Hi, I'm russvz. I've done some mathcrafting and taken in advice from some forums and have determined some of the optimal Vayne build paths. Note that this is more for my own reference than an actual guide.

AD marks, Armor seals, Magic Resist Glyphs, and AS Quintessences usually (although I don't have this exact setup).

Standard ADC, or 24-6 liftlift style.

1. Statikk Shiv can replace a PD, but only if wave clear is desperately needed. A large amount of damage is sacrificed.

2. I don't know how actual defensive items would play into her build paths. That's not usually how Vayne is built, but it is necessary sometimes. You make the call in the meantime!

3. Do not replace a Phantom Dancer with Last Whisper! You will do less damage in every single circumstance. I calculated this myself and this has been calculated elsewhere. The only case where Last Whisper is even equal in damage is against a case where I tested 2540 HP and 320 Armor, Vayne's worst setup (Low HP, High Armor). And it was only even. A second Phantom Dancer is always better than replacing with LW, you will do equal or more damage always.

1. Why is Last Whisper not absolutely necessary? Because of Vayne's attributes, with two phantom dancers, last whisper will not always bring grossly higher damage. For example, with IE, PDx2, BotRK, and Boots, having BT will only bring ~100 less DPS across the board, from ADC's to Tanks. 20% more lifestyle is arguably going to be usually better.

2. TriForce will supply much more damage to Vayne (~150 DPS, not including Trinity Procs of 218 Damage) than just boots, but at the expense of movement speed. Max damage build will have 390 movement speed with 10-30 extra from Rage passive, which is somewhat hard to justify being worth it. Boots with furor enchantment will give 452 movement speed on hit if one has 2 phantom dancers.

4. Why no Youmuu's Ghostblade? The window for Youmuu's is simply too low, and creates inconsistencies in her play. You can get armor pen in better ways, and attack speed in better ways. Who cares for Youmuu's when you have 2.3 Attack Speed with 400+ AD when ulting?

You will notice that this guide does not specify any specific build paths. That's because her build paths are amazingly varied and there are many viable ways to play her (builds 1-8), taking into account 10/20/30% lifestyle, high or lower mobility, and CC countering. As a final note, here are her highest damaging builds that I tested, with the most damaging at the top. I did not test every single possible build; that is not entirely necessary to notice patterns.

1. IE, PD, PD, LW, BotRK, Tri 1120 DPS Placed Higher than 2 - Higher AS, BotRK
2. IE, PD, PD, LW, BT, Tri 1133 DPS
3. IE, PD, PD, BT, BotRK, Tri 994 DPS
4. IE, PD, PD, BT, MS, Tri 994 DPS
5. IE, PD, PD, LW, BotRK, Boots 954 DPS Placed Higher than 6 - BotRK
6. IE, PD, PD, LW, BT, Boots 975 DPS
7. IE, PD, MS, BT, BotRK, Tri 800 DPS Placed higher than 8, 9, 10 - Tri Procs, BotRK
8. IE, PD, PD, BT, BotRK, Boots 854 DPS Placed Higher than 9 - BotRK, Higher AS
9. IE, PD, PD, BT, MS, Boots 860 DPS
10. IE, PD, LW, BT, BotRK, Boots 809 DPS
11. IE, PD, MS, BT, BotRK, Boots 710 DPS

This data is for raw auto attacking DPS. Q and W damage was not included. Thus, higher AS was prioritized due to W and BotRK damage. Higher AD was not prioritized because this was a later-game calculation, and tumbling around isn't preferred unless you need to. The DPS was calculated off of an average over 3 cases: 205, 140, and 90 armor. I omitted a 320 armor case as that is rarer, and it did not change DPS rankings in any situation. Overall, take this ranking with a small grain of salt; I had to make some educated guesses in regards to TriForce and BotRK, although I think it should be pretty solid.