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Damage Dealing Calculation


 

1. Introduction

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 1H damage or 2H damage here: Common Items.

A more detailed procedure is described below.



2. Damage Calculations

There are four steps in the weapon damage calculations:

  1. Base Damage
  2. Weapon Damage
  3. Total Damage
  4. 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:

  1. Base Damage Multiplier
  2. Weapon Damage Percentage Bonus
  3. Weapon Damage Direct Bonus
  4. Total Damage Percentage Bonus
  5. Total Damage Direct Bonus
  6. Final Damage Multiplier
These classifications are listed in child section 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).
 

2.1 Base Damage

Damage calculations begin from determining the normal damage of the weapon. It is the damage listed as the weapon damage (1H or 2H) in Common Items 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.
 

2.2 Weapon Damage

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.
 

2.3 Total 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.
 

2.4 Final Damage

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.
 

2.5 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.




Acknowledgements

Adeyke for informing of many changes in these calculations from 1.09 to 1.10 and for special Double Throw calculations.
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.

© by Tommi Gustafsson
 
Edited