Weapon Damage CalculationsDiablo II Expansion, patch 1.10 Contents:
2. Damage Calculations
3. Damage Bonuses |
A simple formula for calculating the damage of a weapon attack is the following:
Final Damage = (((Normal Damage
x 1.5) (only if ethereal)
x (1 + Enhanced Damage on Weapon / 100) + Bonuses to Minimum/Maximum Damage)
x (1 + Strength or Dexterity / 100 + Off-Weapon Enhanced Damage / 100 + Skill Damage Bonus % / 100) + Elemental Damage)
x (1 - Skill Damage Penalty / 100)
x 2 (only if a critical or deadly strike is scored)Normal damage is the damage listed as the weapon damage in Arreat Summit's weapon pages.
A more detailed procedure is described below.
There are four steps in the weapon damage calculations:
- Base Damage
- Weapon Damage
- Total Damage
- Final Damage
Later steps of damage calculations use the results of previous phases. Thus, an increase to the base damage has the highest potential to greatly increase the damage. Item properties and other effects affect one of the above damages. In total, there are six different bonus types:
- Base Damage Multiplier
- Weapon Damage Percentage Bonus
- Weapon Damage Direct Bonus
- Total Damage Percentage Bonus
- Total Damage Direct Bonus
- Final Damage Multiplier
These classifications are listed in Section 3: Damage Bonuses.
The minimum and maximum damages of a weapon attack are calculated separately in two calculations. Generally, most effects affect both minimum and maximum damage, but there are some exceptions, such as item properties that say "+X to minimum damage." An important rule of thumb in damage calculations is that the result of each multiplication is rounded down (this is indicated by brackets in equations).
Damage calculations begin from determining the normal damage of the weapon. It is the damage listed as the weapon damage in Arreat Summit's weapon pages and the MPQ files. It is referred here to as Normal Damage. The base damage of a weapon attack is calculated as follows:
Base Damage = [...[Normal Damage x Base Damage Multiplier 1] x ... x Base Damage Multiplier M] In the above equation:
- M is the number of base damage multipliers
- [] indicates rounding down
The minimum and maximum base damages are calculated separately, applying bonuses that affect to them.
The weapon damage is calculated as follows:
Weapon Damage = Base Damage
+ [Base Damage x Weapon Damage Percentage Bonus 1 / 100]
...
+ [Base Damage x Weapon Damage Percentage Bonus M / 100]
+ Weapon Damage Direct Bonus 1
...
+ Weapon Damage Direct Bonus N
- M is the number of weapon damage percentage bonuses (e.g. Enhanced Damage properties on the weapon)
- N is the number of weapon damage direct bonuses
- [] indicates rounding down
The minimum and maximum weapon damages are calculated separately, applying bonuses that affect to them. If maximum weapon damage ≤ minimum weapon damage, then maximum weapon damage = minimum weapon damage + 1. This modification takes place before any effects that affect the total damage are calculated.
The damage of the weapon, which is shown in the inventory screen, is calculated from the weapon's own properties that affect Weapon Damage. Effects that affect Weapon Damage on other pieces of equipment do not affect the displayed weapon damage.
A random number rolled in the range of minimum weapon damage ... maximum weapon damage to determine the actual value of the weapon damage.
The total damage is calculated as follows:
Total Damage = Weapon Damage
+ [Weapon Damage x Total Damage Percentage Bonus 1 / 100]
...
+ [Weapon Damage x Total Damage Percentage Bonus M / 100]
+ Total Damage Direct Bonus 1
...
+ Total Damage Direct Bonus N
- M is the number of total damage percentage bonuses
- N is the number of total damage direct bonuses
- [] indicates rounding down
Strength and dexterity are applied as total damage percentage bonuses as follows:
- Total Damage Percentage Bonus 1 = Strength x Strength Multiplier
Total Damage Percentage Bonus 2 = Dexterity x Dexterity Multiplier
- Strength and dexterity multipliers are listed in Section 3.1.
Damage can be of various types. The common damage types are physical, fire, cold, lightning, magic, and poison.
- Weapon damage is physical.
- Strength and dexterity bonuses are physical.
- The type of total damage bonuses are individual to them. For example, Vengeance (paladin combat skill) adds fire, lightning, and cold damages.
The minimum and maximum total damages are calculated separately, applying bonuses that affect to them. Random numbers are rolled to determine the actual values of total damage bonuses.
The final damage is calculated as follows:
Final Damage = [...[Total Damage x Final Damage Multiplier 1] x ... x Final Damage Multiplier M]
- M is the number of final damage multipliers
- [] indicates rounding down
There are only three final damage multipliers: deadly strike, critical strike, and skill damage modification. Deadly and critical strikes have a chance to occur, and when they do, they multiply the total damage by 2. However, both the critical and deadly strike cannot occur at the same time.
Final damage multipliers may affect only the total damage of certain damage types. For example, a deadly strike doubles only physical damage and not other damage types.
The character screen shows Final Damage, except that it does not show the effect Critical Strike and Deadly Strike in its calculations. In some cases, such as with Double Throw (barbarian combat skill), the character screen does not show correct values.
After the final damage is calculated, some effects that convert physical damage into another damage type take effect. Examples of such skills are Berserk (barbarian combat skill) and Fire Arrow (amazon bow and crossbow skill). For instance, Berserk converts all physical damage into magical damage. It is worth noting that any damage bonuses that normally increase physical damage (e.g. critical strike, deadly strike, Might aura, and Fanaticism aura) are converted into another damage type in this step.
Strength and dexterity are applied as total damage percentage bonuses, which increase the physical damage of the attack. Strength and dexterity scores are multiplied by a number depending on the type of the weapon used before they are applied as a damage bonus. The strength and dexterity multipliers for different weapons are the following:
Weapon Strength Multiplier Dexterity Multiplier Melee weapons (except as below) 1.00 0 - Daggers 0.75 0.75 - War hammer, Battle hammer, Legendary mallet
- Maul, War club, Ogre maul
- Great maul, Martel de fer, Thunder maul1.10 0 - Assassin claws 0.75 0.75 - Amazon spears 0.80 0.50 Bows and crossbows 0 1.00 Throwing weapons (except as below) 0.75 0.75 - Amazon javelins 0.80 0.50
Item properties of the same type are summed up first and then used in damage calculations.
Item Property Affected Damage Bonus Type Damage Type Value Example Item Ethereal Base damage Multiplier Physical 1.5 Most weapons can spawn as ethereal +X% Enhanced Damage on a Weapon Weapon damage Percentage Bonus Physical X Many weapons +X% Enhanced Maximum Damage on a Weapon Weapon damage Percentage Bonus Physical Min: 0
Max: XEaglehorn (unique crusader bow) + X to Minimum Damage Weapon damage Direct Bonus Physical Min: X
Max: 0Rixot's Keen (unique short sword)
Bloodfist (unique heavy gloves)+ X to Maximum Damage Weapon damage Direct Bonus Physical Min: 0
Max: XRipsaw (unique flamberge)
Duskdeep (unique full helm)Adds X-Y Damage Weapon damage Direct Bonus Physical Min: X
Max: YDoombringer (unique champion sword)
War Traveler (unique battle boots)Damage +X (see notes below) Weapon damage Direct Bonus Physical X The Redeemer (unique mighty scepter) +X% Enhanced Damage not on a Weapon Total damage Percentage Bonus Physical X Biggin's Bonnet (unique cap) +X% Damage to Undead Total damage Percentage Bonus Physical X Blunt weapons +X% Damage to Demons Total damage Percentage Bonus Physical X Laying of Hands (set bramble mitts) +X-Y to Fire / Cold / Lightning / Magic Damage Total damage Direct Bonus As described Min: X
Max: YBaranar's Star (unique devil star) +X Poison Damage Over Y Seconds Total damage Direct Bonus Poison See Tao of Poison Plague Bearer (unique rune sword) Deadly Strike (see notes below) Final damage Multiplier Players: Physical
Others: All2 Headstriker (unique battle sword) Crushing Blow (see Section 4.1) - - - - Bonesnap (unique maul) Open Wounds (see Section 4.2) - - - - Blood Crescent (unique scimitar) Damage +X. This property is shown incorrectly on the character screen to affect Total Damage, but in reality it affects Weapon Damage (tested by Ruvanal).
Deadly Strike. Deadly Strike doubles the physical component of Total Damage. Deadly Strike is checked only if a Critical Strike does not happen. Thus, Deadly Strike is useless if one has a 100 % chance to score a Critical Strike. Chances of Deadly Strike from different sources are summed up. Deadly Strike above 100 % is as effective as 100 % Deadly Strike. If a Deadly Strike is scored by other than a player character, e.g. a mercenary, it doubles all damage types, rather than just physical damage.
Min refers to the value in minimum damage calculations and max to the value in maximum damage calculations.
Skill property descriptions may slightly differ from those in the game.
Skill Property Affected Damage Bonus Type Damage Type Value Example Skill Damage Bonus: +X percent Total damage Percentage Bonus Physical X Might (paladin offensive aura) Damage: -X percent Total damage Percentage Bonus Physical -X Battle Cry (barbarian warcry) Damage: to Undead: +X percent Total damage Percentage Bonus Physical X Sanctuary (paladin offensive aura) Fire / Cold / Lightning / Magic Damage: +X percent (see notes below) Total damage Percentage Bonus (1) As described
(2) Physical + Appropriate damage conversionX Berserk (barbarian combat skill) Elemental Damages: +X percent Total damage Percentage Bonus Fire, Cold, and Lightning Each element: X Vengeance (paladin combat skill) Damage: +X (see notes below) Total damage Direct Bonus Physical Min: X
Max: 0Bash (barbarian combat skill) Fire / Cold / Lightning / Magic Damage: X Total damage Direct Bonus As described X Cold Arrow (amazon bow and crossbow skill) Fire / Cold / Lightning / Magic Damage: X-Y Total damage Direct Bonus As described Min: X
Max: YIce Arrow (amazon bow and crossbow skill) Poison Damage: X-Y over Z seconds Total damage Direct Bonus Poison See Tao of Poison Venom (assassin shadow discipline) Critical Strike (see notes below) Final damage Multiplier Players: Physical
Others: All2 Critical Strike (amazon passive skill) X Weapon Damage (Skill damage modification) Final damage Multiplier All X Multiple Shot (amazon bow and crossbow skill) Fire / Cold / Lightning / Magic Damage: +X percent. Skills that have one of these properties may either add a normal percentage bonus to total damage, or they may (1) add a physical damage bonus in total damage calculations and (2) convert all or a portion of physical damage into another damage type in the damage type conversion step. For example, Berserk (barbarian combat skill) first adds a physical damage bonus and then converts all physical damage into magical damage (including normal weapon damage and other physical damage, too).
Damage: +X. This ability increases only the minimum total damage, although the character screen reports it to increase both the minimum and maximum total damages.
Critical Strike. A Critical Strike doubles the physical component of Total Damage. The chance of Critical Strike can be increased by the amazon's Critical Strike skill and assassin/barbarian Weapon Masteries. If the Critical Strike is scored by other than a player character, it doubles all damage types, rather than just physical damage.
Min refers to the value in minimum damage calculations and max to the value in maximum damage calculations.
Double Throw (barbarian combat skill) shows miscalculated numbers on the character screen. The damage it inflicts in reality follows the normal damage rules. (This was tested by colds/lemekim.)
Synergy bonuses are always skill dependent, i.e. they increase the bonuses of that skill. The synergy bonuses work in two ways depending on whether the skill adds a percentage bonus or a direct bonus to total damage.
With skills that add a percentage bonus to total damage, such as Vengeance (paladin combat skill), synergy bonuses are added to the normal percentage effect of the skill. For example, level 1 Vengeance without synergy bonuses adds a total damage bonus of 70% to elemental damages. With +2% synergy from level 1 salvation, Vengeance adds a total damage bonus of 72% to elemental damages.
Synergy Bonus Affected Damage Bonus Type Damage Type Value Example Synergy Bonus +X% Damage Total damage Percentage Bonus Physical X Synergy bonus of Bash (barbarian combat skill) from Stun (barbarian combat skill) +X% Fire/Cold/Lightning/Magic Damage Total damage Percentage Bonus As described X Synergy bonus of Vengeance (paladin combat skill) from Resist Fire/Cold/Lightning (paladin defensive auras) +X% Elemental Damage Total damage Percentage Bonus Fire, Cold, and Lightning Each element:
XSynergy bonus of Vengeance (paladin combat skill) from Salvation (paladin defensive auras)
With skills that add a direct bonus to total damage, such as Poison Dagger (necromancer poison and bone spell), synergy bonuses multiply the skill bonus as follows:
Damage with Synergies = Damage without Synergies + Average Damage without Synergies x Sum of Synergy Bonuses / 100
Monster attack damages listed in Arreat Summit's monster pages and the MPQ files are their normal damages. Monster bonuses that affect their attack damage are listed in the table below. Monster bonuses add many other effects, too, but they are not considered here. Thus, for example, the damage of sparks of a lightning enchanted boss is not included.
Monsters that do not have weapons use Weapon Damage = Base Damage.
Monster Bonus Affected Damage Bonus Type Damage Type Value Notes Champion monster, normal Total damage Percentage Bonus Physical 100
- Champion monster, unknown Total damage Percentage Bonus Elemental Min: 33
Max: 50It is unknown which champions use this bonus. Champion monster, berserker Total damage Percentage Bonus Physical 300 The value is unconfirmed for 1.10. Min refers to the value in minimum damage calculations and max to the value in maximum damage calculations.
Many of the unique monster bonuses transfer to minions at lesser effects. Therefore, two values are listed: one for the unique monster and one for its minions.
Monster Bonus Affected Damage Bonus Type Damage Type Value
(Unique Monster)Value
(Minions)Notes Extra Strong Total damage Percentage Bonus Physical 150 75 - Aura Enchanted, Fanaticism Total damage Percentage Bonus Physical Fanaticism bonus Fanaticism bonus / 2 Fanaticism level = [mlvl/4] (*) Aura Enchanted, Might Total damage Percentage Bonus Physical Might bonus Might bonus Might level = [mlvl/4] (*) Aura Enchanted, Holy Shock Total damage Direct Bonus Lightning Holy Shock bonus - Holy Shock level = [mlvl/2] (*) Cold Enchanted Total damage Percentage Bonus Cold Min: 66
Max: 100Min: 33
Max: 50Minions gain this damage bonus on all difficulties. Fire Enchanted Total damage Percentage Bonus Fire Min: 66
Max: 100Min: 33
Max: 50Minions gain this damage bonus on nightmare and hell difficulties only. Lightning Enchanted Total damage Percentage Bonus Lightning Min: 66
Max: 100Min: 33
Max: 50Minions gain this damage bonus on nightmare and hell difficulties only. Mana Burn Total damage Percentage Bonus Mana Normal: 360
Nightmare: 420
Hell: 528Unknown
(Probably 50% of the unique bonus)Values are unconfirmed for 1.10. Spectral Hit, Fire, Cold, or Lightning Total damage Percentage Bonus Fire, Cold, or Lightning Min: 66
Max: 100Min: 33
Max: 50Damage type is randomly chosen. Minions gain this damage bonus on nightmare and hell difficulties only.
Spectral Hit, Poison Total damage Unknown Poison Unknown Unknown
(Probably 50% of the unique bonus)- (*) mlvl = Monster Level. The monster level of a unique boss monster is the base monster level +3. [] indicates rounding down.
Min refers to the value in minimum damage calculations and max to the value in maximum damage calculations.
All monsters have a 5 % chance to score a critical strike with any attack. A monster's critical strike doubles the total damage of all damage types. For example, a lightning enchanted boss can score a critical hit with its sparks.
Game Effect Affected Damage Bonus Type Damage Type Value Critical strike, monsters Final damage Multiplier All 2
Crushing blow is not damage but an ability that modifies the opponent's life amount before normal damage is dealt. It reduces the target's current life amount by the following factor depending on the weapon and the type of the target:
Target Melee Weapon Missile Weapon Normal Monster 1/4
1/8
Bosses and Champions 1/8
1/16
Players and Hirelings 1/10
1/20
As of the patch 1.10, the effect of Crushing Blow no longer scales with the number of players. In practice, this is implemented by dividing the damage by the life scaling factor of monsters. For example, if you score a crushing blow against a monster that has been spawned in an 8-player game, the game first calculates the damage of the crushing blow based on the current life amount of the target and then divides it by 4.5 (monsters have 450% of their normal hit points in 8 player games). In this way, the absolute damage from a crushing blow is the same regardless of how many players there are in the game.
Since a crushing blow is not damage, it is not affected normally by any damage modification effects, such as the PvP penalty and Energy Shield. However, there is a special coding, which reduces the effect of a crushing blow as if it was affected by the physical resistance of the target. In this calculation, a negative physical resistance is treated as 0 % to prevent it from increasing the effect of the crushing blow. Therefore, a crushing blow does not affect monsters immune to physical damage.
There is one chance to score a crushing blow per strike. The chances from different sources are summed up to determine the final chance to score a crushing blow.
Open wounds ability sets the target's regeneration speed to a negative value, which causes it to lose life. Open Wounds overrides the target's natural regeneration speed (it has no effect during open wounds), but item based regeneration still functions. Note that since Open Wounds is not damage but negative life regeneration, it is not affected by any damage modification effects, except what is stated in the Damage Modifiers section below.
Damage Formulas
The damage done by the Open Wounds depends on the level of the character who delivers Open Wounds as follows:
Clvl = Character's level.
Character Level Damage per Frame* Damage Per Second* Duration 1-15 (9*clvl + 31) / 256 0.88*clvl + 3.03 8 seconds 16-30 (18*clvl - 104) / 256 1.76*clvl - 10.16 8 seconds 31-45 (27*clvl - 374) / 256 2.64*clvl - 36.52 8 seconds 46-60 (36*clvl - 779) / 256 3.52*clvl - 76.07 8 seconds 61-99 (45*clvl - 1319) / 256 4.39*clvl - 128.81 8 seconds
*) There are 25 frames in 1 second.Calculated Damages
The damage inflicted by Open Wounds is calculated below for selected character levels.
*) There are 25 frames in 1 second.
Character Level Damage per Frame* Damage Per Second* Total Damage over 8 Seconds 1 0.16 3.91 31.25 15 0.65 16.21 129.69 16 0.72 17.97 143.75 30 1.70 42.58 340.63 31 1.81 45.21 361.72 45 3.29 82.13 657.03 46 3.43 85.64 685.16 60 5.39 134.86 1078.91 61 5.57 139.26 1114.06 99 12.25 306.25 2450.00 Damage Modifiers
The damage of Open Wounds is reduced against certain targets and if one is using missile weapons. Its damage is multiplied by one of the following factors depending on the case:
Target Melee Weapon Missile Weapon Player 1/4
1/8
Boss Monster 1/2
1/2
Other Targets 1 1 Mechanics
There is one chance to open wounds per strike. The chances from different sources are summed up to determine the final chance to open wounds.
Multiple open wounds do not stack with each other in terms of damage but the highest damage from multiple open wounds sources is always used. Each new open wounds resets the bleeding timer to 8 seconds and changes the damage rate only if the new damage rate is higher than the previous one.
The following example shows how to calculate the weapon damage of a rare ethereal great pilum with 32 % enhanced damage and +17 to maximum damage. Great pilum has Normal Damage of 11-26 in melee. Minimum and maximum weapon damages are calculated separately as follows:
Minimum Damage
Base Damage = [11*1.5] = 16
1.5 is the ethereal modifier.
Weapon Damage = 16 + [16*0.32] = 21
0.32 is the percentage bonus from Enhanced Damage.
Maximum damage
Base Damage = [26*1.5] = 39
1.5 is the ethereal modifier.
Weapon Damage = 39 + [39*0.32] + 17 = 68
0.32 is the percentage bonus from Enhanced Damage, and +17 is the direct bonus to maximum damage.
Displayed damage
Thus, the weapon displays the damage of 21-68.
Let's calculate the damage of an amazon with a 100-damage weapon and 200 dexterity, when she fires a level 20 Magic Arrow attack and scores a critical strike. Now minimum and maximum damages won't be calculated separately for the sake of brevity.
Weapon Damage = 100
Total Damage = 100 + [100*200/100] + 20 = 320
200 is dexterity and 20 is the bonus damage from level 20 Magic Arrow. Note that the damage Magic Arrow adds is physical. Now, the critical strike doubles the damage:
Final Damage = 2 * 320 = 640
Level 20 Magic Arrow also converts 20% of physical damage to magic. It takes place next:
Final Magic Damage = [640 * 20/100] = 128
Final Physical Damage = [640 * 80/100] = 512
Thus, the amazon deals 512 points of physical damage and 128 points of magical damage with her attack.
Adeyke for informing of many changes in these calculations from 1.09 to 1.10 and for special Double Throw calculations.
Arreat Summit's monster bonus page for part of monster bonus information.
Colds/lemekim for confirming that Double Throw damage follows normal damage rules and the character screen shows incorrect numbers.
Jarulf for information about damage type modifications, Open Wounds, and Crushing Blow .
King's Spectre for pointing out that Crushing Blow no longer scales with the number of players.
Librarian for reporting that Crushing Blow takes effect before normal damage and the mechanics of Open Wounds stacking.
Myrdinn for reporting that the skill bonus Damage: +X affects only the minimum damage and for confirming that all monster bonuses affect Total Damage.
Ruvanal for confirming that damage penalty and critical strike multiply total damage separately, and for part of monster bonus information. Thanks also for testing that Damage +X item property is shown incorrectly on the character screen to affect Total Damage where it, in reality, affects Weapon Damage. Furthermore, thanks for pointing out that deadly and critical strikes scored by any other source than a player (e.g. hirelings) double all damage types.
ToThePoint for pointing out that sources of the same type are no longer (as of patch 1.10) treated as separate source (for multiplication and rounding purposes) but summed up first.