Damage calculation

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Cleanup It has been suggested that this article should be rewritten, because: needs a rewrite to make it more accessible and coherent to new players.
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This info is a temporary placemarker in place of official information. Use at your own discretion. Caveat lector.

Damage in Guild Wars comes in two different kinds: Armor-ignoring damage and armor-respecting damage. While the calculation of the final health loss in the case of the former is simple and known, the latter is not certain and a formula theorized by players is given below.

Armor-ignoring damage[edit]

Main article: armor-ignoring damage

As the name implies, armor-ignoring damage ignores armor to always deal the stated amount, therefore few calculations are needed.

Armor-ignoring damage usually encompass skills that deal holy damage, shadow damage and "damage" without any specific type mentioned (typeless damage), including "+X damage" from attack skills, although in this case the bonus damage is added with the base damage of the attack which respects armor.

Armor-respecting damage[edit]

Formula[edit]

Damage is calculated differently depending on whether damage is done by a skill or an attack. The theorized formula is the following:

Damage calculation 1.png
Damage calculation formula26.png

Where:

  • Base Damage is the damage stated on the skill or the weapon. In the case of a weapon, the value is anywhere in the weapon's range, with critical hits always dealing the maximum damage.
  • Attribute level is the effective rank in the Mastery attribute of the weapon,
  • Armor level is the final armor rating obtained after Armor calculation.

Without any damage modifiers, characters will therefore be dealing the expected damage to enemies if their "Strike Level" is equal to their target's "Armor Level".

In the case of an attack skill dealing +X bonus damage, such as Executioner's Strike, both an attack and a skill deal damage at the same time in the same packet. In this case, the bonus damage from the skill is always armor-ignoring and added to the base damage of a regular attack, which follows the above equation.

Hit locations[edit]

Each player and hero can wear up to five pieces of armor - a chest piece, leggings, boots, gloves, and a headpiece. Any given attack on a player will hit one of these five locations, and only the armor rating of this location is considered.

In most circumstances, the chest piece and leggings have a higher probability to be hit, with respectively 3/8 and 2/8 while the other pieces each have 1/8.

However as far as melee attacks are concerned, the visual height of an attacking monster actually has an influence on the probability: small monsters or those close to the ground have higher chances to hit the legs or feet, while very tall or flying monsters have higher chances to hit the head or chest.

Hit Location Percentages
Hit Location Low Attack Normal or
Ranged Attack
High Attack
Head 0% 12.5% 27.3%
Chest 18.2% 37.5% 40.9%
Hands 13.6% 12.5% 13.6%
Legs 40.9% 25% 18.2%
Feet 27.3% 12.5% 0%

Additional Parameters[edit]

Attacks[edit]

Weapon Customization and modifiers[edit]

Weapon customization increases Base Damage by 20%, or a 1.20 multiplier.

Damage can further be increased by one of the following inscription bonuses:

Name Bonus Condition/Cost Attaches to Campaign Inherent bonus for
"Strength and Honor" Damage +10...15% while Health is above 50% Weapons Core Martial weapons (Prophecies, Factions), any inscribable weapon
"Guided by Fate" Damage +10...15% while Enchanted Martial weapons (Prophecies, Factions), any inscribable weapon
"Dance with Death" Damage +10...15% while in a Stance Martial weapons (Prophecies, Factions), any inscribable weapon
"To the Pain!" Damage +14...15% Armor -10 while attacking Martial weapons (Prophecies, Factions), any inscribable weapon
"Brawn over Brains" Damage +14...15% Energy -5 Martial weapons (Prophecies, Factions), any inscribable weapon
"Too Much Information" Damage +10...15% vs. Hexed foes Martial weapons (Prophecies, Factions), any inscribable weapon
"Vengeance is Mine" Damage +10...20% while Health is below 50% Martial weapons (Prophecies, Factions), any inscribable weapon
"Don't Fear the Reaper" Damage +10...20% while Hexed Martial weapons (Prophecies, Factions), any inscribable weapon
No corresponding inscription Damage +10...15% Energy regeneration -1 (AKA Zealous strength) n/a n/a Martial weapons (Prophecies, Factions)
Damage +10...15% Health regeneration -1 (AKA Vampiric strength)

In the case of axes, bows, hammers, and swords and (oddly enough) staves, the suffix of <affiliation or creature type>slaying can be used to further increase damage by +10-20% vs. a specific creature type or affilition:

A few weapons have unreplicable modifiers:

Weapon requirement[edit]

Main article: Requirement

As long as their requirement is met, two identical weapons with different requirements will deal the same damage at the same attribute rank.

If you do not meet the requirement of the weapon, the weapon will still keep all modifiers, including internal modifiers such as built-in additions to damage, but the base damage is heavily reduced:

  • Collector or reward weapons: the weapons deals damage like a starter weapon of the same type.
  • Dropped weapons (and bonus weapons ?): (according to the Weapons article), dropped weapons will deal 1/3 of their stated damage. For instance a dropped sword that deals 11-22 will do 5-8 (11 on critical) if you don't meet the requirement. Bonus weapons, from anecdotal evidence, should follow the same rule.

Weapon Attribute rank threshold[edit]

When attacking with a weapon, the rank in the corresponding "Mastery" attribute when applicable (i.e. not for staff or wand) usually increases your "Strike Level" by 5 for each rank.

However, there is a threshold above which Strike level is only increased by 2 instead of 5 for each additional rank, resulting in less than half increase to damage for each rank above the threshold compared to ranks below the threshold.

The attribute threshold is based on your level as follows:

Damage calculation formula4.png

For level 20 characters, the threshold is rank 12. A level 20 warrior with a hammer for instance would have a strike level of 5x12=60 with 12 Hammer Mastery, but a strike level of 5x12+2x2= 64 with 14 Hammer Mastery (and not 5x14=70).

Including the threshold, the damage becomes:

Damage calculation formula5.png
Effect of Attributes on Weapon Damage
(Normalized to level 20)
Rank 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Percent
to rank 0
100.0% 109.0% 119.0% 130.0% 141.0% 154.0% 168.0% 183.0% 200.0% 218.0% 238.0% 259.0% 283.0% 293.0% 303.0% 314.0% 325.0%
Percent
to rank 12
35.6% 38.6% 42.0% 45.9% 50.0% 54.5% 59.5% 64.8% 70.7% 77.1% 84.1% 91.7% 100.0% 103.5% 107.2% 111.0% 114.9%

Caster Weapons[edit]

Wands and staves behave differently from martial weapons: the damage they deal only scales up with your character level, as there is no "Mastery" for these two weapon types. A level 20 player meeting the listed requirement will deal the listed base damage. Aside from this, they behave the same as any weapon.

Critical hits[edit]

Main article: critical hit

Every attack with a weapon of any sort has a chance of landing a critical hit. Each critical hit strikes for maximum damage, with the additional bonus of hitting as though the target had their armor level reduced by 20, which is identical to increasing the Strike Level by 20, or a 41% damage increase.

Damage calculation formula15.png

The frequency of critical hit is dependent upon several factors - both attacker and target's level, and if wielding a martial weapon the attribute rank of that weapon. The exact formula for landing a critical chance is as follows:

Damage calculation formula43.png

In rough terms, your chance of landing a critical hit against a foe of comparable level with a level 12 weapon mastery is roughly 12% - if you're a level 20 character beating up on level 1 targets with a level 12 weapon mastery, your critical chance is close to 90%.

Height advantage/disadvantage[edit]

Attacking with a ranged weapon from a higher position increases your damage output, while attacking from a lower position lowers it. Height advantage effect is currently not well known, but testing has shown that damage increase can scale up to 200% of the initial damage on attacks with ranged weapons.

Skills[edit]

As a baseline, the amount of damage dealt by a skill is listed in that skill's description, rounded to the nearest integer. In actuality the damage dealt is rarely the same as in the description. Notably, the character's level plays a role in how much damage is actually dealt.

Damage calculation formula10.png
Effect of Character Level on Skill Damage
(Normalized to level 20)
Level 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Percent of Skill Damage 37.2% 39.2% 41.3% 43.5% 45.9% 48.3% 50.9% 53.6% 56.4% 59.5% 62.6% 66.0% 69.5% 73.2% 77.1% 81.2% 85.6% 90.1% 94.9% 100%

Damage modifiers[edit]

General damage modifiers (such as damage reduction from skills like Shielding Hands or increase such as from skills like Frenzy) are taken into account at the end of damage calculation for each packet of damage.

Examples[edit]

General Examples[edit]

  • A level 15 Elementalist attacks a level 7 Charr (21 AL) with Fireball Fireball at rank 8 Fire Magic (69 damage in the skill description). Each fireball deals:
Damage calculation formula27.png
  • A Warrior with a rank 2 Hammer Mastery and a customized 5-10 Hammer attacks a level 2 Flash Gargoyle (6 AL) and hitting with a critical hit (+20 to strike level) will deal:
Damage calculation formula28.png
  • A Ranger with a customized, 15-28 Half Moon Bow, and a rank 12 attribute to go with it, attacking a level 28 Rift Warden (118 AL) with Penetrating Attack Penetrating Attack (10% armor penetration) will deal:
Damage calculation formula29.png

Since the skill also deals 21 bonus damage, which is armor ignoring, the attack will be dealing 29.1~36.1 damage.

Example of damage calculation for an attack[edit]

If you had a normal, customized (20% more damage) 15-22 damage Fiery Dragon Sword, and a level 9 Swordsmanship attribute, each swing with the weapon would deal:

Damage calculation formula6.png

While swinging the same sword with a level 12 attribute would deal:

Damage calculation formula8.png


Example of damage calculation for a skill[edit]

A level 6 Elementalist with a Fire Magic attribute of 5. Each Flare Flare (35 damage at attribute 5) you cast is going to be dealing:

Damage calculation formula11.png

If you then gained a level but didn't raise your Fire Magic attribute, your Flares would be dealing more damage regardless, to the tune of:

Damage calculation formula12.png

Unlike weapon damage, you don't exactly have control over your character's level - you're going to be dealing 100% of listed skill damage once you hit level 20. This makes it incredibly easy to min/max your skills, since the damage you're going to deal in combat is the same as the one listed in the skill description. You'll find this effect most useful when planning an attack against a mob who will quite often have levels that vary considerably from your own. For example, take a level 30 Elementalist boss casting a level 12 Deep Freeze:

Damage calculation formula13.png

Example for a wand or staff: Take a customized 6-10 wand, for example - when wielded by a level 10 character, each strike will deal:

Damage calculation formula14.png

Example of critical hit calculation[edit]

Every critical hit with a customized top (6-28) axe and a level 12 Axe Mastery will deal:

Damage calculation formula16.png

Example of armor effect calculation[edit]

A 30 damage physical attack directed at a Warrior wearing armor without Knight's Insignia (80 AL, +20 AL vs. Physical) using a 16 AL shield, would deal:

Damage calculation formula18.png

While that same attack on an Elementalist in a non-max level armor with Pyromancer Insignia (45 AL + 10 AL vs. Elemental, +10AL vs. Fire) would deal:

Damage calculation formula19.png

Note that the Elementalist actually suffered more damage than what the attack would have naturally dealt. This is the case whenever a target has a net armor rating below 60.

If the warrior's armor is upgraded with Knight's insignias and a Rune of Absorption, the shield has the inscription "Run For Your Life!" that reduces damage by 2 while in a stance, and this attribute is active during the hit, then the damage gets reduced to:

Damage calculation formula20.png

Note that this is only one tenth of the damage that would be dealt to an unprepared elementalist facing the same attack against a 60AL.

Now by using a skill such as "I Am Unstoppable!" or Vow of Piety and carrying the same shield, that same warrior can receive:

Damage calculation formula21.png

Armor penetration example[edit]

With the 30 damage attack from the previous examples dealt 11.6 damage to a well-defended Warrior, that same attack with 50% armor penetration would deal:

Damage calculation formula23.png

Example 1[edit]

Two twin level 20 warriors in PvP use the axe attacks Cleave or Penetrating Blow, both while in a stance (such as Sprint) with attributes of 12 in both strength and axe mastery, while wielding a sundering axe (20%) with +15% while in stance modifier, and striking a warrior wearing armor with Dreadnought Insignia of Superior Absorption and carrying a shield with 16AL and -2 damage while in stance:

Strength grants 12% penetration, the axe grants 20% penetration (20% of the time), the axe has 20% increased damage from customization, the axe has 15% increased damage from the modifier and the skill does damage in addition to this attack.
The sum of the armor penetrations makes the armor of the opposing warrior:
Damage calculation formula30.png
The weapon damage is:
Damage calculation formula31.png
The skill damage is 26.
The damage reduction is:
Damage calculation formula33.png
So the damage range for this attack is between 26.970 and 48.858 with an average of 37.914.
The axe grants 20% penetration (20% of the time), the skill grants 20% penetration, the axe has 20% increased damage from customization, the axe has 15% increased damage from the modifier and the skill does its own damage in addition to this attack.
The sum of the armor penetrations makes the armor of the opposing warrior:
Damage calculation formula34.png
The weapon damage is:
Damage calculation formula35.png
The skill damage is 17.
The damage reduction is:
Damage calculation formula33.png
So the damage range for this attack is between 19.011 and 44.718 with an average of 31.865 - slightly less than Cleave and at a slightly higher Adrenaline cost, but without taking the elite skill slot.

Example 2[edit]

If the situation changes and one of these twin warriors is now striking the opposing monk (who only has 60 AL against physical)

The sum of the armor penetrations makes the armor of the opposing monk:
Damage calculation formula40.png
The weapon damage is:
Damage calculation formula41.png
The skill damage is 26.
So the damage range for this attack is between 37.548 and 79.893 with an average of 58.721.
The sum of the armor penetrations makes the armor of the opposing monk:
Damage calculation formula37.png
The weapon damage is:
Damage calculation formula38.png
The skill damage is 17.
So the damage range for this attack is between 29.550 and 75.567 with an average of 52.559 – half again that of this attack against the warrior, which is to be expected since the monk only has about half the armor and does not carry damage reducing shields or runes.

The following analysis is based on level 20 characters with max basic armor and maxed attribute ranks (attribute levels).

Damage calculation formula1.png

References[edit]

A Treatise on Combat Mathematics by Charles Ensign (original source of this article)

The text of this wiki article was originally taken verbatim from Charles Ensign's treatise, used with his permission. It has since been enhanced with additional findings and clarifications from the Guild Wars community and development team.