With the new thorns set for Crusader, I'm wondering which Legendary Gems besides Boyarsky's Chip affect thorns damage.
For instance, does the damage amplification from Bane of the Stricken affect the damage output from my thorns?
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It depends what you mean if you want a more complicated answer, though. It works in general like you think it would, but the damage multiplier might not be as straightforward as I think...that is, I'm fairly sure Stricken is its own multiplier, so it will multiply all damage done after calculations by its multiplier. In other words, if you stack it to 100%, whatever damage you would have done is increased to two times the normal amount.
Regardless, if Stricken didn't affect the damage output from your thorns, then no one would use it on Invoker Crusader, but it clearly works (I've played dozens of rifts as Invoker sader and after wailing with my punish skill on a 7 trillion health rift boss for 2 minutes I'm hitting it for 20 billion per hit as opposed to the 2 billion on the first hit). I'd spend 5+ minutes killing the RG if I didn't have Stricken on in any grift past 75. It takes roughly 2-3 minutes for any RG after 75.
In general I believe thorns damage is affected the same way any other damage is. It depends on the gem; i.e., Bane of the Trapped is its own multiplier whereas Gem of Efficacious Toxin's level 25 passive is an additive multiplier (10% additive).