Resistance penetration

Resistance penetration is a property of hits that reduces the target's effective resistance to specific damage types.

Mechanics
When a target is struck by a hit with resistance penetration, that target's effective resistance is reduced for determining the amount of damage dealt by the hit. Resistance penetration does not modify the target's resistance or maximum resistance stats.

The target's effective resistance to damage type $t$ is $R_t = \min( r_t, m_t ) - p_t$ where $r_t$ is the target's resistance to damage type $t$, $m_t$ is the target's maximum resistance to damage type $t$, and $p_t$ is the resistance penetration of the hit for damage type $t$.

Just like resistance stats, effective resistance can be a negative number. There is no minimum limit on effective resistance imposed by the game mechanics.

Due to the fact that resistance penetration is a property of hits, it cannot apply to damage over time.

Efficacy of resistance penetration versus resistances
It can be shown that resistance penetration is more effective in terms of damage dealt against targets with higher resistances.

The percentage increase to damage type $t$ as a result of resistance penetration is $I_t = \frac{ p_t }{ 1 - \min( r_t, m_t ) }$

Sources of resistance penetration
Currently, resistance penetration exists only for elemental damage types.

'Damage Penetrates x% Fire Resistance' on weapon affects player's skills and spells, not minions (Source: PoB).

Other items

 * can add to belts.
 * Elder sceptres and wands can have.
 * Shaper weapons and amulets can have.
 * can have following modifiers: