damage Negator=====
None

=====Effective Damage=====
The raw damage for your axe is 6-28, giving a final formula of '''ED = [([RD &times; DScale &times; AE] + DShift) &times; DMult] + DNeg'''


The minimum damage is '''ED = [([6 &times; (1.20 &times; 1.15) &times; 2<sup>0.4</sup>] + 21) &times; 0.5] + 0 = 16

The maximum damage is '''ED = [([28 &times; (1.20 &times; 1.15) &times; 2<sup>0.4</sup>] + 21) &times; 0.5] + 0 = 36

== Related Articles ==
*[[Damage]]
*[[Spike damage]]
*[[Damage over time]]
*[[PBAoE|Point Blank Area of Effect]]
*[[Area of Effect]]

==Original References==
The present article is built on the results of the research laid out in the original unannotated version of the following article, with additional original research conducted by users of the GuildWiki.

This is a clearer, more elegant explanation of the Simplified Damage Formula
[http://www.guildwarsguru.com/content/game-mechanics-id674.php A Treatise on Combat Mathematics] on Guildwars Guru.
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*[http://www.guildwars.com/competitive/articles/stateofthegame/damagecalc.php State of the game: A Guide to Guild Wars Damage Calculations] (official, but full of errors)
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==External links==
* [http://www.oildrip.com/calc/index.php Online Damage Calculator]