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So will it actually be more efficient to lifetap during PI, ToEP, ZHC instead of shadowbolting now?
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According to my quick math, at least for the ToEP it will be, as funny as that is. I haven't considered the other trinkets/buffs.
First off, this assumes the worst case scenario, where Imp LT gets you (420*1.2) + .8*dmg, rather than (420+.8*dmg)*1.2. If the 20% is taken into account after the +dmg bonus, it becomes even more worth it to use the ToEP.
The math:
ToEP gives 175*.8 extra mana per LT
Or an extra 140 mana from LT
Or an extra .37 SBs (140/380 = .37) per LT
Assume you're at +600 damage so you take 420 + 480 = 900 damage upon tapping. Tapping 5 times for 4500 damage seems like a reasonable number, and makes my calculations work out easier. The same calculation could be done with 6 Taps if you want messy fractions.
Life Tapping 5 times takes 7.5 seconds of your ToEP, earning you an extra 5*.37 = 1.85 shadow bolts. In those 7.5 seconds you could SB three times, getting (3/3.5)*175*3 = 450 extra damage, or maybe half a shadow bolt? Tapping seems to be the much more efficient choice, unless my math is wrong.