You may think I'm insane.

Lack of a Phantom Dancer, lack of a Runan's... Lack of several "core" item sets.

This is a different playstyle Ashe, that still allows her to do massive amounts of critical damage, but while allowing chase. My playstyle varies much from the standard ashe realm, and I have managed to get a quadra out of this build. I focused this build around Ashe's chase and Kite abilities, Furor allowing her to poke you with her Q active, and run away just a bit faster, and her flash being able to be saved by using Youmuu's 'ghost' active. This allows for a lot more escapes, and a lot more damage.

Keep in mind, Ashe's W has a 100% ad ratio. This, paired with Static Shiv's critical ability, and Youmuu's 10% CD reduction, allows for an incredible amount of team-wide damage when in teamfights. The single-target capabilities of Furor and BLOTRK allow you to quickly blast away even tankier foes, such as Olaf. An Olaf with a Randuins, Frozen Mallet, and a Warmog's Armor wasn't enough to kill me from the sheer damage I dealt out. The auto-attacks quickness, paired with the 12% life-steal and 5% current health damage allowed me to steal more health from him than he could deal back. I did get in a pinch with low health after a teamfight where Olaf and I were the only ones alive, and Youmuu's ghost and a well-placed flash landed me a kill in enemy jungle.

This isn't your standard "Sit-back and crit" build. It's based around /extreme/ awareness of you, and your lane-mate's capabilities. If your support is a sustain support you may benefit much more from a different build, but a Blitz, Thresh, or Taric support might benefit much more-so, due to the time the enemy is locked down and you chunk them while they're immobilized.

This is designed for experienced players. Players who know when, where, and how to use their Ulti and Hawkshot to ensure kills. Your W is a massive portion of damage, and using it relies on your knowing where the enemy is. It's risky if your team doesn't know ward-coverage well.

All in all, choose a build that fits, and works, for you. Never try to fit into a build's playstyle.