Damage calculation

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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 is governed by two distinct sets of effects - those that affect the damage of the attack, and those that affect the defense of the target. These two sets are separable - if you just want to analyze weapon damage, for instance, you can completely ignore the effects of armor in your calculations and analysis.

In mathematical form, this means that:

Damage calculation formula1.png

Sometimes a given attack will deal damage multiple times - such as with Dancing Daggers or Stone Daggers. In these cases, treat each instance as a separate attack and add it all up in the end, exactly as you would if the attacks were done in sequence.

Attacking and damage[edit]

The base damage of an attack depends on both your character's statistics, and on situational modifiers, such as attacking a target over a cliff. The latter are maddeningly difficult to evaluate quantitatively, and thus we'll limit ourselves to discussions of the former. As a basis for our analysis, we'll use characters ready to set foot into the Hall of Heroes - level 20 characters with max basic armor and maxed attribute ranks (attribute levels). As we'll see later, the whole system works on a sliding scale.

Weapon damage[edit]

If you are attacking the target with a melee weapon (sword, axe, hammer, daggers, scythe) or a ranged weapon (bow, spear) the amount of damage that you'll naturally deal depends on both the inherent damage of the weapon, and your level in the corresponding attribute. The relationship between your attribute level and damage is a simple exponential over a normal attribute level range:

Damage calculation formula3.png

However, there is a threshold beyond which additional attribute levels provide less benefit. For level 20 characters, that threshold is 12. Each additional attribute level beyond 12 provides only 40% as much benefit as levels under 12 provide. This attribute threshold is based on your current character level, as follows:

Damage calculation formula4.png

Thus, if you include the effects of the threshold, the full equation is:

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%

Example of weapon damage calculation[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

While pumping up your weapon attribute continues to give outstanding returns on damage all the way to level 12, it drops off quickly after that. For a level 20 character, attribute level 13 is less than half as effective as the previous level at raising your damage. So while having a high attribute level certainly looks impressive on your stat screen, it isn't providing as much benefit as one might think.

Skill damage[edit]

The vast majority of the time, you aren't just attacking, you're using skills to augment, replace, or just outright deal damage to your opponent. As a baseline, the amount of damage that you'll deal with a skill is listed in that skill's description - rounded to the nearest integer. The damage you deal is almost never the same as in your description. In the case of skills, your character's level plays a role in how much damage you'll actually deal:

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%

Example of skill damage calculation[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

There's one more category of attacks to consider - attacking an enemy with a wand or staff. Wands and staves aren't weapons in the purest sense - a more apt description is 'skill on a stick', as the damage they deal scales up with your character level, not your weapon attribute. In other respects, they act like all other weapons. Take a customized 6-10 wand, for example - when wielded by a level 10 character, each strike will deal:

Damage calculation formula14.png

Critical hits[edit]

Every time you strike a foe with a weapon of any sort you have a chance of landing a critical hit. Each critical hit strikes for maximum damage, with the additional bonus of hitting as though your target has their armor level reduced by 20. This translates into each critical hit dealing 141% of your maximum effective weapon damage, every time.

Damage calculation formula15.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

The frequency with which you will land a critical hit is dependent upon several factors - your character level, the level of the target, and, if you're using a sword, axe, or hammer, the appropriate attribute level. 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%.

Weapon requirements[edit]

Main article: Requirement

Many of the weapons that you'll find require you to have a certain level in a linked attribute to be effective: Swords that require 9 Swordsmanship, Bows that require 7 Marksmanship, and the like. If you do not meet the requirements on a given weapon, your effectiveness with it will be greatly reduced.

In simplest terms, if you do not meet the requirements on a given weapon it will deal damage like a starter weapon of the same type. Thus, if you find a 10-20 wand but don't meet the requirements, it'll deal damage like a 2-4 wand of the same type. However, the weapon will keep all modifiers. Thus, if you were using a 14-20 Sword Of Enchanting (+20% enchantment durations) and don't meet the requirements, it would only deal the 2-4 damage, but you would still get the +20% enchantment duration from the modifier. This includes internal modifiers - some weapons have built-in additions to damage, and these will remain even if you don't meet the requirements. This is most readily apparent on a focus - if you find a normal +10 energy focus and don't meet the requirement, you will only get +3 energy from equipping it. However, if you get a +12 focus - a +10 focus with an internal +2 modifier - you'll get 5 energy from equipping it, even if you don't meet the requirement. Thus you are always better off using a weapon with a requirement you can reach - unless the only thing you want access to is the weapon's modifiers.

NOTE: It has been noted elsewhere in this wiki (in the Weapons article), that dropped weapons have different rules if you don't meet the requirements than collector or reward weapons. According to the Weapons article, dropped items do 1/2 damage, rather than the damage of a starter weapon, so a sword that does 11-22, which was a dropped item, should do 5-11 if you don't meet the requirement. There is no reference in either article as to bonus weapons, though from anecdotal evidence, it follows the same equation as dropped weapons.

Armor and defense[edit]

Once you know how much damage an attack is supposed to do, you can start thinking about the defense of the target, to figure out how much damage you will actually do - or how much damage you will take when someone swings back. This means talking about how your armor works, as well as any defense boosting skills.

Hit locations[edit]

Each player can use 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 at that location is considered - all the other pieces are ignored. Additional defensive measures, such as an armor-boosting enchantment or a shield, are added to the target's defense, regardless of hit location.

Exactly where a given attack will strike depends on the height of the attacker and the type of the attack. Player characters always use normal attacks, for all attack types. Monsters that are very low to the ground generally use low melee attacks, and those that are very tall or flying generally use high melee attacks. However, if a monster uses a missile weapon, then the monster's height is ignored.

Hit Location Percentages
Hit Location Low Attack Normal or
Missile 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%

Your chest piece is your most important piece of armor, as it receives the highest percentage of hits. Leggings come in a close second. Other than that, mixing up your armor can make for some unique aesthetics, but it is unlikely to have any practical effect.

Effect of armor[edit]

All that needs to be done now is to figure out what effect the target's armor is going to have on your damage. The relationship is a simple exponential function, the form of which you should be familiar with by now - simply add up all of the target's defenses and calculate:

Damage calculation formula17.png
Effect of Armor on Damage
Armor Defensive
Adjustment
Relative
Change
0 282.8% N/A
5 259.4% -23.5%
10 237.8% -21.6%
15 218.1% -19.7%
20 200% -18.1%
25 183.4% -16.6%
30 168.2% -15.2%
35 154.2% -14.0%
40 141.4% -12.8%
45 129.7% -11.7%
50 118.9% -10.8%
55 109.1% -9.8%
60 100% -9.1%
Armor Defensive
Adjustment
Relative
Change
65 91.7% -8.3%
70 84.1% -7.6%
75 77.1% -7.0%
80 70.7% -6.4%
85 64.8% -5.9%
90 59.5% -5.3%
95 54.5% -5.0%
100 50% -4.5%
105 45.9% -4.1%
110 42.0% -3.9%
115 38.6% -3.4%
120 35.4% -3.2%
125 32.4% -3.0%

As you can see from the table, the target will take exactly the amount of damage they are expected to when they have an armor level of 60, and adding or subtracting 40 defense will result in them suffering half or double damage, respectively.

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[edit]

Armor penetration is incredibly straightforward - it simply allows you to ignore the listed percentage of the target's total defense. If a given attack has 10% armor penetration and the target has an armor level of 100, he will only have an armor rating of 90 for the purposes of defending against this attack. Thus the armor penetration equation:

Damage calculation formula22.png

To give you an idea of how this works, here's a piece of the armor effectiveness table, adjusted for various levels of Armor Penetration:

Effect of Armor Penetration
Armor Level 0%
Penetration
5%
Penetration
10%
Penetration
25%
Penetration
50%
Penetration
40 141% 146% 152% 168% 200%
50 119% 124% 130% 148% 183%
60 100% 105% 111% 130% 168%
70 84.1% 89.3% 94.9% 114% 154%
80 70.7% 75.8% 81.2% 100% 141%
90 59.5% 64.3% 69.5% 87.8% 130%
100 50% 54.5% 59.5% 77.1% 119%

So 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

If you're having trouble taking down a target with an exceptional armor rating, attacks with armor penetration are exactly what you're looking for.

Ignoring armor[edit]

Some skills, such as Illusionary Weaponry, allow you to deal damage that ignores the target's armor entirely (as well as the level-based damage multiplier on non-weapon damage). In the absence of non-armor damage reduction effects, figuring out the damage actually dealt by a skill that ignores armor is trivial, as they work exactly as advertised - they literally do ignore the target's armor, dealing the damage listed in the skill description directly to the target. Mathematically, this means that an attack that ignores armor always considers the target's Defensive Adjustment to be 1, and the original equation reduces to:

Damage calculation formula24.png

So if a skill's description says it will deal 40 damage ignoring armor, it'll deal 40 damage every time unless some other damage modifier, such as damage reduction, interferes. Not only does ignoring armor help immensely when attacking someone with a lot of armor - it makes your calculations easier as well.

Because armor ignoring damage also ignores the skill damage multiplier, a level 1 player character or NPC will deal the same damage with an armor-ignoring skill as a level 20 player character or NPC or a level 28 NPC with the same skill and attributes.

Consolidation[edit]

While it makes combat easier when you understand each aspect, you lose sight of the so-called 'big picture' and how all of these aspects are intertwined. It's time to put them all together into a single equation that shows what's ultimately going on.

As mentioned before all of the numbers, equations, and charts are normalized for level 20 characters. While this is necessary to present the data in a reasonable manner, it's important to note that the choice of basis is arbitrary. Indeed, you might have picked up already what happens when a character with a level 0 attribute attacks a target with 0 armor:

Damage calculation formula25.png

The result is exactly the same as what would happen if your level 20 character with a weapon attribute of 12 attacked an opponent with 60 defense! The underlying truth of the matter - the damage equations we've been talking about so far are just different aspects of a single, self-normalizing equation. With no further ado:

Damage calculation 1.png
Damage calculation formula26.png

Consequently, characters will actually be dealing base damage to enemies as long as their Strike Level is close to their Armor Level - which, if they're following the normal progression of the game, will be pretty much all of the time. Game mechanics don't revolve around characters at level 20, but at whatever level you happen to be at the time.

Damage affecting skills and situations work by manipulating one of these three values. Weapon customization increases your Base Damage by 20%. A critical hit increases your Strike Level by 20, while 50% armor penetration reduces their Armor Level by 50%. Attacks that ignore armor forget about Strike and Armor Levels entirely and just deal base damage. Every damage effect in the game can be represented in a similar fashion. Examples:

  • A level 15 Elementalist attacks a level 7 Charr(21 AL) with 69 damage, level 8 Fireballs. Each one you cast is going to deal:
Damage calculation formula27.png
  • A level 1 Warrior with a level 2 Hammer Mastery and a customized 5-10 Hammer (with critical hit: +20 damage) attacking a level 2 Flash Gargoyle (6 AL) is going to deal:
Damage calculation formula28.png
  • A level 20 Ranger with a customized, 15-28 Half Moon Bow, and a level 12 attribute to go with it. Attacking a level 28 Rift Warden(118 AL) with Penetrating Attack Penetrating Attack:
Damage calculation formula29.png

That's all there is to it. You now have the tools needed to figure out the damage from any attack in the game, and choices can be made based upon actual effects experienced in the game world, not just numbers shown on your character screen.

Example 1[edit]

To add the calculation of an exceedingly complex situation with twin level 20 warriors in PvP using 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, 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.

See also[edit]

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.