Damage (LWR)

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Damage Calculation

Complete Damage Formula

Damage Taken = ([((Weapon Damage + Barrel Modifiers) <-- Randomization ) * Target Modifiers] * (1 - Percent DR) + Penetration)

This can be broken down into 5 categories:

1) Weapon Damage = Weapon Damage

2) Barrel Damage = Weapon Damage + Barrel Modifiers

3) Travel Damage = Barrel Damage is Randomized (and for explosives fall off is then calculated)

4) Damage Dealt = Travel Damage * Target Modifiers (include crit)

5) Damage Taken  = Min(Damage Dealt, Damage Dealt * (1 - DR/100) + Penetration)

Each category represents a section of the damage calculation (as explained below).

Weapon Damage

This is simply the listed damage of each weapon (for XCOM) or base damage (for aliens). Alien weapon damage increases with alien level and leader upgrades.

Barrel Damage

Barrel Damage = (Weapon Damage + Barrel Modifiers)

Damage from the barrel is: Weapon Damage + Barrel Modifiers (e.g. ranger, alloy-jacketed rounds, burst etc.). It is truncated after calculation. Some Barrel Modifiers give straight damage (e.g. +1 damage) and others give damage based on the weapon damage (e.g. +50% weapon damage). These are all summed together. For example, a sniper with ranger (+1 damage), mayhem (+70% weapon damage), and a sniper rifle (6 weapon damage) would have a barrel damage of 6 + 1 + 4 = 11.

Almost anything that modifies Weapon Damage (e.g. +50% weapon damage) is added as a Barrel Modifier.

Critical Damage flat bonuses (e.g. +1 crit damage) are added as barrel damage, but only if the shot is a critical hit.

Barrel Damage can be viewed in-game by pressing F1.

Travel Damage

Travel Damage = Barrel Damage is Randomized

Travel Damage is basically the Barrel Damage that is modified by Randomization.

After it leaves the barrel and is travelling towards the target, the damage is Randomized.

For all damage 1-9, the damage is randomized from -1 to +1, with an even chance of being -1, 0, or +1.

For all damage 10-19, the damage is randomized from -2 to +2, with an even chance of being -2, -1, 0, +1, or +2.

The same occurs for damage of 20-29, 30-39, etc.

The minimum damage is always at least 1.

The actual formula is: Randomized Damage = Max(1, Damage + Rand[1 + (2 * (1 + Damage / 10))] - (1 + Damage / 10))

The randomization works in integer values so all values are constantly truncated (e.g. If x is 6 then x/10 = 0).

Randomization can occur twice or not at all if certain second wave options are enabled.

Critical Hit Randomization

If this is a critical hit (from an explosive or a shot), any damage that would be randomized lower than the Barrel Damage is instead set to the Barrel Damage.

Damage Dealt

Damage Dealt = Travel Damage * Target Modifiers

Once it reaches the targets, Target Modifiers are applied. If the shot or explosive rolled a critical hit, the damage is increased by 50%. Other target modifiers also applied include: Shred, VPT, CST, Graze, Distortion, TK Field, Brawler. The last target modifier applied is critical damage. After each calculation the damage is truncated to an integer.

Damage Dealt cannot be lower than 1.

Damage Taken

Damage Taken = Min(Damage Dealt, Damage Dealt * (1 - DR/100) + Penetration)

Damage Resistance (DR) is applied first, then Penetration. The Damage Taken is truncated only after all DR has been removed from the Damage Dealt. Damage Dealt cannot be reduced below 1 by Damage Resistance.

Every 10 Damage Dealt against targets increases penetration by 1. So if the damage taken is 30 damage, an additional 3 penetration will be added to any other forms of penetration.

To calculate total %DR, see Base DR

Exceptions

Mins and Maxes

The Damage Taken cannot be reduced below 1 by Damage Resistance.

Randomization will never set the damage below 1.

Truncation

All damage is stored in an integer form, thus it is always being truncated during each step. This means 5.6 becomes 5, 9.1 becomes 9, and 9.9 becomes 9.

The exception to this is that Damage Resistance is not truncated and is removed from damage after calculation.

So Damage Dealt is truncated only after all DR is removed.

This is important, because having DR NOT truncated until it's removed from the Damage Dealt means that you can have small amounts of DR (i.e. 2% DR) be effective.

Explosive Damage

Each unit damaged by explosive damage has the Travel Damage reduced based on distance from the center after it is randomized. Damage falls as [half of the distance:radius ratio + 0.5], down to [50% + 0.5] at the periphery. The exception to this is that damage within 1 tile of the center has no fall-off.

Note: The 0.5 damage is added on explosive fall-off to accommodate for truncation.

Explosive Travel Damage = 0.50 + Travel Damage * (1.0 - FMin[0.50, 0.50 * Distance_to_Target/Radius_of_Explosive])

Special Damage Types

Psi Damage have their own methods of determine damage and are not affected by Target Modifiers or Damage Resistance.

Example Calculations

Mental In-Game Calculation

A soldier with a 3 damage assault carbine and ranger (+1 damage) fires at a drone who has 37% DR.

You'd expect it to do 4 damage (range 3-5), minus 37% DR down to 2 damage.

Detailed Calculation

A soldier with an Assault Rifle and the Ranger perk fires at a Drone

The Assault Rifle has 4 Weapon Damage, receives +1 damage as a Barrel Modifier from Ranger, and has no innate Penetration.

The Drone is Hardened (30 Percent DR) and has 10 base DR. Total DR = Base DR + (100 - Base DR)*(Percentage DR) = 10+[(100-10)*0.3] = 10 + 27 = 37. The Total DR is 37%

The Drone is not Shredded and does not have Distortion. The soldier does not have CST and the shot does not graze, so there are no Target Modifiers to the damage.

The shot does not 'Crit' so Crit Dmg is 1.0 and the Randomization does not change the value.

Damage Dealt = ([((Weapon Damage + Barrel Modifiers) <-- Randomization ) * Target Modifiers] * (1 - Total DR) + Penetration)

Damage Dealt = ((((4 + 1) + 0) * 1.0) * (1 - 0.37) + 0) = 3.2 = 3 Damage Taken

Environmental Damage

Environmental damage is the damage done to objects and structures around the battlefield (like walls, chairs, cars, etc.).

Each weapon has a specific environmental damage based on its size and type:

Weapon Type	Environmental Damage
Shots	15
Explosives	35

Environmental damage is mostly unaffected by perks and abilities and just considers the weapon's specific environmental damage. However, there are 2 exceptions: Explosives do tapper their environmental damage down to 35% at their periphery (and Tandem Warheads does prevent this tapper) and Sapper increases environmental damage.

Fire will also cause a lot of environmental damage and can spread. Be careful taking cover behind objects that are on fire!

All objects have a certain amount of HP. The less sturdy the object the less HP it will have. When an object's HP is reduced to 0 or less it will crumple.

Most cover has between 30 and 90 HP, based on what they are made of -- stone is tougher than wood, for example. Some map elements are entirely invulnerable and non-cover objects usually have less than 30 HP. Meld Canisters have 3 HP. Vehicles take 250 before catching on fire and 500 will cause them to explode immediately. Examples of the HP of objects can be found in the pictures below.