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/Caitl...00000&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/Caitl...00000&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!

maybe youre missing something because i think lw helps me more then another pd,dmg vise..

There is a point: If you start building IE + PD, the third item you build (BT or LW) depends if the target has armor greater or equal than 111. That means that if enemy has an armor greater than 111, LW brings more damage than BT. As you complete your build though and you increase further your damage, the amount of armor that makes LW better increases, making it less efficient.

However if you start BT + PD, it's better to build IE before LW, and by that point, the amount of damage you get makes LW less efficient than adding another PD.

It's curious . The value that makes this numbers dance so far is the crit.

Why bother buying Last Whisper? , The AD carry should not focus someone who has an high armor rating in the first place. Last whipser has no place in the meta in my point, its just not worth it. Well maybe if the Carrys are starting to buy armor, then maybe. But then again why not buy Black Cleaver instead? After 3 Attacks you lower their armor rating by 45, and you get 30 Ats and 55 AD.

That's a common misconception at the lower level of play, after playing a few hundreds of games as ad bot I can tell you confidently, that AD carry will be your best bet to kill the metagolem bruisers in mid and late game, and as they will most likely try to eliminate you as soon as possible, you will HAVE to target them sooner or later.

So AD carry usually focuses on the biggest threat to itself first, most likely being the bruiser unless enemy carries are out of position/bruiser cced or underfed. Kill the biggest threat to yourself without getting out of position is the name of the game.

Black Cleaver is a much better item then LW.
always was, always will be.

214 armor to break even in a finished build?
The odds of not having enemies with that armor endgame are kinda slim.

Average bruiser has 250 armor lategame which will already make LW worth buying and tanks can have armor >300.

Also u have to factor in that with LW every one of ur attacks will be doing more damage, while with PD u'll have increased AS but in reality its better to hit harder fewer times than hit more over a period of time cause that period can be shorter than expected.

Second PD only worth buying on vayne who benefits maximum from extra mobility and doesn't need armor pen at all with the %true damage passive. Also it can be viable on caitlyn for again for extra mobility purposes not for the DPS increase.

The math is a lot more complicated than that because you forget several other variables : Runes / Masteries / Itemisation.
Also the 1st build costs 600G more (which is a lot).

ArPen is "usually better" even on "very tanky targets" unless you specifically build otherwise.

Dude, you really opened a gate in my mind. After doing maths, I've seen that Black cleaver is way more effective as final item than a PD for targets with 224 armor or less. For targets with Armor greater than 224, PD becomes better. But at that time, LW is better than PD, so PD as final items is not a good idea.

What's more, BC works as a good for the team.

Great finding!