Damage

For the XCOM: Enemy Unknown (2012) version, see Damage (EU2012)

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Overview

Damage in the world of X-COM follows a series of rules that define how damage is dealt and taken. This article will explain the basics of how damage works.

Definitions

For the purpose of this article, damage will be differentiated into two main categories:

Impacting damage - damage striking the target's armour
Penetrating damage - damage penetrating the target's armour and causing reduction in Health, and possibly Fatal Wounds.

Impacting damage can also be categorised according to the algorithm used to calculate the amount of impacting damage, as follows:

EU Direct: This damage type covers most EU damage types as per the table below. The damage types generally only affect a single target at a time, with the exception of area-effect stun.

Enemy Unknown/UFO Defense
Armour Piercing (AP) Laser Plasma Acid Spit (Celatid) Stun (Melee and Area Effect)

EU Explosive, and TFTD: This damage type covers all TFTD weapons, and all EU weapons that use the High Explosive damage type, from grenades to rockets and blaster bombs.

Incendiary: This covers Incendiary/Phosphor damage. Because this type of damage follows its own quite different damage model, it will not be covered here. Refer to its article for the particulars.

Each damage category above will affect three different target categories, unit, terrain, and object, in slightly different ways.

Unit: Cover all actors in the field from X-COM units to aliens to tanks.

Terrain: Cover all floors, ceilings, walls and any other fixtures that are contained in a tile such as light poles, post boxes, tables, 'middle' walls, oil drums, etc.

Object: Covers all items that can be picked up off the ground and manipulated by units, including weapons and bodies.

Effects of Damage

If a target is attacked and the damage dealt is a negative number or zero, no damage is done. Player units will still earn Firing Accuracy experience if the target is an alien controlled unit.

If the bullet does damage, henceforth called Penetrating Damage, the target's health will be deducted while terrain or objects will be destroyed.

Against units there are additional effects such as adding critical wounds, stun damage, morale loss and a chance that the armour plate that it struck will deteriorate by a few points, as shown below.

Formula

In its purest form, the amount of damage a target will take from a weapon is:

Penetrating Damage = Impacting Damage - Armour

The Impacting Damage component, being the main subject of this article, is broken down into the following formula:

Impacting Damage = Base Weapon Damage × Random Weapon Range × Damage Modifier

After the final Damage value is calculated, any fractions are dropped and only the integer value is used.

Let's expand on the variables a bit:

Base Weapon Damage: This is the number that you see for the weapon in the UFOpaedia. In effect it is the average damage that will be suffered by an unarmoured target which has normal damage modifiers.

Random Weapon Range: This is the random number roll that alters how much damage is to be dealt. For EU firearms, a value between 0% and 200% is rolled, while TFTD weapons and EU explosives will perform a 50% to 150% roll. However in TFTD, damage from all sources has been equalized to 50-150%.

Damage Modifier: This is a percentage value that controls how weakly or how strongly the attack will affect certain classes of targets.

Armour: The armour section the attack hit. Armour is pure damage reduction.

Random Damage Ranges

When calculating damage, the game first performs a random dice roll to determine what percentage of the base weapon damage is to be dealt to the target.

This variability allows for a simple simulation of critical hits that defeat the target instantly, deal normal damage or dud shots that hit but are absorbed/deflected by the target's armour.

The following table shows the damage ranges for the two main weapon categories, against the three different target types.

Target \ Damage	EU Firearms	EU Explosive / TFTD ?
Units	0 - 200%	50% - 150%
Terrain	25% - 75%	50%
Objects	n/a^*	100%^#

^* Objects are only damaged by high explosives.

^# Objects technically use the Unit damage ranges to determine how much damage to compare against.

Damage Modifiers

The term Damage Modifier was coined through discussions on various X-COM web forums and is used on this wiki to describe the target's resistance and vulnerabilities to certain damage types. These numbers are not visible to the player in the game. The standard damage modified is 100%, meaning no increase and no decrease - no special vulnerability, no special resistance.

Units are typically divided into various armour classes. While many units have their unique armour classes, there are some groups that share the same class. For example civilians, unarmoured X-COM units, Sectoids, Celatids and Floaters are classed as having humanoid armour. Muton or Lobsterman on the other hand have their own unique armour classes.

Each class has a table of percentages that tell how susceptible they are to all the possible damage types.

When calculating damage, the result of the random damage roll (as mentioned above) is multiplied by the damage modifier to provide the amount of raw damage done by the attack.

See the main Damage Modifiers or Damage Modifiers (TFTD) for the data tables of all the damage modifiers used in either game. For another way to view the same info, see this.

Effects of Armour

Armour is the protective plating found on any of the possible sides that the attack may hit. Its role in the damage calculation is simply to reduce the final calculated damage after the random roll and damage modifiers have been applied.

For firearm damage, units can be hit from the Front, Rear, Left and Right armour.

Explosive and area-effect stun damage will target Under armour if the target is at or adjacent to the centre of the explosion (i.e. a Direct Hit). For all other ranges in the blast radius are treated as directional damage originating from the centre of the explosion.

Terrain and Object Armour

Terrain and Objects do not have hit-points and rely solely on their fixed armour levels. If damage exceeds their armour, they are destroyed, otherwise they survive.

When terrain is destroyed, it is replaced by the next "damaged" tile in its sequence. When all available tiles are destroyed, only a regular earth tile will remain on the ground. In the case of tiles suspended in the air, nothing will remain or in some cases the last damaged tile that is not solid.

See Object Destruction for the specifics.

Examples

Note that negative damage values in the following examples are treated as no damage.

Example 1:

The first example shows two attacks that are altered by a normal and a reduced damage modifier.

You are attacking a Floater soldier and a Cyberdisc. Both are attacked with a standard rifle from the front. What sort of damage are you going to expect to get from these attacks?

Rifle

Damage = 30 AP

EU AP damage range = 0 - 200%

With the rifle we know that it can normally can do between 0 to 60 impacting damage per bullet.

Floater Soldier

Susceptibility vs. AP = 100%

Front Armour = 8

Since the damage modifier is 100%, there's no change to the rifle's 0 to 60 damage range.

After armour deduction, the rifle will do between -8 to 52 penetrating damage.

Cyberdisc Terrorist

Susceptibility vs. AP = 80%

Front Armour = 34

With the 80% damage modifier, the Rifle's damage is reduced and will do 0 to 48 impacting damage.

After armour deduction, the rifle bullet will do between -34 to 14 penetrating damage.

Example 2:

You are attacking three Lobsterman Soldiers head on. One is attacked with a Sonic Cannon, one with a Disrupter Pulse Launcher and the last one with a Thermal Shok Launcher. Assume all shots hit.

Lobsterman Soldier

Susceptibility vs. Sonic = 50%

Susceptibility vs. HE = 30%

Susceptibility vs. Freeze = 110%

Front armour: 20

Under Armour: 10

Sonic Cannon

Damage: 130 Sonic

TFTD Damage Range: 50 - 150%

The Sonic Cannon's expected to deal between 65 to 195 impacting damage. Altered by the Lobsterman's hefty 50% resistance, it is reduced to a range of 32 to 97 impacting damage.

After armour deductions, 12 to 77 penetrating damage.

Disrupter Pulse Launcher

Damage: 210HE

HE/TFTD Damage Range: 50% - 150%

The Disupter Pulse Launcher can do between 105 to 315 points of impacting damage. After the Lobsterman's HE damage modifier is applied, this is reduced to 31 to 94 points of impacting damage(note that the fractions are dropped).

After deducting 10 under armour, penetrating damage is reduced to 21 to 84.

Thermal Shok Launcher

Damage: 120 Freeze

Freeze Damage Range: 0 - 200%

Thermal Shok bombs can do between 0 to 240 non-lethal damage. Factoring in the Lobsterman's 110% vulnerability to freeze, Shok Bombs can deal between 0 - 264 non-lethal impacting damage to them.

After the 10 under armour is deducted, the Lobsterman Soldier will take between -10 and 254 penetrating stun damage.

Advanced Example

Adapted from Zombie's kindly example:

Scenario: Beginner level Muton mission. Your soldier is carrying a normal Pistol and you want to know what is the chance that a Muton Soldier's front armor will absorb a direct hit without lowering health.

Vitals: 
Muton Soldier front armor = 10
Muton Soldier health = 125
Muton susceptibility to Armor Piercing ammo = 60%
Pistol listed power = 26 (average)

Calculation: 

Max damage for a Pistol against a Muton is lowered due to susceptibility:

 Modified max damage = INT(26 * 2 * 60 / 100)
                     = INT(52 * 60 / 100) 
                     = INT(3120 / 100)
                     = INT(31.2)
                     = 31

where 2 is the max modifier (200% of UFOpaedia listed power) and 60/100 is the damage modifier (60%)

The range of values the Pistol can deal is 0 to 31 points of damage (or a range of 32 different values). The equation's steps are shown because XCOM's math sometimes leads to slightly unexpected values in subsequent steps.

The Muton Soldier has a front armor rating of 10. It will absorb up to this much damage without changing health. In other words, it will negate the first 10 points of damage a Pistol can dish out (0-10; 11 possible values). Since the Pistol has a range of 32 possible values, the probability that a direct hit will be blocked by Muton armor is simply 11 / 32 = 34.4%.

Okay, say you want to know the probability of doing damage to a Muton's health. The pistol still has 32 values, but instead of absorption we want penetration. 10 points of damage is absorbed, so we need at least 11 to penetrate. 32 - 11 = 21 values which will breach. 21 / 32 = 65.6%.

21 is also the maximum number of damage points which might be deducted from the Muton's health. Assuming the Muton was initially uninjured, in the worst case (for him!) he will have an ending health of 125 - 21 = 104.

On average, there will be 15.5 damage dealt (0-31). Then armor (10) reduces this to an actual (penetrating) average damage of 7.22. (It's not simply 15.5-10=5.5 because initial damage that's less than ten becomes zero penetrating damage, not negative penetrating damage. The removal of these negative values causes the expected average to rise, as it were.)

If you need precision while testing, note that the game applies truncation after making its damage roll. It does not first determine the maximum (including damage modifiers), and then roll randomly/evenly from 0 up to the maximum, per se. To wit: if you hack a pistol to an average damage strength of 1, there would not be an overall roll of 0 to a maximum of 1 (with average damage of 0.5) as might be implied from the Muton-versus-AP example above. Instead, there is a roll of 0, 1, or 2, to which the .6 modifier is applied. Only a roll of 2 results in non-zero damage (INT(2x60/100)= INT(1.2)= 1), and the Muton only takes an average of 0.33 damage, not 0.5. Usually this effect is insignificant relative to the large damage values found in the game, but it could matter in testing situations involving very low damage strengths. It also means you need to take into account all possible values versus individual truncation effects, if you want an ultra-precise listing of e.g. how often armor is breached.

Note that the calculations of average expected penetrating damage is much simpler when there is no possibility of "negative" penetrating damage. This is the case when ever the minimum impacting damage (modified by damage modifiers) is greater than or equal to the target armour value. In this case (quite common with explosives or in TFTD), the average expected penetrating damage is the simple average of the minimum penetrating damage and the maximum penetrating damage.

Penetrating Damage vs Armor Damage, Health Damage and Fatal Wounds

Penetrating Damage is simply the final, modified damage (modified by all susceptibility and vulnerability factors), minus the current armor level on the relevant facing of the target.

When there is Penetrating Damage (i.e., damage is >0 and not all blocked by armor), Health and Armor Damage occurs, i.e. Health and Armor levels are reduced.

Health Damage - the reduction in the target's current Health - is simply equal to Penetrating Damage. Health is allowed to go to negative values (negative values are only really relevant to Stun damage - otherwise, dead is dead).

Health Damage, in turn, dictates the probability of suffering Fatal Wounds (normally just for XCom soldiers):

Between 1 to 10 points of Health Damage, the chance of Fatal Wounds increases more or less linearly from 9% to 90%
There is 100% chance of Fatal Wounds if taking 11 or more points of Health Damage
Whenever a target affected by Fatal Wounds, there is always an equal chance of 1, 2 or 3 Fatal Wounds, regardless of Health damage sustained.

For more information on Health Damage versus Fatal Wounds, see Fatal_Wounds#Probability_of_Fatal_Wounds.

Armor Damage - the amount that the target's current Armor level is reduced by, on the impacted facing - is equal to one tenth of Penetrating Damage, rounded up (to a maximum of the current Armor Level, since it can't go below zero). This means that an opponent who is almost invulnerable to your weapons, will slowly become more vulnerable, with every successful penetrating hit.

Note that Stun/Freeze damage, and Fire damage, do not reduce Armour level, and do not cause Fatal Wounds.

Relationship Between Health and Armor Damage

This section is really confusing and I suggest it should be removed, especially as the results seem to be only tentative Spike 09:35, 20 September 2012 (EDT)

For situations where Penetrating Damage is less than the current Armor level, Health and Armor Damage have a very simple relationship to each other:

 Health Damage = 10 * Armor Damage, minus 1 to 10

Or the other way around:

 Armor Damage = INT( Health Damage / 10 ) + 1

In table form:

Armor  Health Damage
Damage   Min  Max
   0      0    0
   1      1    9
   2     10   19
   3     20   29
   4     30   39
   5     40   49
   6     50   59
   7     60   69
   8     70   79
   9     80   89
       etc.

Of course, this assumes armor is not zeroed out by the hit. Also note that you will always have armor damage if you have health damage and vice-versa, if there was damage penetration. Stated another way, you will never have armor damage if you don't have health damage (i.e., when there is insufficient damage to breach the armor).

You will see this health/armor relationship if you watch damage from individual hits. However, the relationship is muddied if you only look at a unit after a number of hits (or, of course, if armor is broken through). The most extreme example would be if a unit were hit with e.g. five hits of 1 penetrating damage point each. The unit would have 5 health damage and 5 armor damage, which would appear contrary to the above table.

This relationship has been been tested for a wide variety of explosions and some light weapons vs. Mutons, and some hits on soldiers. It has not otherwise been widely tested, but is presumed true unless/until found otherwise.

As stated, the above is for damage that penetrates. It is possible for hits (guns or explosions) to do zero damage. This happens on the rare occasion that a weapon damage roll is actually zero, or, much more commonly, when armor has blocked all the damage. You still get an experience point toward Firing Accuracy if damage fails to penetrate. You only have to hit the target(s) to get Firing experience; there doesn't have to be damage.