Today - the hp% values at which Necrolyte's Reaper's Scythe is fatal, and the process to find them.
This is a fun little calculation that I hate to memorize because calculating DotA math fresh is so gosh darn entertaining (don't judge me).
As always, I'll walk you through this one.
Scythe deals 0.4/0.6/0.9/1.2 dmg per hp missing.
Scythe will kill its target when the target's missing hp multiplied by damage factor is equal to or greater than their remaining hp.
But don't forget spell Resistance. For our purposes, we will assume the default 25% spell resistance. This 25% resist is the same thing as reducing damage factor by 25%.
Variables - the variables involved are "h" current hp, "d" damage factor, "r" spell resistance. Missing hp is the same as (100%-h).
Therefore, here is our equation:
Current Hp = (1-Resist)(Damage Factor)(Missing Hp)
h = (1-r)(d)(100-h)
h = (.75)(d)(100-h)
h = 75d-.75dh
And now you just plug in numbers.
h = 75(.4)-.75(.4)h
h = 30-.3h
1.3h = 30
h = 23.07%
h = 75(.6)-.75(.6)h
h = 45-.45h
1.45h = 45
h = 31.03%
h = 75(.9)-.75(.9)h
h = 67.5-.675h
1.675h = 67.5
h = 40.30%
h = 75(1.2)-.75(1.2)h
h = 90-.90h
1.90h = 90
h = 47.37%
Buying Aghanim's for Necro solely for the ultimate boost is not worth it. The only time that you should get it is in a situation where you can really make use of the stats and survivability (+390hp, +290mp) too.
Composed with love and care from my iPhone 3gs, this has been a day of maths with KuroNeko. Hopefully you learned something. More to come.