Hi,

trying some builds for my AD Carries and doing some maths, I think I've proved mathematically that Last Whisper is not that of a good item...

Imagine these typical final builds for an AD Carry (for example, Caitlyn) and supposing 21/0/9 masteries, with the 10% ArP mastery:

With Last Whisper (#1):

http://leaguecraft.com/builder/Caitlyn/?items=83,97,60,89,33,73&runes=38,38,38,38,38,38,38,38,38,10,10,10&masteries=1300400410013030100000000000000001031030001000000&level=18

This build brings 5178 DPS over 5 seconds with 46% ArP (%ArP stacks multiplicatively)

Without Last Whisper but another Phantom Dancer (double BT brings less damage than double PD according to numbers) (#2):

http://leaguecraft.com/builder/Caitlyn/?items=83,97,73,89,60,89&runes=38,38,38,38,38,38,38,38,38,10,10,10&masteries=1300400410013030100000000000000001031030001000000&level=18

This build brings 7030 DPS over 5 seconds with 10% ArP.

Then, the question is: how much armor must the target have in order for last whisper to become better than adding another PD to the final build? Let's find out:

To calculate the damage factor a champion recieves after armor, the formula (according to wiki http://leagueoflegends.wikia.com/wiki/Magic_resist) is 100/100+X where X is the armor of the target without considering armor pen. With 10% ArP X becomes 0.9x (we just take into account 90% of enemy armor) and with 46% ArP 0.54x.

So, in order to discover the minimum armor required for LW to become better, we must find the moment which build #1 deals the same damage as build #2.

So, for the build #1, the formula is 5178*100/(100+0.54x) = y

For build #2, the formula is 7030*100/(100+0.9x) = y

remember that "x" is the amount of armor of the target.

so, if we solve the equation, x = 214.

So, in order to last whisper to become better than adding another PD, **the target must have a minimum armor of 214**. The typical tanky DPS of fratma's or atmogs must also build a randuins in order for LW to become EQUALLY effective as another PD (and ofc, with LW you deal less damage to squishies).

I've been really surprised by the finding. I think that from now onwards I will rarely get LW when playing AD Carries.

I just wanted to share this. Open discuss!