This is not a guide. The only content here is number crunching. This is an exposure-test to determine community feedback regarding the build and purchase order. I wanted to open up discussion about the itemization and math behind it to help improve the actual still-in-progress guide for this build
This is not a build for Bot Lane ADC Ezreal
This is not a build for AP Mid Ezreal
This is a build for Mid Ezreal assuming you already have an AD Carry going Bot Lane.
Most of the damage dealt early game will be physical but by endgame most of it will be magic damage due to Muramana's toggle effect doing magic damage.
Early physical damage is good mid as your lane opponent more than likely focused their runes / masteries for MR rather than Armor. It also allows you to farm with ease during laning phase.
Your damage begins to convert to magic damage after Manamune upgrades to Muramana. This is also good because in Season 3, MR is more difficult to itemize for on the majority of champions. This also helps to ensure that your team composition has a balanced damage source. Your ADC will be doing physical damage and you will be doing magic damage, allowing your top and jungler to choose champions / build for whatever suits the game without having to worry about balancing the team's damage out.
The math for how this works
Ezreal's Mystic Shot applies on-hit effects, including Muramana's damage.
Base Mana: 235 +45 per level // 1045 @ LVL.18
Expanded Mind: +7 per level // +126 @ LVL.18
Muramana: +1000 mana
Seraph's: +1000 mana
Iceborn Gauntlet: +500 mana
Frozen Heart: +400 mana
Banshee's Veil: +300 mana
TOTAL MANA: 4371
Base AD: 47.2 + 3 per level // 101.2 @ LVL.18
Muramana: +20 AD +2% of max mana as AD (4371 x 0.02) = 20 + 87.42 // 107.42
Masteries: +15 AD
Runes: +15 AD
TOTAL AD: 238.62
Base AP: 0
Masteries: +18 AP
Seraph's: +60 AP +3% of Max Mana as AP (4371 x 0.03) = 60 + 131.13 // 191.13
Iceborn Gauntlet: +30 AP
TOTAL AP: 239.13
Now we can calculate the total damage on Ezreal's spells.
115 base +100% AD +20% AP = 115 + 238.62 + 47.826 = 401.446 physical damage
Bonus DMG on Mystic Shot from Muramana:
2 x 3% of current Mana
(we can calculate this damage at various mana levels but for starters we'll assume max mana)
4371 x 0.06 = +262.26 magic damage
Bonus DMG from Iceborn Gauntlet:
125% of base AD = 1.25 x 101.2 = +126.5 physical damage
Total DMG on Mystic Shot: 401.446 + 262.26 + 126.5 = 790.206 mixed damage
Mystic Shot base CD: 4 seconds
30% CDR = 4 x 0.7 = 2.8 seconds
790.206 damage per 2.8 seconds or ~ 282.216 DPS from Q
Of course Mystic Shot reduces the CD of all spells by 1 second everytime it hits so as long as you're not missing the spell, the de facto CD is 1.8 seconds not 2.8 which leads to higher DPS...
790.206 damage per 1.8 seconds or ~ 439.003 DPS from Q
250 base + 80% AP = 250 + 191.304 = 441.304
Total DMG on W: 441.304
base CD: 9 seconds
30% CDR: 9 x 0.7 = 6.3 second CD
441.304 dmg per 6.3 seconds or ~ 70.05 DPS from W
If you hit a Q every 1.8 seconds, W is redued to 5.3 immediately, ticks down to 3.5 during Q's CD, and gets reduced another second to 2.5. So you can hit Q twice during Essence Flux's CD leading your W to have a de facto CD of 4.3 seconds.
441.304 dmg per 4.3 seconds or ~ 102.629 DPS from W
275 base + 75% AP = 275 + 179.3475 = 454.3475
+DMG from Muramana (single target spells also apply passive) // 454.3475 + 262.26 = 716.6075
Total DMG on E: 716.6075
Base CD: 11 seconds
30% CDR: 11 x 0.7 = 7.7 second CD
716.6075 per 7.7 seconds or ~ 93.066 DPS from E
If you land Q every 1.8 seconds, E's CD immediately drops to 6.7, ticks for 1.8 seconds down to 4.9, gets reduced 1 second to 3.9, ticks for 1.8 down to 2.1, gets reduced 1 second to 1.1 second CD. So you can land Q 3 times inside of E's CD, giving E a de facto CD of 4.7 seconds.
716.6075 per 4.7 seconds or ~ 152.47 DPS from E
650 base +100% bonus AD +90% AP = 650 + 137.42 + 215.217 = 1002.637
Total DMG from R: 1002.637
We don't calculate the DPS of Ezreal's R because regardless of how many times you hit Q you are still only going to get off 1 ult during an engage.
The following calculation is for total damage done from abilities over a 10 second engage.
1002.637 + (10 x 439.003) + (10 x 102.629) + (10 x 152.47) =
1002.637 + 4390.03 + 1026.29 + 1524.7 = 7943.657 Total DMG in 10 seconds from Abilities
Of course, this is not calculating the 2% increase from Havoc and it is also not taking into account your Auto Attacks.
Ezreal's Auto Attack DMG:
238.62 AD + 262.26 DMG from Muramana w/ base attack speed of 0.981
500.88 damage on hit w/ 0.981
500.88 DMG at 0.981 attacks per second. 500.88 x 0.981 = 491.36328 DPS from Auto Attacks
Over a 10 second engage, 4913.6328 total DMG from Auto Attacks
Giving a TOTAL DMG during a 10 second engage to be:
4913.6328 + 7943.657 = 12,857.2898 Damage in 10 seconds
We can also just calculate how much damage you get off INSTANTLY with one combo.
(Q) 790.206 + (W) 441.304 + (E) 716.6075 + (R) 1002.637 + (1 AA) 500.88 =
3,451.6345 Burst Damage
That is a large amount of damage, especially for how durable this build makes you. You also have AWESOME kiting with Iceborn Gauntlet's slow being applied every Mystic Shot.
I am sorry for not going into extreme detail regarding game play and why the Runes and Masteries are what they are. I know this looks like a big wall of text at the moment but I will go in and add coding at a later time. I might expand this guide to include strategy and tactics when I have more time. I just wanted to lay out the math for an unconventional build to show viability. I hope everyone gives this idea a chance and recognizes the possible uses for such a thing.