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Some reading there but generally speaking intelligence indeed increases minion damage by +4%.
You can make your little doods hit like trucks. Minion builds are probably the easiest to build up too as they do most content well.
https://maxroll.gg/last-epoch/resources/damage-explained
Penetration is powerful, however if you are able to stack sources of "more damage" as those are multiplicative with each other you reach higher numbers then any other "type" of damage modifier, if you are able to secure a few sources.
There is also a somewhat hidden stat for minions: "minion power" that is a character level dependent "more damage" up to 45% and "take less damage" 45% at level 100.
So all things being equal a level 100 characters minions start with 45% more damage, making each source of more damage out scale a lot of other options. As stacking "more" damage is generally the path to the highest numbers, this is even more true for minion builds thanks to the free "more" damage.
There is also some variance on the type of minions you are using, you can see the minions and how they scale here:
https://www.lastepochtools.com/minions/
And unlike PoE, "more" modifiers are not additive with each other, they are multiplcative with each other.
If you have 700% increased minion damage, then that's 800% damage. If you have 50% more from the Bone Curse buff, that's 1200% damage. If you have 50% more from some minion passive we're now up to 1800%, NOT 1600%. It's 1.5x1.5, not 1 + 0.5 + 0.5.
INT also gives minion health. So INT gives 3 stats you need: minion damage, ward retention, and minion health. Of course, any of these stats on their own will give you more of its stat, but INT is very good.
The tooltip just means damage to YOU doesn't affect your minions (except in some niche scenarios like that poison spear unique). Minion damage and at least 1 stat, depending on the minion, increases damage. But so does minion melee/bow/spell, depending on what they are, as well as minion physical/necrotic/fire/etc.
https://maxroll.gg/last-epoch/resources/damage-explained#base,-added,-increased,-&-more-damage-header
(Base + Added 1 + Added 2... )*(Increased 1 + Increased 2...)*(More 1)*(More 2)*...
The three dots (...) represent that we can scale this up to however many sources we have of that Damage Type.
After that its just properly applying the numbers, the only few potholes come in the form of easily overlooked things. Each skill applies added damage differently, this can trip up your math, and as pointed out above minion power is not as transparent a stat as it could be.
Once you have mathed out that formula its simple to include "other" sources of damage such as shred/penetration or the more conditional types of "more damage taken" all outlined in the link provided.
The neat thing is bosses use the same formula so if you look them up you can get a decent idea as to how much incoming damage you have to deal with, just make sure to account for the variables like from corruption/modifiers.
The quick TLDR is think of each "type" of increase as going into a "bucket". Everything in the same bucket is applied the same way depending on what type of "bucket" it is.
Basically it works the same as PoE, except for "more", which is stronger than in PoE so it's better in LE.
Increased applies first, then "more", and the order of "more" doesn't matter because A x B x C is the same as A x C x B or C x B x A, etc.
From the page that Ravenkid linked:
"(Base + Added 1 + Added 2... )*(Increased 1 + Increased 2...)*(More 1)*(More 2)*..."
So I forgot to mention added but that's first. So like "+12 melee damage" would be before "60% increased melee damage". Then at the very end, all the mores multiplied together.
FLAT damage ("added") is stronger than "increased", usually, because base amounts are so low and flat damage is hard to come by compared to increased.