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The damage system in this game isn't easy to get used to, but once you get used to it, it makes sense. Pets benefit from bonuses that are specifically for pets, either on gear or from talents/skills. They only benefit from bonuses that improve things they actually do; any other bonuses are wasted.
https://img.kirmiziperfect.com/20170714155127/Grim-Dawn-DAIL-Compilation-Mod-Legendary-Cap-Remover-Mod-Items.jpg
You can see on the left side that it says "+x vitality damage" below the "Bonus to All Pets" bracket
So unless it specifically says "Bonus to All Pets", pets that "Scales with Pet Bonuses" do not profit from your stats. There are some pets that "Scales with Character Damage", such as the Shaman Dust Devils, only those scale with damage stats from you.
well that mean, i could stack Posion dmg even it dont say "posion dmg for pets"? i am very confused. sorry for my noobness
Let me try. if i want to bring my blight dmg up i need to get +posion damage under "to all pets"
https://i.imgur.com/hyjEIOc.png
Anything in the red box applies to Pets whose skill text say they scale with Pet Bonuses.
Suppose you have a pet that does 100 points of physical damage, 100 points of vitality damage, and 100 points of fire damage. You equip the item AO showed. Now your pet will do 155 physical damage, 226 vitality (100 X [1.55 x 1.46 because the bonuses for different types stack multiplicatively, iirc - if I'm wrong then it's 201 Vitality damage]), and 155 fire damage.
Suppose your pet did 100 Aether and 100 Pierce and you equipped that same item. Your pet would do 155 Aether and 155 Pierce, because you get no benefit from the +46% Vitality damage since your pet does not do vitality-type damage. So you "waste" that bonus.
Your total DPS for your pets would go up no matter what, though, because of the increase in attack speed but I'm skipping that for simplicity's sake.
Did that make sense?
Thanks for your Hhelp