Ezreal Build Guide
Ezreal ADC Build Guide, an intelligent look: Trinity or Infinity Edge? Manamune?written by Himner
Late Game / Luxury Items
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Trinity Force, or Infinity Edge? : Answered
Ezreal ADC Build Guide, an intelligent look: Trinity or Infinity Edge? Manamune?
Foreword: This is a guide is based on calculated damages of the champion Ezreal comparatively between the items Infinity Edge (IE) and Trinity Force (Trinity), in order to better understand the pros and cons of both, and choose the better of the two for an Attack Damage Carry (adc) build. This guide claims level 18 stats, which biases towards Trinity Force because of increased base attack damage with the sheen effect. This guide is also biased towards Trinity Force because it assumes perfect timing in spell casts on a 2 second interval, where possible, to maximize the sheen effect. Difference in Trueshot Barrage (ult) damage is noted, but left out of calculations as it can be used a maximum of once per battle and the damage difference is negligible in terms of comparison between these 2 item builds. Two major calculation segments follow after item data: Mystic Shot + auto attack and 8 Second Burst and Prolonged 30 Second Battle, to better identify item pros and cons, note again these calculations reflect perfection in cast timing at 2 second intervals, which favors Trinity Force because with an Infinity Edge there would be no need to space casts, and with all 3 casts of non-ult spells encounters could be started with 3 stacks of EZ’s passive, raising dps. This further biases this guide in Trinity Force’s favor. The guide also contains a brief look at the item Manamune.
IE: cost: 3625g (-445g from trinity, so add on a dagger) 80dmg +25%crit @250% 101.5 dmg/hit base @18 +15%AS (dagger) Base AS: 0.665
So, Avg hit dmg=(base+80+dmg added from crit x crit chance)=(101.5+80+[272.25 x .25])=249.56 dmg
AS=0.7648; auto attacking= 190.86dps; with +50%AS from Rising Spell Force=1.1471AS= 286.28dps
Mystic Shot= 115+181.5 (can’t crit)= 296.5/ 6 second cd
Essence Flux= 250/ 9 sec cd
Arcane Shift= 275/ 19 sec cd
Trueshot Barrage= 650+181.5= 831.5
Trinity: 4070g 30dmg 30ap +30%AS +15%crit +12% move, 250hp 250mana (slow) +150%base attack, 2 sec cd. @ lvl 18= 152dmg/2 sec. 101.5 dmg/hit base @18. Base AS=0.665
So, Avg hit dmg=(base+30+ dmg added from crit x crit chance)=(101.5+30+[131.5 x .15])=151.23 dmg
AS=0.8645; auto attacking= 130.74dps; with +50%AS from Rising Spell Force= 1.2968AS= 196.11dps
+152dmg/2 sec= +76dps= 272.11dps for the 1st 8 seconds in a cd burst (3x mystic shot, essence flux, arcane shift)(at the 10th second all cd’s are off, and cds vary after that)
Mystic Shot= 115+131.5+6= 252.5/ 6 sec cd
Essence Flux= 250+24= 274/ 9 sec cd
Arcane Shift= 275+22.5= 297.5/ 19 sec cd
Trueshot Barrage= 650+131.5+27= 808.5
Single Mystic Shot + auto attack: (1 mystic shot+single shot at avg damage, plus sheen proc from trinity)
IE: (296.5+249.56)= 546.06 on average; actually 478 (75%), or 750.25 (25%)
Trinity: (252.5+151.23+152)= 555.73 on average; actually 536 (85%) or 667.5 (15%)
With a single q, IE does more damage, but when auto attacking afterwards the majority of the time the trinity build will deal +58 damage, which can add up. But if you’re talking about ‘adding up’ you should use probability averages; Trinity build does an average of +11 damage with this burst, and the IE build’s crit (25%) with the auto attack will make the IE build deal +82.5 damage.
Probability-wise, Trinity build does +11 more damage with this 2 hit combo.
8 Sec Burst: (8 sec dps+ 2x mystic shot, essence flux, arcane shift) (accounts for increased attack speed with passive stacks after each of the 4 casts, cast at 2 second intervals. Calculations begin with one stack assuming battle start with a mystic shot)
IE: ([209.95 x 2] + [229.03 x 2] + [248.12 x 2] + [267.20 x 2] + [296.5 x 2] + 250 +275])=
->3026.6 damage in 8 seconds
Trinity: ([219.81 x 2] + [232.89 x 2] + [245.96 x 2] + [259.04 x 2] + [252.5 x 2] + 274 + 297.5=
->2991.9 damage in 8 seconds
Infinity Edge does +34.7 damage in an 8 second cd burst maximizing Trinity’s sheen procs.
Infinity Edge does better! Who’da thought huh? However, Trinity does have the chance at the slow, but EZ’s arcane shift and range helps him to chases well enough to not need the slight slow in a 1v1 fight where both champs are engaging each other at the start of the 8 second fight. You’ll notice, however that with Trinity Force your dps is going to be higher at the start, but only in the first 4 seconds, and realistically with an Infinity Edge you’d get those 3 stacks instantly, and wouldn’t wait for the 4 seconds to be up that are only used to maximize the sheen proc of trinity.
Let’s look at what happens over a prolonged 30 second fight shall we? (Let’s use the base damage from the 8 seconds above and continue on, but since cds aren’t going to be able to shoot off every 2 seconds anymore Trinity dps will drop to its base (196.11dps with 5 stacks of EZ’s passive after the 5th cast at second 15) and 7 more procs of the trinity damage of 152dmg will be added. 3 mystic shots, 3 essence fluxes and 1 more arcane shift could be used in the 20 seconds remaining) On the 6th second after the 8 second burst (second 14, the 5th spell can be cast: an essence flux, however, one second later a mystic shot can be fired, and for Trinity calculations spells will be delayed for maximization of the sheen proc, and you want to focus on mystic shot for greater dmg output, so the IE will gain the 5th stack at second 14, the Trinity will gain the 2nd stack at second 15.
Prolonged 30 Second Battle:
IE: (3026.6 + [267.20 x 6] + [286.29 x 16] + [296.5 x 3] + [250 x 3] + 275= 11,124.94dmg
Trinity: (2991.9 + [183.04 x 7] + [196.11 x 15] + [152 x 7] + [252.5 x 3] + [274 x 3] + 297.5= 10,155.83dmg
Infinity Edge does +969.11 damage in a prolonged 30 second battle, again focusing to maximize sheen procs with Trinity.
Conclusion: Go with the Infinity Edge. Even with all the biases I put towards the Trinity Force, math says Infinity Edge wins. There is no slow, but in team battles your tanks and supports will do the slowing for you. Some people have told me “Go trinity force cause ur damage is in ur q, and with Trinity u can stay at a range of 1000+ with ur q and do all ur damage” Well, that’s stupid, because your q will deal more damage with Infinity Edge because of added attack damage; Sheens don’t increase your q, they increase the auto-attack after the q, which means you have to be in auto-attacking range, so why not focus on auto-attacking and do more damage? Ezreal is an ADC, he needs to be auto-attacking. He has some cool pokes, but his passive and his w’s attack speed slow both scream “Ezreal is supposed to be up there, in the fight auto-attacking!” Trinity’s are not for ADC’s, they are for tanky ad’s that need some extra burst damage on their quick cds, and sheen effects don’t scale with damage item increases to attack damage, only base attack, and ADC inventories are full of attack damage items.
One on one, putting the two items head to head, Infinity Edge wins hands down, and not one on one, with inventories exemplary of level 18 champions, Infinity edge will cause dps to scale a lot higher than this study shows. Increasing attack speed, damage, and crit rate improve dps exponentially with an infinity edge, not so with trinity, your build is based upon a +152 damage proc that can occur only every 2 seconds if you have a cd available to blow and mana to cast it.
Also, don’t go with a manamune.
Manamune: 2110g 20dmg +7manareg/5 +2% dmg for max mana: w/ 1350 mana= 27 added dmg; 47 total. 3 sec cd to gain 4 mana= 12.5 minutes non-stop casting on 3sec cd. +625 mana from banshee’s & trinity: +12.5dmg= +59.5dmg total + a ton of mana… not really adc material.
Submitted by Himner
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