Vayne Mechanics!

Bad Vayne Built Phantom Dancer

I can't even tell if I'm a bk scrub noob anymore. A mere six months ago you could safely mock anyone who built Zeal or Phantom Dancer first on Vayne. What point was attack speed when you had no damage to back it up? You have to start Bloodthirster, I was told, it's the only viable option given her low range and survivability. And yet now you see (predominantly Asian) teams frequently starting with a Phantom Dancer on Vayne and even maxing Silver Bolts first, both of which go against the strongly ingrained habits of Western players. So what's the motivation behind each build path, and more importantly (to me), what do the numbers say on the comparison?

Basic Justifications

So what is the rationale behind each build? Completely ignoring numbers here, a Bloodthirster is commonly built because Vayne is quite short ranged and will have to be within range of taking damage in order to deal damage. Therefore we'd really like to build a lot of lifesteal on her so we stay alive in teamfights and can sustain through the inevitable poke we'll weather while CSing. Besides that, a maxed Tumble gives +50% AD as bonus damage on a tiny 2s cooldown and Condemn scales hard at 1.0AD. Both of these skills give further motivation to get an early Bloodthirster. 

The most common Bloodthirster build path is simply two Doran's Blades and Berserker's Greaves into a Vampiric Scepter, B.F. Sword, and finally Bloodthirster. This mimics the exact same path other AA based AD carries will go when building Infinity Edge, but Bloodthirster will be completed long before IE and give a power spike over the opponent. A Phantom Dancer basically has to follow the BT - no other item gives as much damage per gold after a BT. After that you'd typically go Last Whisper for the armor penetration or get a defensive item to stay alive. This path does put Infinity Edge as the sixth item, which is slightly tragic since IE is by far the biggest damage boost of any item. 

The contender is Phantom Dancer. Here you trade off lifesteal and attack damage for movement speed and attack speed, with many arguing that the more frequent/easier stacking of Silver Bolts on enemies compensates for the AD loss. Phantom Dancer is certainly a different approach to survivability in fights - rather than assuming you'll take damage and have to sustain back through it, Phantom Dancer opts for movement speed that can help avoid the damage. There is an unquestionable benefit to being able to kite more easily, reposition quickly in teamfights, or even travel to lanes/camps for more expedited farming. 

If an advantage of BT over Infinity Edge is that it is purchased more quickly, then Phantom Dancer gets another point going for it. Building Doran's Blade + Berserker's Greaves + Vampiric Scepter into a Zeal and a Phantom Dancer will be completed with less gold than any other common starting path. Phantom Dancer also has the benefit of being flexible for future options - even Infinity Edge is viable after PD if you're quite fed and have a lot of gold income. 

Calculation Corner

First to make it very clear what item builds I'm comparing two level 11 Vaynes that have the following item builds:

• Bloodthirster Vayne
• Items: Berserker's Greaves, Doran's Blade, Doran's Blade, Bloodthirster
• 25% Attack Speed
• 80 to 120 Attack Damage
• 18% to 26% Lifesteal
• 160 HP
• Cost: 570g + 475g + 475g + 3000g = 4520g
• Phantom Dancer Vayne
• Items: Berserker's Greaves, Doran's Blade, Vampiric Scepter, Phantom Dancer
• Season 2 Stats: 
• 80% Attack Speed
• 10 Attack Damage
• 13% Lifesteal
• 30% Critical Strike
• 12% Movement Speed
• 80 HP
• Cost: 570g + 475g + 450g + 2845g = 4340g

AFK Autoattacks

The starting point of the comparison will simply be the damage per second when autoattacking the same target with no skill usage. My friends will know this is my favorite number to tout when comparing builds simply because it is by far the easiest to calculate. Factoring in critical strikes as an averaged out bonus damage, the equation is simply

AS*AD(1+(crit_damage-1)crit_chance)

Well this is interesting. The "Autoattack Damage" column confirms that 30% critical strike does not add more power to your autoattacks than 60-100 attack damage. But the final column shows that the increased attack speed from Phantom Dancer makes your weak and puny autoattacks add up to pretty much the exact same damage as an unstacked Bloodthirster.

But what should really bake your noodle are the values with Final Hour activated. Critical strikes get better and better the more damage you've already built, and Final Hour gives her an extra 40 attack damage. With her ultimate, Phantom Dancer suddenly way outdamages an unstacked Bloodthirster and approaches (ninety-seven percent!) the damage of a fully stacked Bloodthirster. She has 10 seconds of God Mode. I've maintained that the activation sound is the scariest sound in the game and this just backs me up even more.

As a small diversion before continuing to skills, lets picture Silver Bolts as a two-component move. Imagine you max out Silver Bolts when building Phantom Dancer and are a mechanical prodigy when it comes to getting the 3rd hit on targets. You'll now do an extra 60 true damage every three attacks, so we can say the first component of W is 20 true damage on hit. The second component would be the %HP damage, but that just introduces yet another variable into the equation and I'll defer that mess until later. The interesting thing about true damage is that it's armor independent, so there should be an armor value where Phantom Dancer outdamages even a stacked Bloodthirster. In comparison, a Q-max BT build would only have three points in W and would deal 13 damage "on-hit". Math math away! 

Without her ultimate, a Phantom Dancer Vayne does less damage than a fully stacked Bloodthirster to a target any amount of armor (sorry, the AD delta is too big to overcome). However, with Final Hour on, the cutoff moves to... basically zero. For those 10 seconds of destruction, a right-click only Vayne with PD will always outdamage her BT brethren. Sure, this is an unrealistic scenario with no abilities and no %HP, but it's cool anyway and goddamn it it's my blog. I'll math what I want.

Combos Complicate Everything

For this section, I consulted my Vayne expert who told me that Vayne's whole ability sequence is AA -> Tumble -> TumbleAA -> Condemn -> AA with the E stunning the target against the wall for the bonus damage. I'm interested in comparing this killing burst combo between the two builds, as well as a standard Vayne trade of AA -> Tumble -> TumbleAA -> AA. These two comparisons along with the AFK autoattack values from above should be enough to roughly compare the damage output of the two builds. 

It's really not too hard to compare the kill combo. The three autoattacks' numbers can be pulled from the earlier tables, the Tumble bonus damage is AD dependent but cannot crit so it doesn't play weirdly with Phantom Dancer, and Condemn is a simple 90+1.0AD. Here, I'm assuming that PD maxes W and has three points in Q by 11 and BT maxes Q and has three points in W by 11.

Well that looks bleak as hell for Phantom Dancer. The "Reduced Damage" row is how much damage a 70 armor target would take (except for W procs all of this damage is physical) and "Total Damage" is the armor-reduced physical damage plus the true damage from the W on a 1500HP enemy. The choice of 70 armor and 1500HP is pretty arbitrary, but trust me when I say that PD basically never breaks even with an unstacked BT in this full combo. You won't approach the same damage levels until you're hitting a 3000HP 200 armor tank with your ult on. Vayne just has less bursty kill potential by going Phantom Dancer first because her Q and E scale so damned hard on attack damage.

The one extra thing to note here is that PD Vayne will get this whole chain off a little faster because of the increased attack speed and might squeeze another AA in within the same time window. There's no way to know if this actually happens without knowing the cast/animation times of Q/E so if you're that interested go to some in game tests. Attack speed does quicken it but my gut says you won't outdamage BT even with an extra autoattack.

Finally, what about the quick trade sequence of one Tumble and enough autos to get a W proc? The gap should lessen between Bloodthirster and Phantom Dancer here because we're eliminating a 1.0AD scaling ability by not including the Condemn. Shooting the same 1500HP 70 armor target dummy, we get: 

As predicted, the delta is less although BT still wins out even when unstacked because Tumble hits like a truck. Similar to the kill combo, this will be overall faster with the Phantom Dancer because of attack speed, but this is nigh impossible to really quantify. 

Conclusion

I would say that either build is truly an option (what a bold statement!). Each has strengths in different areas and caters to a different style of play. A Bloodthirster build deals significantly more damage in a burst combo. If your support is capable of setting up opportunistic wall Condemns then getting a Bloodthirster will likely lead to many kills before teamfights even break out. The BT build will take towers more quickly (since you cannot critically strike structures) and does have higher sustain if you're forced to endure high levels of poke from the opposing laners. 

The Phantom Dancer build churns out a surprisingly high amount of damage, but the saving grace of that damage is coming from critical strikes. If you're prone to quick AA pokes here and there while farming, then Phantom Dancer is likely better than Bloodthirster. You'll get it sooner, the movement speed quickens farming, it takes large objectives like buffs/Dragon/Baron at the same speed, and with ult you can immediately match the damage of even a stacked Bloodthirster. Kill potential is admittedly quite lessened and your potency in jungle fights drops, but if you're with a support that aims to keep you nice and safe rather than get you a ton of kills, Phantom Dancer isn't bad. Bonus points if you're with a Lulu or Janna who can lend you on-hits or extra AD to synergize with PD's AS even more.

Both will play out quite differently in teamfights and aspiring Vaynes should try both before really settling on a build (or better yet, build for the lane in that particular game!). In any case, the numbers make enough sense that I should really stop ridiculing those who build attack speed first. Curse you older Leaguers who made me think that was so dumb!