Damage calculation
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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:
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. For example, if you attacked with a bow while you had Conjure Flame up, the general equation would be:
Let's approach the two terms in turn, first the offensive part, then the defensive.
[edit] Attacking and Damage
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 as a basis - level 20 characters with top armor and maxed attributes. As we'll see later, the whole system works on a sliding scale.
[edit] Weapon Damage
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:
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:
Thus, if you include the effects of the threshold, the full equation is:
Or, in tabular form, for a level 20 character:
| Attribute Level | Percent dmg relative to 0 rank | Percent dmg relative to 12 rank |
|---|---|---|
| 0 | 100% | 35.6% |
| 1 | 109% | 38.6% |
| 2 | 119% | 42.0% |
| 3 | 130% | 45.9% |
| 4 | 141% | 50.0% |
| 5 | 154% | 54.5% |
| 6 | 168% | 59.5% |
| 7 | 183% | 64.8% |
| 8 | 200% | 70.7% |
| 9 | 218% | 77.1% |
| 10 | 238% | 84.1% |
| 11 | 259% | 91.7% |
| 12 | 283% | 100% |
| 13 | 293% | 104% |
| 14 | 303% | 107% |
| 15 | 314% | 111% |
| 16 | 325% | 115% |
As an example, 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:
While swinging the same sword with a level 12 attribute would deal:
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.
[edit] Skill Damage
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:
[Effective Damage] = [Skill Damage] × 2^((3 × [Character Level] - 60) / 40)
Or, in tabular form:
| Character Level | Percent of Skill Damage |
|---|---|
| 1 | 37.2% |
| 2 | 39.2% |
| 3 | 41.3% |
| 4 | 43.5% |
| 5 | 45.9% |
| 6 | 48.3% |
| 7 | 50.9% |
| 8 | 53.6% |
| 9 | 56.4% |
| 10 | 59.5% |
| 11 | 62.6% |
| 12 | 66% |
| 13 | 69.5% |
| 14 | 73.2% |
| 15 | 77.1% |
| 16 | 81.2% |
| 17 | 85.6% |
| 18 | 90.1% |
| 19 | 94.9% |
| 20 | 100% |
Example: - A level 6 Elementalist with a Fire Magic attribute of 5. Each 
Flare (35 damage at attribute 5) you cast is going to be dealing:
35 × 2^(( 3 × 6 - 60 ) / 40) = 16.90 damage
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:
35 × 2^(( 3 × 7 - 60 ) / 40) = 17.81 damage
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:
70 × 2^(( 3 × 30 - 60 ) / 40) = 117.73 damage
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:
6 × 1.20 × 2^(( 3 × 10 - 60 ) / 40) = 4.28 minimum damage 10 × 1.20 × 2^(( 3 × 10 - 60 ) / 40) = 7.14 maximum damage
[edit] Critical Hits
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 weapon attribute were four levels higher.
Example: [Effective Damage] = [Max Weapon Damage] × 2^(( 5 × [Attribute Level] - 40 ) / 40)
This translates into each critical strike dealing 141% of your maximum weapon damage, every time. Every critical hit with a customized top (6-28) axe and a level 12 Axe Mastery will deal:
28 × 1.20 × 2^(( 5 × 12 - 40 ) / 40) = 47.5 damage per critical
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 unknown, and due to it being a matter of statistical analysis it is rather difficult to test. In rough terms, your chance of landing a critical hit against a foe of comparable level with a level 12 weapon mastery is roughly 20% - 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 100%.
[edit] Weapon Requirements
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.
[edit] Armor and Defense
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.
[edit] Hit Locations
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 | Low Attack | Normal or Missile Attack | High Attack |
|---|---|---|---|
| Head | 0% | 10% | 27.3% |
| Chest | 18.2% | 40% | 40.9% |
| Hands | 13.6% | 10% | 13.6% |
| Legs | 40.9% | 30% | 18.2% |
| Feet | 27.3% | 10% | 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 asthetics, but it is unlikely to have a practical effect.
[edit] Effect of Armor
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:
[Defensive Adjustment] = 2^((60 - [Armor Level]) / 40)
Or, in tabular form:
| Armor Level | Defensive Adjustment | Difference from Previous |
|---|---|---|
| 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% |
| 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% | -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.
So, for example, 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:
30 × 2^(( 60 - (80 + 20 + 16) ) / 40) = 11.4 damage
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:
30 × 2^(( 60 - (45) ) / 40) = 38.9 damage
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 a handle that reduces damage by 2 while in a stance, and this attribute is active during the hit, then the damage gets reduced to:
11.4 - 3(Knights Insignia) - 3(Absorption) - 2(Shield Handle) = 3.4 damage
Note that this is nearly 1/10th of the damage that would be dealt to an unprepared elementalist facing the same attack against a 60AL.
Now by using a tanking skill such as Defensive Stance and carrying the same shield, that same warrior can receive:
30 x 2^(( 60 - (80 + 20 + 16 + 24) ) /40) - 3 - 3 - 2 = 0 damage.
[edit] Armor Penetration
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:
[Armor Rating] = [Armor Level] × (1 - [Armor Penetration] / 100)
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:
| 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:
30 × 2^(( 60 - (80 + 20 + 15) × (1 - (50 / 100)) ) / 40) = 31.3 damage
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.
[edit] Ignoring Armor
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:
[Actual Damage] = [Base Damage]
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.
[edit] Consolidation
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:
2^(( 5 × 0 - 60 ) / 40) × 2^(( 60 - 0 ) / 40) = 100% of listed damage
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:
Where, for weapons:
[Strike Level] = 5 × [Attribute Level]
For skills:
[Strike Level] = 3 × [Character Level]
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 level 7 Charr(21 AL) with 69 damage, level 8 Fireballs. Each one you cast is going to deal:
- 69 × 2^((3 × 15 - 21 ) / 40) = 104.6 damage
- A level 1 Warrior with a level 2 Hammer Mastery and a customized(+20 damage) 5-10 Hammer attacking a level 2 Flash Gargoyle(6 AL) is going to deal:
- 10 × 1.20 × 2^((5 × 2 + 20 - 6 ) / 40) = 18.2 damage
- 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:
15 × 1.20 × 2^(( 5 × 12 - (118 / 2) ) / 40) = 18.3 minimum damage 28 × 1.20 × 2^(( 5 × 12 - (118 / 2) ) / 40) = 34.2 maximum damage
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.
[edit] Example
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 :
For Cleave: 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: 116 x .8 x .88 = 81.664 AL
The weapon damage is: 6 x 1.35 x 2^((60 - 81.664) / 40 ) = 5.565 28 x 1.35 x 2^((60 - 81.664) / 40 ) = 25.969
The skill damage is: 26 x 2^((60 - 81.664)/40) = 17.862
The damage reduction is: -3 from the Rune and -2 from the shield for a total of -5
So the damage range for this attack is: 18.427 to 38.831 Leaving the average damage of this skill at 28.629
For Penetrating Blow -
Strength grants 12% penetration, 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: 116 x .8 x .88 x .8 = 65.331 AL
The weapon damage is: 6 x 1.35 x 2^((60 - 65.331) / 40 ) = 7.385 28 x 1.35 x 2^((60 - 65.331) / 40 ) = 34.464
The skill damage is: 17 x 2^((60 - 65.331)/40) = 15.5
The damage reduction is: -3 from the Rune and -2 from the shield
So the damage range for this attack is: 17.885 to 44.964 Leaving the average damage of this skill at 31.425 - only slightly more than Cleave and at a slightly higher Adrenaline cost, but without taking the elite skill slot.
If the situation changes and one of these twin warriors is now striking the opposing monk (who only has 60 AL against physical)
For Penetrating Blow -
The sum of the armor penetrations makes the armor of the opposing monk: 60 x .8 x .88 x .8 = 33.792 AL
The weapon damage is: 6 x 1.35 x 2^((60 - 33.792) / 40 ) = 12.756 28 x 1.35 x 2^((60 - 33.792) / 40 ) = 59.529 The skill damage is: 17 x 2^((60 - 33.792)/40) = 26.772
So the damage range for this attack is: 39.528 to 86.301
Leaving the average damage of this skill at 62.915 - double 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.
For Cleave -
The sum of the armor penetrations makes the armor of the opposing monk: 60 x .8 x .88 = 42.24 AL
The weapon damage is: 6 x 1.35 x 2^((60 - 42.24) / 40 ) = 11.02 28 x 1.35 x 2^((60 - 42.24) / 40 ) = 51.42 The skill damage is: 26 x 2^((60 - 42.24)/40) = 35.37
So the damage range for this attack is: 46.39 to 86.79
Leaving the average damage of this skill at 66.59 - nearly two and a half times that of this attack against the warrior.
[edit] See also
[edit] References
(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.
