impale and increased damage taken

Welcome.

I kinda have a hard time finding a reliable source about that.
I know that impale damage is technically reflected damage, and is calculated before mitigation, but i'm not sure if it's affected by modifiers to damage taken, more specifically those:

> flesh and stone - increased physical damage taken
> pride - more physical damage taken
> vulnerability - increased physical damage taken
> intimidate - increased attack damage taken

Thanks in advance for your time =]

First 3 work because they are generic physical damage modifiers on the enemy. Intimidate will not work because impale damage is secondary, not an attack.

Out of curiosity, I delved a bit in the Wikia.

Impale:
https://pathofexile.gamepedia.com/Impale

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When a hit applies impale to a target, 10% of that hit's physical damage is recorded before any damage mitigation is applied. Impale deals the recorded damage to that target each time it is hit. Impale does not have a limited duration; it remains in effect until the maximum number of hits is reached. By default, impale lasts for five hits. A target may have multiple impale effects on it at once, all of which deal damage to that target each time it is hit.[1]

The damage dealt by impale is considered reflected damage. The source of the reflected damage is the impale debuff; there is no interaction with effects that pertain to damage you reflect, as seen on Crown of the Pale King.

Reflected damage (the most interesting bits)
https://pathofexile.gamepedia.com/Damage_reflection

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Reflect cares about the damage taken after mitigation, not the amount of life removed.[1][2] The offensive stats of a creature can affect whether it takes reflected damage (accuracy, block chance reduction, etc.), but cannot affect the amount of damage dealt (critical strikes, penetration, ignoring resistance, damage modifiers, etc).[3]

Although reflected damage hits, it intentionally doesn't trigger most on/when hit effects[4] and, accordingly, cannot cause status ailments[5], stun[6], critical strikes and other similar effects that require a hit. Reflected hit, however, is able to yield a flask charge if the Flagellant's prefix is present there.

And, Finally, some word from Reddit on a similiar question of yours
https://www.reddit.com/r/pathofexile/comments/c18906/lets_talk_impale_and_reflected_damage_mechanics/

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It's correct to use it as an effective %more multiplier.

Things that boost the damage your attack would deal modify the initial stored value of the Impale.

Things that boost the damage a target takes modifies the damage of the impale when the damage is actually taken.

The reason it's considered reflected damage is to make sure it doesn't benefit from your offensive stats twice (if it just deal damage a second time, it would be boosted twice by everything, like old double-dipping). To prevent it from being mitigated twice, they have it store the premitigation damage of the initial hit, so that it's only mitigated one time.

We can already see there is a contradition on the damage mitigation part. If, as stated, usually a Reflect takes into account anything that have a damage mitigation (which is why a high elemental resistant character can take a bit more brunt from an elemental reflect), in case of Impale the base value will take into account the damage of the attack, disregarding any physical damage reduction from the opponent.

This means that, when hitting a 90% PhysDamageReduction opponent with a 100 physical damage attack, we will deal (100*0.1) = 10 physical damage, but we will store an Impale base damage for 100*0.1 = 10 (rather than 10*0.1 = 1). Next 5 attacks will deal (100+10)*0.1 = 11 damage - this way we have what the reddit user implied: the reflected damage is not double-nerfed (first from the mitigation of the main attack, then once again because Impale is a physical damage)

Since the damage of Impale is based on the actual hit damage output minus opponent's physical damage reduction, I deduce it will actually also calculate Intimidate's bonus when determining "the 10% of the hit's damage"