Setting an enemy on Fire (via Fire shot, Death Fire or Flamethrower)
Each “hit” is 25% of your Loadout Attack, there is 1 hit per 0.25 seconds and there are 7 hits.
Improved Fire Shots doubles this to 50%.
This was buffed in 1.11, previously it was 15% and 30% respectively.
If you are using Flamethrower, while the enemy is in the flame there’s also 60% of Loadout Attack every 0.2 seconds. Note that this hasn’t been buffed in 1.11.
Poisoning an Enemy (via Poison shot, Death Poison or Dr. Toxic’s Venom)
Each poison “hit” is 60% of your Loadout Attack and there is 1 hit per second indefinitely.
Improved Poison shots doubles this to 120%.
This was buffed in 1.11, previously it was 30% and 60% respectively.
Dr. Toxic’s Venom shots hit at 30% of Loadout attack, as it was prior to 1.11.
Verdict
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Flamethrower is useful for actively burning an enemy (especially without getting hit - e.g. through ice in Ice event/castle) but not so useful for setting them on fire and moving away
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I think DeathFire is rather useless - it does a bit of damage and then it’s gone (but the 7 x 25% = 175% damage is still more than the 75% that Death Blast delivers, although it takes the Death Fire 1.75 seconds to do the damage that the death blast does more or less instantly)
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If you had to choose between Fire shots and Poison shots, I think poison is better if you’ve got a lot of spread shots + bouncy that are only occasionally hitting, but otherwise fire is better (you are likely reigniting them before the fire goes out)