Damage (LWR)
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/Received = 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. Weapon Damage can be viewed in-game by pressing F1.
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 (+50% weapon damage), and a sniper rifle (6 weapon damage) would have a barrel damage of 6 + 1 + 3 = 10.
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.
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 (AKA Damage Received)
Damage Dealt = Travel Damage * Target Modifiers
Once it reaches the targets, Target Modifiers are applied. The first target modifier applied is critical damage. 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. After each calculation the damage is truncated to an integer.
This can also be termed Damage Received (as opposed to Damage Dealt) if being considered from the target's point of view.
Damage Dealt cannot be lower than 1.
Damage Taken
Damage Taken = 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.
After all penetration is calculated, it is reduced by any penetration resistance.
To calculate total %DR:
Total %DR = 1 - [(1 - DR) * (1 - DR) * (1 - DR) * (1 - DR) * etc. etc.]
Example of 30% DR and 50% DR and 20% DR:
Total %DR = 1 - [(1 - 0.3) * (1 - 0.5) * (1 - 0.2)] = 0.72 = 72% DR
Or you can just apply the DRs to damage sequentially.
Example: 100 damage shot against someone with 30% DR, 50% DR and 20% DR:
100 damage with 30% reduced = 70 damage 70 damage with 50% reduced = 35 damage 35 damage with 20% reduced = 28 damage (overall 72% DR)
Exceptions
Mins and Maxes
The Damage Taken cannot be reduced below 1 by Damage Resistance.
The Damage Taken can never go higher than the Damage Dealt.
For example, someone with a high amount of penetration could calculate final Damage Taken numbers higher than Damage Dealt, but this would be capped at the initial Damage Dealt.
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
Both Psi Damage and Neutrino 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 42% DR.
You'd expect it to do 4 damage (range 3-5), minus 42% 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 (35 Percent DR) and has 10 base DR for a total of 42% DR.
The Drone is not Shredded and does not have Distortion. The soldier does not have VPT or CST, and Fragmentation does not apply to rifles, 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 - Percent DR) + Penetration)
Damage Dealt = (((((4 + 1) * 1.0) + 0) * (1 - 0.42) + 0) = 2.3 = 2 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 50% 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. You can find the HP of an object by pressing "L" when the mouse is hovered on top of an object.
