Diablo II Expansion, patch 1.09d
Contents: 1. Introduction | 2. Damage Calculations | 3. Damage Bonuses | 4. Special Effects | 5. Examples | Acknowledgements
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.
Damage Calculations
Briefly, the damage is calculated as follows:
- Base Damage = [Normal Damage x Base Damage Multipliers] + Base Damage Direct Bonuses
- Weapon Damage = Base Damage + [Base Damage x Weapon Damage Percentage Bonuses] + Weapon Damage Direct Bonuses
- Total Damage = Weapon Damage + [Weapon Damage x Total Damage Percentage Bonuses] + Total Damage Direct Bonuses
- Final Damage = [Total Damage x Final Damage Multiplier]
See Section 2: Damage Calculations for details.
Bonus Classes
Item properties and other effects belong to one of the bonus classes:
- Base Damage Multiplier
- Base Damage Direct Bonus
- 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.
Special Effects
Some effects, such as Crushing Blow, are not normal damage at all. See Section 4: Special Effects for details.
Examples
Section 5: Examples includes examples of using damage formulas.
There are two important rules of thumb in damage calculations:
- The result of each multiplication is rounded down (this is indicated by brackets in equations).
- Each damage enhancement property is applied separately and the result is rounded down. For example, Enhanced Damage modifiers from different sources (even if summed up on the screen, e.g. as with jewels) are each treated as a separate bonus.
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]
+ Base Damage Direct Bonus 1
...
+ Base Damage Direct Bonus NIn the above equation:
- M is the number of base damage multipliers
- N is the number of base damage direct bonuses
- [] indicates rounding down
There are two special base damage direct bonuses:
- +1 if there is any Enhanced Damage on the weapon from magical properties (not counting jewels).
- +1 if there is any Enhanced Damage on the weapon from being superior quality.
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]
...
+ [Base Damage x Weapon Damage Percentage Bonus M]
+ 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]
...
+ [Weapon Damage x Total Damage Percentage Bonus M]
+ 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 / 100
Total Damage Percentage Bonus 2 = Dexterity x Dexterity Multiplier / 100
- 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 damage penalty. 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.
Conversion of Physical Damage into Another Damage Type
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
All item properties, including those from jewels and charms, are calculated separately. For example, an armor with four Enhanced Damage jewels is considered to have four separate enhanced damage bonuses.
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/100 Many weapons +X% Enhanced Maximum Damage on a Weapon Weapon damage
(maximum only)Percentage Bonus Physical X/100 Eaglehorn (unique crusader bow) + X to Minimum Damage Weapon damage
(minimum only)Direct Bonus Physical X Bloodfist (unique heavy gloves) + X to Maximum Damage Weapon damage
(maximum only)Direct Bonus Physical X Duskdeep (unique full helm) Adds X-Y Damage Weapon damage
(minimum and maximum)Direct Bonus Physical Min: X
Max: YWar Traveler (unique battle boots) +X% Enhanced Damage not on a Weapon Total damage Percentage Bonus Physical X/100 Biggin's Bonnet (unique cap) X% Damage to Undead Total damage Percentage Bonus Physical (X-100)/100 Blunt weapons +X% Damage to Undead Total damage Percentage Bonus Physical X/100 Gravepalm (unique sharkskin gloves) +X% Damage to Demons Total damage Percentage Bonus Physical X/100 Laying of Hands (set bramble mitts) +X-Y to Fire / Cold / Lightning / Magic Damage Total damage Percentage Bonus As described Min: X
Max: YBaranar's Star (unique devil star) +X Poison Damage Over Y Seconds Total damage Percentage Bonus Poison See Tao of Poison Plague Bearer (unique rune sword) Deadly Strike (see notes below) Final damage Multiplier Physical 2 Headstriker (unique battle sword) Deadly strike. Deadly strike is checked only if a critical strike does not happen. Thus, deadly strike is useless if one has 100 % critical strike. Chances of deadly strike from different sources are summed up. Deadly strike above 100 % is as effective as 100 % deadly strike.
Skill property descriptions are from Chippydip's skill information page and may differ from those in the game.
Skill Property Affected Damage Bonus Type Damage Type Value Example Skill Damage: +X Weapon damage Direct Bonus Physical X Magic Arrow (amazon bow and crossbow skill) Minimum Damage: +X Weapon damage
(minimum only)Direct Bonus Physical X Bash (barbarian combat skill) Damage Bonus: +X percent Total Damage Percentage Bonus Physical X/100 Might (paladin offensive aura) Damage: -X percent Total Damage Percentage Bonus Physical -X/100 Battle Cry (barbarian warcry) Fire / Cold / Lightning / Magic Damage: +X percent Total Damage Percentage Bonus As described X/100 Berserk (barbarian combat skill) Elemental Damages: +X percent Total Damage Percentage Bonus Fire, Cold, and Lightning Each element: X/100 Vengeance (paladin 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) Damage: +X to melee attacks Total damage Direct Bonus Physical X Sanctuary (paladin offensive aura) Critical Strike (see notes below) Final damage Multiplier Physical 2 Critical Strike (amazon passive skill) Damage Penalty: -X percent (see notes below) Final damage Multiplier Physical 1-X/100 Multiple Shot (amazon bow and crossbow skill) Critical strike. A critical strike doubles total physical damage. The chance of critical strike can be increased by the amazon's Critical Strike skill and assassin/barbarian weapon masteries. Masteries are bugged at the moment so that they give always a 100 % chance of critical strike. Normally characters do not have any chance of critical strike.
Damage penalty. For example, the amazon's Multiple Shot and Cold Arrow have this ability. It affects only physical damage, but the character screen erroneously reports it affecting all damage types.
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
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.
Monster Bonus Affected Damage Bonus Type Damage Type Value Berserk Champion monster Base damage Multiplier Physical - Normal difficulty: 3.60
- Nightmare difficulty: 3.00
- Hell difficulty: 2.64Normal Champion monster Base damage Multiplier Physical - Normal difficulty: Min 0.90, Max 1.80
- Nightmare difficulty: Min 0.75, Max 1.50
- Hell difficulty: Min 0.66, Max 1.32
Monster Bonus Affected Damage Bonus Type Damage Type Value Extra Strong Base damage Multiplier Physical 2 Aura Enchanted, Fanaticism Total damage Percentage Bonus Physical Fanaticism level = [mlvl/4] (*) Aura Enchanted, Might Total damage Percentage Bonus Physical Might level = [mlvl/4] (*) Aura Enchanted, Holy Shock Total damage Direct Bonus Lightning Holy Shock level = [mlvl/2] (*) Cold Enchanted Total damage Direct Bonus Cold Normal Damage Fire Enchanted Total damage Direct Bonus Fire Normal Damage Lightning Enchanted Total damage Direct Bonus Lightning Normal Damage Mana Burn Total damage Direct Bonus Mana - Normal difficulty: 3.6 x Normal Damage
- Nightmare difficulty: 4.2 x Normal Damage
- Hell difficulty: 5.28 x Normal DamageSpectral Hit, Fire, Cold, or Lightning Total damage Direct Bonus Fire, Cold, or Lightning Normal Damage Spectral Hit, Poison Total damage Direct Bonus Poison Damage per frame = Normal Damage / 16 (*) mlvl = Monster Level. The monster level of a unique boss monster is the base monster level +3. [] indicates rounding down.
Crushing blow is not damage but an ability that modifies the opponent's life amount after normal damage has been dealt. The crushing blow is based on the scaled life amount of the target (modified by the number of players in the game). 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
All other targets 1/10
1/20
Since a crushing blow is not damage, it is not affected normally by any damage reduction 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. Because of this coding, the effect of a crushing blow is effectively cut in half in hell difficulty where monsters have a global 50 % physical resistance, and, furthermore, 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 reduces the target's regeneration speed and may cause it to lose life. The damage of open wounds is as follows:
Target Damage per second 1) Duration Normal monster 0.88 * Clvl + 3.91 4 seconds All other targets 0.44 * Clvl + 1.95 4 seconds 1) This is the reduction in the target's regeneration speed (per second). Clvl = Character level. The exact formula is (Clvl * 9 + 40)/256 * 25 against normal monsters. The damage is halved against other targets.
For example, Open Wounds from caused by a level 99 character makes a normal monster to lose 90.9 life per second for 4 seconds (not counting the effect of the normal regeneration speed). "Prevents Monster Heal" ability, which sets the monster's regeneration speed to zero, does not work when Open Wounds is in effect.
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.
Monster regeneration speed
Normally, monsters regenerate at a rate of MaximumLife * DamageRegenerationSpeed / 4096 * 25 life per second. DamageRegenerationSpeed is 2 for most monsters. It is never less than 1. For example, a typical monster with 2000 life regenerates at a rate of 24.4 life per second.
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] + 1 = 17
1.5 is the ethereal modifier and +1 is the bonus from having Enhanced Damage on the weapon.
Weapon Damage = 17 + [17*0.32] = 22
0.32 is the percentage bonus from Enhanced Damage.
Maximum damage
Base Damage = [26*1.5] + 1 = 40
1.5 is the ethereal modifier and +1 is the bonus from having Enhanced Damage on the weapon.
Weapon Damage = 40 + [40*0.32] + 17 = 69
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 22-69.
Arreat Summit's monster bonus page for part of monster bonus information.
Chippydip for his very informative skill information page.
Dectgap for the original post about the weapon damage formula.
Gakerd for pointing out some capitalization inconsistencies.
Hammerman for information about open wounds, prevents monster heal, and monster regeneration rates.
Jarulf for information about damage type modifications and the majority of monster bonus information.
Naturelover for pointing out that not all maces have a strength multiplier of 1.10.
Nookiestar for pointing out the +1 bonus to the base damage from superior quality.
RTB for reporting the generally accepted weapon damage formula.
Rivo/Karon for reporting mana burn boss bonuses for different difficulties and testing that "Damage Penalty" skill modifier does not reduce non-physical damage, even though the character screen reports otherwise.
RogueMage for pointing out an error in the crushing blow table.
Ruvanal for confirming that damage penalty and critical strike multiply total damage separately.
Spirea for open wounds and crushing blow information.