Ugh, I did some math and brought some different Ideas for many posts regarding the new Ezreal. I am acutally really excited to see him on the rift with his new W. He may be a healthier AP EZ then ever before. I will share this post below. Also I do not understand 1 thing, why does he have to be AP mid, I mean he could be hybrid or AD mid with this new ability. you will see what I mean below.
Dude you are too focused on the "AP" part of Ezreal. AP Ezreal will still be viable, but what you are not looking at is hybrid or Double tear Ezreal will be absolutely disgusting. I am even thinking it would be broken strong and will have to be tuned down. with his New W he gets mana sustain, and high single target damage just thinking putting the numbers alone here lets look.
Old EZ Lvl 18 with just Lich Bane
ATTACK DAMAGE 102.5
Lich Bane - 80 AP - 75% base AD + 50% AP (76.875 + 40) 116.875 damage
OLD W rank 5 - (250 + 80% AP) (250 + 64) 314 damage
Q Rank 5 - 115 + 110% total AD + 40% AP (115 + 112.75 + 32) 259.75
Total combo - 116.875 + 314 +259.75 = 690.625
New EZ Lvl 18 with just Lich Bane
ATTACK DAMAGE 102.5
Lich Bane - 80 AP - 75% base AD + 50% AP (76.875 + 40) 116.875 damage
New W rank 5 - (255 + 60% bonus AD + 40% AP) (255 + 32) 287 damage
Q Rank 5 - 115 + 110% total AD + 40% AP (115 + 112.75 + 32) 259.75
Total combo (Q damage + Lich bane and W proc) - 116.875 + 287 +259.75 = 658.625 damage
Now looking at this with 80 AP with the Lich bane you only lose 32 Damage. What you haven't though about was how much better his lane will be. He gets a refund on mana, and now AP Ezreal scales really well with Gun blade I want you to look at this. This would Make AP ezreal able to sustain in lane no problems.
Old EZ Lvl 18 with just Gun blade
Base ATTACK DAMAGE 102.5
Gun blade + 40 AD and 80 AP
Total AD 142.5
Total AP: 80
OLD W rank 5 - (250 + 80% AP) (250 + 64) 314 damage
Q Rank 5 - 115 + 110% total AD + 40% AP (115 + 156.75 + 32) 303.75
Total combo - 314 +303.75 = 617.75
New EZ Lvl 18 with just Gun blade
Base ATTACK DAMAGE 102.5
Gun blade + 40 AD and 80 AP
Total AD 142.5
Total AP: 80
New W rank 5 - (255 + 60% bonus AD + 40% AP) (255 + 24 + 32) 311 damage
Q Rank 5 - 115 + 110% total AD + 40% AP (115 + 156.75 + 32) 303.75
Total combo - 311 + 303.75 = 614.75
That is a total loss of 3 Damage from 1 combo, and you now have passive sustain from W for mana and heal for all damage dealt.
For AP ez I would recommend
Starting either + or or or
With mana not being as much of a concern as there was no mana refunds on EZ's you can build much differently
I would go with either or (I wonder if Luden's Echo Passive procs new Ezreal W)
Full build I would think
Although This Build would probably be disgusting for AP ezreal for straight damage with the AD and AP scalings.