What causes damage variance?

Question

What causes damage to vary when no other conditions change. Many times I have fought foes who almost kill me in one hit, so I heal them and stall until the foe uses a non aggressive move. Sometimes I will die from the move that I survived last time. What causes this variance? I don't think it is random.

Answer 1

Ahem

Allow me to explain.
This is the equation for damage calculation, quoted from Serebii

((((2 Level / 5 + 2) AttackStat AttackPower / DefenseStat) / 50) + 2) STAB Weakness/Resistance RandomNumber / 100

Simple enough equation, just a bunch of variables to plug in. If you see that "Random Number" variable, this is what causes the variation in damage. The random number is generated between 85 and 100. Take the following situation:

Lv. 500 Magikarp uses Explosion on Lv. 500 arceus. Let's call Magikarps attack 10,000, and arceus's defense 8,000 (Just for kicks and giggles). We input the statistics:

(((2500/5 +2) 10,000 250 / 8,000) /50) +2) (No STAB, 1) 1 (No weakness or resistance) 94/100 (Random Number). Now we can calculate, with this random number that Magikarp does 1188.63 HP in damage. This could range all the way up to 1264.5 damage, or as low as 1074.825 damage.

And please, nerds, don't come in and tell me that magikarp can't learn explosion-- take it from me

Comments

I really worked way too hard on this.

Answer 2

Ok, so this is how damage is calculated.

The damage dealt when a Pokémon uses a damaging move depends on its
Attack or Special Attack stat, the opponent's corresponding Defense or
Special Defense stat, and the move's base damage. In addition, the
various circumstances explained above will also affect the damage
dealt. The damage formula is the following:

Level is the level of the attacking Pokémon.
Attack and Defense are the working Attack and Defense stats of the attacking and defending Pokémon, respectively. If the attack is Special, the Special Attack
and Special Defense stats are used instead. Some moves like Psystrike
use other stat than usually move of this category would use (in case
of Psystrike, it uses Special Attack and Defense).
Base is the base damage of the attack.

The only value that isn't constant here is the Modifier, so the random values have to come from there.
Modifier is calculated as follows:

STAB is the same-type attack bonus. This is equal to 1.5 if the attack
is of the same type as the user, and 1 if otherwise.
Type is the type effectiveness. This can be either 0, 0.25, 0.5, 1, 2, or 4 depending
on the type of attack and the type of the defending Pokémon.
Critical is 2 for a critical hit, 1 otherwise.
other counts for things like held items, Abilities, field advantages, and whether the battle is a Double Battle or Triple Battle or not.
rand is a random number from 0.85 to 1.00. The result is rounded down as remainders are not kept. It is possible to do zero damage 1.

So in the damage calculation, there is always a number that is "irregular" causing the moves to do different amount of damage each time they are used.

Source: http://bulbapedia.bulbagarden.net/wiki/Damage_modification