# i was bored and came up with this forumla for mages....

so most players have probably heard that the void staff is a lot stronger than most people think and in some cases even stronger than rabadons. since i was bored i thought id try making a formula to calculate how much magic resist an enemy needs in order for the void staff to be more efficient than rabadons and came up with this (this only compares damage, void staff is a LOT cheaper than rabadons):
x=the scaling on that ability (80% scaling=80 for this formula)
y=the base damage of that ability
z=the amount of ap you have before the purchase
{(x:y):2+(0,4678+z:1000)-[0,0000007584*(z-250)^2-0,0474]}:2*1000*(x:y)
this formula then calculates how much magic resist an enemy needs to have in order for the void staff to deal more damage than rabadons would deal. its actually really precise until it reaches 200 magic resist or so. for an even more precise result:
175-200 mr: multiply by 0,955
200-250 mr: multiply by 0,93
250+ mr: multiply by 0,85
lets just make an example to show that it actually works:
lets say we are playing annie and use a full spell rotation at level 9. the scalings equal 80%+85%+65% (230%), the base damage equals 220+115+150 (485) and lets say we have 150 ap already because of morello, two dorans and runes. therefore:
{(230:485):2+(0,4678+150:1000)-[0,0000007584*(150-250)^2-0,0474]}:2*1000*(230:485)=212,15
212,15*0,93=197,3
so an enemy would need about 197 magic resist in order for the VS to deal more damage according to the formula. if you calculate it exactly youd end up with 201,1 mr. so thats pretty damn close. sadly i was so dumb and didnt take gold efficiency into account (you cant simply add it somewhere because the formula is made out of formulas which i calculated using their graphs) so this compares just the two items. generally though the lower the scaling, the higher the base damage and the less ap you already have before the purchase the more efficient the void staff is going to be. i actually spent almost 5 hours on this (yes i kinda suck at math). sadly this formula is too complex to actually make use of it but maybe somebody wants to......well i dont know what to really do with it as i said i was just bored as hell. have fun with it and good night im tired.
EDIT: VS is 1150 gold cheaper than raba which would equal almost 53 ap (1 ap is worth 21,75 gold)

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