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Serpents milk - the math

I’m investigating this item: Serpent's Milk

It’s usefulness depends on some questions, and some math I’m unsure of:

  1. Does poison stack infinitely? Some sources say ailments have a maximum of 20 stacks, others say poison is infinite

  2. It seems unclear whether pet poison synergises with player poison. Does 20 stacks of pet poison apply a 100% increased poison damage only from pets, or will it apply a 100% increased poison damage from both pets and the player?

Now to the math. Let’s say a single hit applies one stack at 7 DPS. Is it correct to say the item would now apply 3 stacks, then reduce the pet damage as shown in line 2 here?

damage increased more less total stacks increase new total
7 1 1 1 7 1 0.05 7.35
21 1 1 0.1 2.1 3 0.15 2.415

If so, then Serpents milk is reducing minion poison damage to about 30% of the same hit without the item equipped. The loss to minion damage is more marked if minions already have a high chance to poison. For example, with 1000% existing poison chance, equipping the item drops minion damage to about 12% of the same hit without the item:

damage increased more less total stacks increase new total
70 1 1 1 70 10 0.5 105
84 1 1 0.1 8.4 12 0.6 13

Now, say minions can hit 10 times rapidly. With serpents milk this makes 30 stacks of poison, and the increased player damage from 30 poison stacks (150%) starts to get a little more exciting compared with the 50% increased damage your minions would provide without the item.
But, this only works if minion poison stacks can help increase player poison damage.

Theory crafting
Based on all this, it would seem serpents milk can be a build defining item if
a) You can get lots of minions hitting rapidly, but those minions do not do much poison damage
b) You can get a nice source of poison damage you apply yourself
c) You can easily scale increases to your damage, but cannot easily scale increases to minion poison damage, minion poison chance, or poison shred.

example 1 - Acolyte with wandering spirit or hungering soul poison being magnified immensely by a swarm of other minions applying tons of poison stacks
example 2 - Shaman’s storm totems applying lots of poisons ahead of the shaman coming in and applying poison of their own, say with serpent strike

Anything that says poison is capped is wrong, they’re probably assuming that because resist shred is capped at 20 stacks and poison has resist shred built in that therefore poison is capped at 20, which is not the case. It could potentially be that the shred from poison stacks is capped at 20 but that might be difficult to work out and might be simpler to just ask the devs.

It does, the game doesn’t track the source of a stack of poison once that poison has been applied and it’s stats calculated.
My understanding is that when a hit can poison hits a target,

  • the game calculates the duration and damage per tick (before the inherent shred is applied since the shred, IMO, needs to be calculated & applied “live” rather than being baked into the stack’s stats, but I could be wrong) based on the applying entity’s stats (player or pet). This is the poison stack’s “outgoing” damage.
  • Then the game calculates how many stacks are currently on the target.
  • The game then calculates the “damage received”, this is the target’s “incoming” damage which can be modified by shred, penetration, resistance & any other “damage taken” type effects.

IMO, after the stats of the poison stack have been calculated/snapshot/etc, the game doesn’t care about the source because all of the stats that matter (chance to poison, various damage modifiers, etc) have all been calculated and applied. I think the devs have already confirmed this, but I’m not entirely sure.

Only if the minion already has 100% chance to poison since the item adds 2 stacks per hit. But yes, it’s effectively a 90% less damage modifier as you have shown.

It does, just like Khorne, the game cares not from whence the poison flows, only that it flows.

Yes, that’s how I’ve assumed it “should” be best used is as a build defining item. IMO, it’s an item to try & buff hybrid builds, that both have lots of minions to “prep” the target with limited damage but lots of hits (say, 50 poison/fire Wraiths, or a load of Primalist minions) then the player comes in and kill steals saves the day!

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Really interested in this. I’m trying to build a Serpent Strike Beastmaster that will theoretically utilize the unique for massive poison stacks from minions which should, in turn boost Serpent Strike’s dot damage.

So far what I am planning on getting are
Serpent Strike
Summon Wolf → ~4 wolves
Summon Scorpion → Baby Scorpion path - more minions more poisons (i hope)
Entangling Roots → Minion buff path (+150% poison chance)
Frenzy Totem → Global Poison chance + Frenzy buff

That build is super good with minions alone, it has a lot of synergies which mean you can passive and gear into defences. It’s gonna be very hard to give up all the natural minion damage to stack your serpent strike damage - it already melts bosses and you don’t have to attack anything. But, it’ll be a good test to see if the item can improve on it!

I’m not entirely sure that the baby scorpions will benefit from the amulet since they aren’t your minions, they’re your scorpion’s minions.

yeah, that makes sense. however i guess you would still want to go baby scorpions for the maximum number of hits, they still have decent poison chance and attack speed built in.