Damage types

In Dota 2, there are several different types of damage that can be cause by abilities and spells. Each type varies in how it affects enemy units. These types are magical, physical, mixed, pure, and direct HP removal.

Physical
Physical damage is caused by all regular attacks from all units, and by some spells. It is reduced by both Armor and Damage Block, is unaffected by Magic Resistance or Magic Immunity, and cannot effect Ethereal units. Examples of physical damage are Juggernaut's Omnislash and Slardar's Slithereen Crush.

There are several attack types that cause physical damage, depepending on the source, which are reduced by various types of Armor.

Hero Attacks
Hero Attacks do normal damage (100%) against everything except buildings and siege creeps, which take only half damage (50%) from heroes.

Piercing Damage
Piercing attacks, such as Venomancer's Plague Wards, do reduced (50%) damage against heroes but enhanced (150%) damage to Lane Creeps, making piercing damage more effective at lane control than hero harassment.

Siege Damage
Seige attacks, from siege Lane Creeps and Towers, do enhanced (150%) damage against Buildings and siege creeps but reduced (75%) against heroes.

Chaos Damage
The Chaos attack type is effectively the same as the Hero type (does 100% to all), but does slightly less (40%) against the fortified armor on Buildings and siege creeps. Chaos is done by Witch Doctor's Death Ward (the only hero controlled source), by Roshan, the Fountain, and several Neutral Creeps.

All physical damage, regardless of attack types are further reduced (or increased) by Armor after the reduction of armor types is accounted for. Example: a Plague Ward with 100 damage attacking a hero with 10 armor would do 100 * .5 for armor type * .625 for armor value (37.5% reduction) or 31.25 total damage.

The only exception to this is damage from Cleave, which is reduced by armor type but not by armor value. Practically speaking this means armor is worthless against cleave damage. Splash (from ranged attacks) is reduced as normal.

Magical
Magical damage is caused primarily by spells, although not all do magic damage. Magic damage is reduced by Magic Resistance, does not affect magic immune units, and does 1.4 times damage against Ethereal units. Examples of magic damage are Leshrac's Split Earth and Beastmaster's Primal Roar.

Mixed
Mixed damage is a combination of magical and physical damage types. It is reduced by Armor, Magic Resistance, and Damage Block, but goes through Magic Immunity. It does not affect Ethereal units. Examples of Mixed damage are Beastmaster's Wild Axes and Leshrac's Diabolic Edict.

Pure
Pure damage is just that, pure. It ignores all Magic Resistance. It does not affect units under Magic Immunity and does normal damage against Ethereal units. Examples of pure damage are Chen's Test of Faith, Tinker's Laser and Enchantress' Impetus.

HP Removal
HP Removal works by directly subtracting hitpoints from the affected unit. It ignores all damage reductions and affects units under Magic Immunity and Invulnerability and does normal damage against Ethereal units. Unlike all other damage types, HP Removal does not count as being attacked, so it will not interrupt Bottle or trigger any other on-attack effects. Examples of HP Removal are Necrolyte's Heartstopper Aura and Vengeful Spirit's Wave of Terror.