Calculated the Damage Added by Liandry's Torment's Passive
A convenient idea of the damage added by Torment. These aren't exact numbers but they're close enough for anything reasonable.
These numbers account for health decreasing over the duration of the burn.
##If the target is not slowed and burns for three seconds
Damage: HP x 0.058
For example: on a target with 1,000 HP, Liandrys will add 58 extra damage (1000 * 0.058)
On a target with 2,000 HP, Liandrys adds 114 extra damage (2000 * 0.058)
##If the target is slowed and burns for three seconds
Damage: HP x 0.114
On a target with 1,000 HP, 114 damage is added.
With 2,000 HP, 228 damage is added.
##If the target is being hit constantly and is not slowed and burns for one second
DPS Increase: HP x 0.02
At 1,000 HP, there is an increase of 20 damage per second.
At 2,000 HP, an increase of 40 damage per second.
##If the target is being hit constantly and is slowed and burns for one second
DPS Increase: HP x 0.04
At 1,000 HP, there is an increase of 40 damage per second.
At 2,000 HP, an increase of 80 damage per second.
Some observations.
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The three-second damage on a slowed target pretty much always trumps the damage from Ludens on any target with more than about 1200 health when considering the magic penetration
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On the other hand, the one-second damage added by Liandrys pales compared to Luden's instant burst
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The raw DPS increase from continuous-damage on non-slowed targets is pretty small, with it being roughly only 40 extra DPS on 2000 health targets and only getting smaller as the fight continues. Sunfire Cape would deal more overall damage.