Damage

Or, how much damage can a weapon do to a unit with so much armour.

Formula

 Damage to Unit = (Weapon Damage * Damage Modifier) - Armour 

If the bullet does negative or zero damage, then the bullet is ignored (for damage purposes, but you still get Firing Accuracy experience if it did hit). If the bullet does damage, then there's a chance that the armour plate that it struck will deteriorate by a few points.

That's the basic idea. Let's expand on the variables a bit:

Armour: The armour section the bullet hit.

Damage Modifier: 0.5 if the unit resists and 2.0 if the unit is weak against the weapon's damage type. I'm not sure, but there's probably also a 1.0 for units that neither resist nor are weak against the bullet type.

Weapon Damage: Weapon damage will be a random number between 0 and the damage level of the weapon. In reality, all weapons do half their listed damages, on average (but see below re: damage to soldiers).

A critical hit is therefore anything above 50% to 100% of the listed damage (or 100-200% for double damage, or 25-50% for units that take half damage).

Note that X-Com units take double damage from practically every major weapon type. So the Ufopaedia damage amount should be multiplied by 2, for practical purposes. Or, looked at another way, the Ufopaedia shows average damage for soldiers.

This is for sure with AP, Laser, Plasma, and Stun Bomb. For example: rifle bullets do up to 60 points of damage to X-Com units when they're only rated for 30. At least this is true for unarmoured soldiers. No wonder your units drop like flies. I'm not too sure if armour helps reduce this to normal damage.

-- NKF, Dec 18 2003, reposted by --JellyfishGreen 16:01, 21 Apr 2005 (BST)

Modifiers

Everything's 100% except the following:

Vulnerable to...

Incendiary:
    Reaper             170%

High-Explosive:
    Silacoid           130%

Laser:
    Sectopod           150%

Melee:
    Unarmoured Soldier 120%
    Civilian           120%
    Sectoid            120%
    Celatid            120%
    Floater            120%

Celatid Acid Spit:
    Unarmoured Soldier 160%
    Civilian           160%
    Sectoid            160%
    Celatid            160%
    Floater            160%
    Personal Armour    110%

Resistant to...

Armour-Piercing:
    Cyberdisc       80%
    Muton           60%
    Zombie          60%

Incendiary:
    Personal Armour 80%
    Chryssalid      80%
    Ethereal        70%
    Snakeman        70%
    Tanks           40%
    Power Suit       0%
    Flying Suit      0%
    Silacoid         0%

High-Explosive:
    Sectopod        80%
    Zombie          80%
    Tanks           70%
    Cyberdisc       60%

Laser:
    Zombie          70%

Plasma:
    Sectopod        80%
    Zombie          70%

Stun:
    Personal Armour 90%
    Chryssalid      90%
    Power Suit      80%
    Flying Suit     80%
    Ethereal        80%
    Zombie           0%

Melee:
    Tanks           90%

Celatid Acid Spit:
    Tanks           40%

"I find it amusing that Celatids are vulnerable to their own spit" -- Danial

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 and 60/100 is the damage modifier

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's range is 32, 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. Weapon range of the pistol is still 32, 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 (0-31). Taking into account an armor reduction of 10, the actual (penetrating) average damage is 7.67.