Mainly I just want to clarify that NOT ALL AD CARRIES NEED THIS ITEM
Namely Kog'maw,Vayne and Corki
Quoted from GentlemanGustaf
To start, as we saw here, you want 2 points of AD for every % of Attack Speed. Well, as DiffTheEnder observes, we have this when we have IE + PD + Berserker's Greaves. Then we go out and get LW and BT, which gives 140 AD and no AS. And to be fair, it's very understandable. After all, we can't sacrifice our IE, we can't sacrifice our Armor Pen, and we NEED our sustain. Right? Well, I'll take the need for sustain as true, for now, since it can't really be replaced. But Armor Pen and IE both just give damage. There's no rule that says where you have to get your damage from, you just have to maximize it. I think you'll trust my basic, unstated math that getting rid of IE is a bad idea. But why is it such a bad idea to get rid of Last Whisper? The basic, logical answer is that PD will increase your damage vs squishies, but not tanky champions, and the squishies already die right away anyway, and you spend most of your time attacking tanky champions anyway. So explain this, a graph of dps as a function of third item: Phantom Dancer or Last Whisper. The assumptions are 21/x/x and AD mark/quints, and the use of 'dps' is a bit of a misnomer, as I really mean '8 seconds of auto attacking and using abilities whenever they come up', and a target with 3000 health (a bruiser or a tank) and 0 armor:
But Gentleman Gustaf, of course LW loses to Phantom Dancer at 0 armor. Its main stat is Armor Penetration!
Ok, fair enough, but you have to go to 63 armor to break even with MF:
79 for Sivir:
89 for Graves
92 for Ezreal:
110 for Tristana:
111 for Ashe:
138 for Caitlyn:
You'll notice three champions left off of this list, Corki, Kog'Maw, and Vayne:
This is because on these champions, the breakeven point is unreasonably high or non-existent. To reach a break-even point where LW beats PD on Kog, you have to assume an average enemy health of under 2500. This is somewhat misleading, as your W will not always be up. On Vayne and Corki, because of the true damage, no amount of armor can cause LW to beat out PD. In fact, past a certain point, more Armor makes LW a less palatable choice, simply because the amount of true damage you are getting is far outstripping how much physical damage you could gain.