This guide will not deal with how to play Ezreal, since that is covered in better guides such as Hare Hare Ezreal and this guide could not even compare to such guides. Thus it will talk about what those guides do not deal with as well as my opinion of AP/Hybrid Ezreal.

AP Ezreal! In the past, this was the "correct" way to play Ezreal, but nowadays AD is considered the correct way.

The truth is, both are almost identical!

Ezreal's skill, Mystic Shot (Q) deals physical damage regardless of how you play him.

After obtaining Lich Bane, the damage of Mystic Shot increases drastically, as it both scales from 0.2 per AP AND the total AP Ezreal has.

The reason the Armor Pen Mark is still included, even though this guide is about AP, is because the same reason stated as above, this Mystic Shot deals physical damage.

Since Mystic Shot will be the primary source of damage Armour Pen is still the primary Rune that you will need.

You can change the Quint for something different, but since rest of the skills are Magic Damage, and this guide deals with AP, Magic Pen will be useful.

The reason behind the masteries is the same justification as the reason for the choice of runes.

If any does not suit you, please feel free the change them to your own accord.

Pros of AD:

Very sustainable through early and mid game
Q scales higher with AD, which is the primary source of damage
R also scales with AD with benefits in team fights or other situations
The players also benefit from the passive, which increases attack speed.

Cons of AD:

Rest of the 2 skills, W and E does not scale with AD
At late game, damage output is significantly lower than AP

Pros of AP:

After Lich bane, Damage output is very high
AP scales with all 4 skills
Late game damage output is higher than AD

Cons of AP:

Not sustainable in early game to utilize maximum damage because of lack of Mana
Passive is highly ignored

The item choices utilizes both Pros of early game sustainability of AD in early game and damage output of AP in late game

The Wiggles Lantern allows the player to ward their own area, and lets the player sustain on his own during the early lane phases much like AD

Obtaining Sheen increases the damage output for Mystic Shot until it finishes building in to Lich Bane.

Buying Archangels Staff increases the total mana and mana regen; at this point you can spam as many skills as you want, and still have enough mana left over.

Rabadons Death Cap is the next obvious choice

The reason behind the Hextech Gunblade, is because it is a huge increase in the damage output for Mystic Shot (127 more damage from Lichbane passive + AD scale + AP scale) as well as giving spell vamp to heal from W, E, R, and lifesteal for Q.

The last item is really an option, you can keep your wriggles lantern till the end, or buy a bloodrazor to increase damage. Another item you can choose from is a voidstaff/abyssal sceptor to deal more magic damage with the rest of the skills, or Morello's Evil Tome to maximize cooldown reduction if you cannot secure a blue buff.