When is damage calculated for DOTs and summons?

are they snapshotted when you use the skill or calculated for every tick of damage?
specifically, if i use blackwater cocktail or mortar trap before arcane will procs, will subsequent damage ticks benefit once arcane will procs or would i have to recast the skill?

For DoT damage (Burn, Frostburn, Electrocute, Poison, Vitality Decay, Trauma, Bleed), you’d have to recast the skill to override the current application with a higher damage one.

For the direct damage part of BWC that is the Fire/Chaos or Fire/Lightning/Physical for Mortar Trap though, the damage increase on Arcane Will will take effect immediately provided they are still dealing damage, no recast needed.

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for further clarification, if they keep standing in BWC, the DOT refreshes right? its my understanding that its duration will refresh but youre saying the damage value will not be changed?

DMG/hit calculation on True Dots are done on the first hit, regardless how long ex Burn duration is
psudo dots (like that flat fire and chaos) are done per tick
this is why Baka says you’d need to reapply it to get the burn to benefit from Arcane Will

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