League of Legends (LoL) Question: ADC items

Twitch, Caitlyn and Ashe are about the only carries who rush Infinity Edge. The rest of them is supposed to rush Bloodthirster. BotRK has been nerfed too much to rush it; the only champion who can still do that is Tristana to fix her godawful mid-game though I'm no Trist expert so I can't be sure.

Generally those champions who have great AD scalings rush BT and those who are more auto-attack reliant rush IE. Varus and Draven are examples who generally rush BT because they have great AD scalings.

Bloodthirster provides a high amount of AD, making it ideal for champions who may spam AD-scaling spells, and provides plenty of lane sustain with its lifesteal. Most people will build the Vampiric Scepter early for lane sustain.

Infinity Edge is normally a third or fourth item on any ADC that isn't Ashe (who may get it as their second item on occasion). While increased crit damage is nice, you really need increased attack speed and crit chance first, which makes it a follow-up item for Static Shivv or Phantom Dancer.

Blade of the Ruined King works well with champions who scale well with attack speed ( Twitch or Varus) or if the enemy is stacking a lot of HP via a tanky jungler and bruiser top. I would consider getting Bilgewater Cutlass or at least a Vampiric Scepter early if you plan on building Blade of the Ruined King and then finishing it after the enemies have stacked their health.

Phantom Dancer is a good item for kiting champions, as its passive lets you avoid unit collision and it has a natural movement speed bonus. There's no reason not to build it unless you prefer using skills to attack opponents (in which case, an attack speed and crit chance bonus is useless).