Vayne ADC starting BotRK is terrible
Disclaimer: I am not a 'Vayne main'. I do not regularly play Vayne, and from my memory I have not played Vayne since 2016. I do, however, consider my experience in the game since July of 2012 to be worth the lot of you stopping here to understand where I am coming from. I am also bronze 3 currently, my highest ranking only being silver 5. The statements you are about to read and have read from the title are opinionated (although coming from my own experience and match history logs) - I hope that Vayne mains and higher ranked Summoners will come here to shed some light on Vayne starting BotRK and what is required to make this option work i.e. composition of champions, expectations, and pure skill - whilst using the item.
Vaynes  starting BotRK  - why? I have lost every game where a Vayne has started BotRK. I see this happen time and time again. With Vaynes' passive "W" dealing true damage every 3rd hit, why would you build an attack speed item first? It would make more sense to use your "W" passive in combination with already dealing high amounts of damage early on.
Even though I say it is a terrible starting item I am not saying that it should not be the first item that you complete. My goal is to raise awareness that damage on an ADC is of utmost importance. Buy a short sword if you have to back with a minimal amount of gold, but please, please do not recall to purchase double daggers early in the game. The best route in my opinion is to try and start with a B.F. Sword or a Pickaxe, and then you start to build BotRK with cutlass first. This will help you to manage your lane if you are against a hard pushing enemy. It will also help you to deal modest damage with quick pokes to the enemy without needing to rely on stacking "W" to the third hit.
Another key point is to be aware of the enemy. Not many champions that you will encounter bot-lane have high enough armor, or health stats or tank stats in general, to force you to rely on stacking your "W" for true damage. Being that your passive "W" and BotRK are necessary to shred tanks, think of what scenario you would need armor-piercing true-damage. _Definitely not for a kai'sa and a blitzcrank who starts ancient coin._ (You know who you are, and I'm certain you lost that game).
The math was:
vs IE
, no runes) VS. Lvl 5 Xayah (no items, no runes)