This build focusing on playing ezreal the cool way, which is the AP way.

If you're used to AD ezreal, this wont be much different because your Q's will still be doing tons of damage with this build. But on top of that you'll also have tons of damage on your W and tons of damage on your ult, as well as full CDR. (well, 39% but close enough)

Try it out, and you'll see the amazing damage you do.

This guide may look a little boring, but I'm short on time, so I'll make it short and sweet.

Your core item is your Lich Bane. Like TriForce or Iceborn Gauntlet, it will proc on your Qs, meaning each Q you'll be shooting will deal 50+75% AP. Unlike TriForce, which deals 200% of your BASE AD, Lich Bane scales with your current AP. This means that while TriForce dmg stays constant, Lich Bane dmg will increase as you increase your AP. Also, it gives you AP, mana, and movespeed.

tl;dr
Lich Bane > TriForce

Next item on the list is Nashors Tooth.
This will overcome the barrier of other AP ezreals not being able to farm easily. It gives you attack speed, CDR, and bonus magic damage on your autos (which include your Qs).

tl;dr (this one was short you lazy bum)
Nashors = Bonus magic damage

Now, to sum it up, what does this all mean?

Ezreal's Q (lvl 5): 115 + 100% AD + 20% AP
Bonus:
Lich Bane -> 50 + 75% AP
Nashors -> 15 + 15% AP
Spellsword Mastery -> 5% AP

Total - 180 + 100% AD + 115% AP
PER Q, with a CD of 4+CDR (if these are the only two items you have it would be a 3 sec CD; with Ionian Boots, it would be 2.44 sec CD...(If you land those Q's though, the CD will be 2 sec or 1.4 seconds. 1.4 seconds!)

Now lets say these are the only two items you have (besides tear for mana and dorans blade from start), which is likely during midgame due to the high costs.

Each Q will do: 180 + 111.2 + 196.8 = 488 damage on 3 sec cooldown (if the Q lands, it'll be a 2 second CD)

Now later in the game add a Rabbadons Deathcap.

180 + 111.2 + 439.4 = 730.6 dmg. This is with EACH Q.

You get the idea, so I wont put up more calculations for the other last items.


!!!!!!!!!!!!!!
BASICALLY:
With Ionian boots, Lich Bane, Nashors, and Rabbadons, you'll do 730 dmg on a 1.4 second cooldown!!!!!
!!!!!!!!!!!!!!


But this whole time I talked about only the Q, which would start doing massive damage. But your W would be doing equally huge amounts of damage with this much AP, not to mention your ulti.

So basically, by building like this, each one of your skills will do tons of damage on short cooldowns.