I will start out saying that this build is for confident Ahri players only. though this is not a standard build it can be put to great use by those who maintain it.

just a few corrections/additions i feel need made
-After achieving full Arch Angels Staff, your mastery health/5 and base health/5 adds up to 36.46 health/5
-the actual Ability Power after Arch Angels staff and Rabadin's is AP is about 644
-actual movement speed with Lich bane and masteries is is 408.75
-and Cool-down reduction will be 38.83% at the end

This build is centered on creating a great mid-late game with Ahri.

At the beginning the large Cool down buff you get from your runes and masteries can be put to use using your orb to consistently harass the enemy/enemies in your lane, while you are particularly squishy at level one, this is fixed once you level up. During Mid game you want to be targeting the enemy champion over minions to try to force a recall so that you can be ganking bottom and top lanes. In late game you want to poke at the enemy as much as possible. Then during team fights you will want to hang around the outskirts harassing the enemy team without using your ult. Once the fight is coming to an end, you can decide whether your ult would best be used to chase down enemies or to escape. Keeping in mind your Flash summoner spell.

The Runes i picked are based heavily on early game poking, but the downfall is that is relies on base damage, while the magic penetration counters some of it, it is not entirely full proof. as i said in the begining, THIS IS FOR CONFIDENT PLAYERS ONLY.

The masteries are based around cool down reduction, together with runes you will have over 20% CDR at the beginning of the map, which will make mana regeneration a necessary at the beginning.
The other part that is key is the Movement, this will help Ahri stay up with other champions as well as get away.

The items are built to give early mana regeneration with tear of the goddess, at this point depending on how frequently you back the build can be different, you might be able to grab an early Death-cap which is great for early AP as well as allow you to build through your build quicker with the increased farming ability. The build will focus on a lot of late game AP, this particular build took me a while to get down, but now allows me to dominate the field.

addition item stats:
Deathfire grasp active: 30+ 21= 51% of a persons current health in Magic damage end game

The skill sequence is a typical build, mastering Orb of Deception first to maximize poking damage, and keeping the rest balanced, Charm normally will be taking priority over fox-fire, and can be up to two levels ahead of Fox fire if necessary, though some circumstances may require you to put more points into fox-fire earlier. This will allow you the most poking potential early and mid game.

Flash is used as an escape tool, occasionally it will be used offensively. This is a key for Ahri considering her low base movement speed.

Clarity is used to counter the early game lane sustain. though it is often used mid and late game as well during team fights

In this build you focus mainly on lane sustain in the early game. This build will also allow for maximum late game A.P. output. Items can be used to a large advantage in this game, if used correctly, it will take a heavy toll on enemy teams during team fights.