Dorans Blade
In season 6 Dorans Blade got buffed, due to the big Marksman Update.
Right now it proves to be the best starting Item for every ADC, including Ezreal.

Bonus HP will make you tanky.
Will make last hitting easier.
Getting some sustain with the 3% Lifesteal.

Look at the complete Core
In season 6 nothing much has changed, except due to the cost reduction of Last Whisperer we will get our Armorpen a little bit sooner. We are still hitting like a truck and with the new LW Upgrades every hit will make the game for your opponents harder.

Why would we build this instead of a normal ADC build?
This Build will give us a lot of Cooldown Reduction, therefor we won't Auto Attack much.
We normally will sit back and spam our Mystic Shot over and over again, until we fell comfortable enough to all-in.
It brings Soft-CC to Ezreal who usually doesn't have CC at all.
In Teamfights the enemy team will be perma-slowed due to Iceborb Gauntlet as long as you hit your Mystic Shot.

Its is more a "kite" build against literally anyone who tries to kill you. You are easily able to kite them and still deal a lot of damage.

When Muramana is active, your Damage is incredible.
Usually Blue Ezreals DPS is "lower" then Normal ADCs Ezreals, but he has to be close to his target in order to do so.
Blue Ezreal can stay far away from his opponents and push in for damage, sometimes more damage (not DPS) then Normal ADC Ezreal, because you are unable to get caught where as Normal Ezreal can easily get CCed, because he relies on his still "close ranged" Autoattacks.

Your Ultimate has a really low cooldown, so don't hesitate to use it to get farm from lanes that are far away.
Every time you hit your Mystic Shot, the Cooldown will be reduced by one second,
sometimes you are able to cast your ultimate two times in a teamfight..

Compared to a usual ADC Build its much cheaper, gives more survive ability and still a surprisingly good amount of damage.


Can "Noobs" build this?
Well this build is completely based of Ezreal's Mystic Shot, so it is not recommended for "unskilled" Players, because its pure based on hitting Skillshots.
Practise Ezreal in a custom game, once you get used to his Kit, you should be able to easily adapt to this Build.

Ionian Boots of Lucidity:
T get more Cooldown Reduction so that Mystic Shot can be spammed. Although your other Abilities will come up sooner.
It is necessary to hit the 40%/45% CDR.

Manamune/Muramana:
Attack Damage increase.
Infinite Mana.
If fully Stacked a massive Damage increase (if it is activated).

For Blue Ezreal this is one of the Key items through out the entire game. Not only provides Manamune infinite Mana, but once its evolves into Muramana, it adds a lot of damage to Ezreals Mid-Game Damagespike.

Iceborn Gauntlet:
Cooldown Reduction.
Sheen- Effect to increase the Damage of Mystic Shot.
Mana increase.
Slow Effect, Perma Slow = Ability to Kite much better.
Armor Increase.

This item is basically a utility, defensive and an offensive Item combined.
Iceborn stat wise, only gives defense and utility.
Which are Armor, Mana and CDR. Iceborn increases the damage of Mystic Shot due to the Sheen-Effect, Sheen is an On-hit effect, therefor it procs on Mystic Shot, our main ability.

On top of all the defense and utility stats, it offers another defensive/utility effect.
The slow on the sheen empowered autoattack, which procs on Mystic Shot as well.
In conclusion: with the low cooldown on Mystic Shot and the slow effect from Iceborn, PLUS the stats this item gives, it is well rounded in terms of offense, defense and utility and is pretty much one of the most important parts of this Item Build.


Lord Dominik's regards:
Attack Damage increase.
Armor Penetration will help to kill Targets with a lot of Armor (over 150 Armor).

This is really important to keep our damage up when our opponents starts stacking armor, if you want to continuously deal damage against your opponent, you have to build this item.


Banshee's veil:
More HP.
Increases Magic Resist .



Mercurial Scimitar:
Attack Damage increase.
Lifesteal Increase
Cleanse is sometimes necessary to stop or negate the damage of certain champions, if this is the case Mercurial Scimitar is the choice to go.

Guardian Angel:
Armor and Magic Resist increase.
Buy it if you get focused in Teamfights.

Marks

Flat Attack Damage
AD Marks are the staple choice on ADs/Marksman, they help with last hitting, they increases your overall damage output and they help you to be relevant in the early stages of the game.

Seals

Armor
These Runes do a lot of work for you, especially in the early levels. Making you take less damage from Autos/Monsters/Turrets or Minions. They are great overall and make you have an easier time.

Glyphs

Flat Magic Resist/Attackspeed
Some MR is useful if your opponents will deal Mixed Damage/Magical Damage (kog'maw,corki)
or their support will poke you a lot with magic damage (zyra,morgana).
Running Full MR Glyphs can be a good option versus tripple AP comps (Mid/Jungle/Top), generally it is recommended to run 5 MR Glyphs plus 4 Attackspeed Glyhps, as this will provide enough MR to stand against the Magicpen Marks most AP Champions use, while still making your runes be more effective stat-wise.

Quints


Attackspeed
Even if Ezreal is an AD-Caster Type AD-Carry, he still auto-attacks a lot regardless of what build he uses.
Attackspeed Quints do much more work in this regard then AD Quints do, as your gameplay feels much more fluid with AS Quints, then with AD Quints.
It also allows for playing more aggressively, rather then staying back and poking with Mystic Shot.

Ability Explanation

Rising Spell Force:
Rising Spell Force is a pretty strong Attack-Speed Steroid, it can go up to 50%, making it one of the best self buffs in the game. It helps Blue Ezreal quite a lot, as Blue Ezreal tends not to buy any Attackspeed early in the game.

Maintain this passive by using your abilities at the right time is key on Ezreal, to make use of this passive effectively.

In between ability-casts you have enough time to sneak in an extra Autoattack or two, resulting in more overall damage, this is especially usefull in close combat and when kiting.

Also Rising Spell Force has different usages.
One of them is checking brushes, or areas where you don't have vision.
Shooting one of your abilities inside the brush or the fog of war, where you expect your opponents to be, is a key strategy on Ezreal. If you gained a stack of Rising Spell Force, it tells you that someone is inside.


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Mystic Shot:
Your main ability and pretty much the reason why the Blue Build exists.
It has a good AD-Ratio, it has a low cooldown, which gets even lower when you hit it (the cooldown of all your abilities gets reduced by one second if you hit it).

But the most unique thing about this spell is:


It procs pretty much all on-hit-effects!


The exception being, it cant crit. However we aren't building any crit, so not a big draw back.

Pretty much all the items we build are involved to support this ability. Lifesteal, Sheen, Muramana everything is great for Mystic Shot.

Mystic Shot is treated as a bonus long range Autoattack, attacking continuously and casting Mystic Shot in between Autoattack is the most common usage.
It makes Ezreal one of the safer ADC as it has a really long range.


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Essence Flux:
Back in the day this Ability was never considered worth putting one point in it.
Even now people still debate, if it is good to put one point in it or not. My recommendation is, puttin in a Point into Essence Flux at level 4 is really good as an utility tool and early game harassment.

The attack speed buff is good for taking down Turrets, Dragons and Barons quicker as a Team.
Not only for this sole reason, but it also helps keeping your Passive stacked up while there are no target to hit with your Mystic Shot.

Early on, around the levels 4-6, you can still use it as a harassment tool. The Manacosts are mediocre and the base damage is good, using Mystic Shot and following it up with an Essence Flux is great for early pressure.

One of the most unique ways to use Essence Flux is, to Arcane **** into it.
You gain +20% Attackspeed from it making you attack faster and therefor taking objectives down quicker.
Even if it is used really rarely, this trick is great for an all in combo as it can surprise people off guard.


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Arcane Shift:
Pretty much the best Ability to escape, reposition or simply kite.
The only down side is, that it has a fairly long Cooldown early on.
With enough CDR and putting multiple points into it, Arcane Shift should be back up after landing one, or two Mystic Shots, making Ezreal one of the hardest ADCs to chase.
Its even better then Flash, because it has a higher range and it even denies the "all mighty Blitzcrank Hook".

Arcane Shift primarily will be used defensively, but it can be used for All-Ins as well.
Don't underestimate its damage, especially in the early levels.



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Trueshot Barrage:
Trueshot Barrage is a really important part of your kit and it should be your main priority to land a good ultimate in a teamfight. Landing a devastating ult in a teamfight can solely decide if your team wins the fight, or not.

Your teams position, your opponents team position and your Teams mass CC, these are the important factors to land a good Ezreal Ult.

If you are new to Ezreal and you feel uncomfortable in landing a good ult, I can give you the advice that shooting your ult slightly before a fight breaks out, is pretty good as well. You deal some damage to your opponents team frontline and you usually gain 5 Stacks of your passive right at the bat.

Sona:
Awesome Auras for Ezreal.
Heavy Magic damage Poke.
Their Ultimates work great together.
Great Sustain.

Taric:
Armor increase will make Ezreal even more tanky.
Provides Sustain.
Low Cooldown Stun, so Ezreal can land Skillshots.
Deals a good amount of damage with his Passive

Leona:
CC Lock so Ezreal can land Skillshots.
Passiv will proc with Mystic Shots and ofc with the Ultimate.
Agressiv Lane/Kill Lane.

Nami: (BEST SUPPORT FOR EZ!)
You get a lot Sustain with her Heals.
Her CC will help you to hit Mysticshots as well as your Ultimate.
Her Ultimate synergies really good with your Trueshot Barrage.
Her E will proc on your Mysticshot.

I prefer to hear music while I play League Of Legends(lol) and this is what i prefer to hear when I ma playing Ezreal:

https://www.youtube.com/watch?v=HFKtYCcMWT4