Damage Calculation

A high-level overview of the damage calculation process could be:

```
Damage = Base Damage
        × (1 + Sum of Critical Damage Bonus)
        × (1 + Sum of Regular Damage Bonuses)
        × (Product of (1 - Damage Reductions))

```

## Base Damage

A weapon's base damage numbers can be viewed on its own wiki page's *Statistics* section:

* Stygian Blade
* Eternal Spear
* Heart-Seeking Bow
* Shield of Chaos
* Twin Fists
* Adamant Rail

### Base Damage Bonuses

The following types of damage bonuses are base damage bonuses:

* Any weapon aspects / Daedalus Hammer upgrades that replace the weapon's move with a new one. The new base damage number is displayed in the in-game tooltip. Notable examples:
	+ Aspect of Hestia's empowered attack
	+ World Splitter

* Any hammer upgrade that replaces **Attack** / **Special** with a charging attack
	+ Notable example: Charged Skewer

* Consecutive hit damage bonus
	+ Concentrated Fire
	+ Concentrated Knuckle

## Critical Hit

### Critical Hit Chance

Certain boons and weapon aspects can grant the ability to do critical damage:

* Various boons offered by Artemis
* Duo boon Deadly Reversal from Artemis/Athena
* Aspect of Nemesis
* Heart-Seeking Bow's Aspect of Zagreus

The critical chance from different sources are additive. e.g.:

* An **Attack** from a rank 5 Heart-Seeking Bow's Aspect of Zagreus has +15% crit chance.
* A Pressure Point boon of Epic rarity grants +4% crit chance
* Together, they grant 19% crit chance per attack.

Only when the critical hit check succeeds, the critical hit damage bonus actually applies.

### Critical Damage Bonus

The base value of critical damage bonus is +200%. Other possible sources of critical damage bonus are:

* Clean Kill: +15% / +22% / +30% / +37%
* Heart Rend, the Duo boon from Artemis/Aphrodite: +150%

## Regular Damage Bonuses

Most +% damage bonuses fit in this category. Examples:

* +% attack / special damage from boons
* +% damage against armor. Examples:
	+ Breaching Skewer
	+ Hide Breaker
* Backstab bonus damage
* +% damage debuff on foes. Examples:
	+ Boiling Blood and Privileged Status
	+ Sweet Surrender
* General +% damage without any specifics. Example:
	+ Billowing Strength
	+ Aspect of Eris
* +% damage to Power Shot
	+ Minotaur Rush
	+ Perfect Shot
* +% damage to distant foes

All the regular damage bonuses are added together first before being multiplied with in the formula. Thus they are called "additive" bonuses among the communities.

## Damage Reduction

Damage reductions are multiplicative. Example: a player has the following sources of damage reductions:

* 10% from Bronze Skin
* 30% from a Rank 3 Myrmidon Bracer

The player will take `(1 - 10%) × (1 - 30%) = 63%` damage from foes. It is a 37% damage reduction.

The theorical maximum can reach near 95% damage reduction.

## Irregular Factors

The following factors can also affect the damage calculation. They're omitted from the formula for simplicity but they do exist.

### Rounding Floating-Point Number to Integer

In a computer, a decimal number is actually "emulated" with binary number (see the industry standard of floating-point number, IEEE 754). When rounding a decimal number to integer, loss of accuracy may happen. Rounding could happen in any step of calculations to introduce inaccuracy.

### Self-damage Damage Modifier

When the attacker and victim are the same unit, there is an extra step of damage modification (i.e. "multiplicative") between base damage and critical damage.

For now the only case of self-damage is Hazard Bomb: it reduces damage down to 1%.