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With the release of Pulsefire Ezreal, a lot of players have been picking up Ezreal and trying to learn him in time to prepare for the day they can play with the skin. I've come across a lot of these new-Ez players and their builds ranged from full AP to full AD to hybrid and everything in between. I was intrigued by two popular options however. It is widely known that Ezreal (along with Corki/Urgot) is one of the best users of Trinity Force among AD carries. It comes as no surprise then that a lot of these new Ez players rush a Trinity Force and forgo the traditional Infinity Edge rush. My curiosity was piqued and I had to get the math done behind this to see how much damage you stand to lose by rushing Trinity Force. So I present to you - Ezreal: Trinity Force vs. Infinity Edge.
Abilities
Ezreal has 4 abilities which scale off AP and 2 off AD. It stands to reason that the AP from Trinity Force would help him quite a bit in terms of damage output. Let's take a quick look at his ability set for reference.
Now having gone through his abilities. The next logical step is to take a look at the item builds in question.
Items
So cue the item descriptions:
The official LoL website fails to show all of Trinity's information in one box. They are missing the mana/health components in the above picture but more importantly Trinity Force also gives the following passives:
Unique: Your basic attacks have a 25% chance to slow your target's movement speed by 35% for 2.5 seconds.
Unique: After using an ability, your next basic attack deals bonus physical damage equal to 150% of your base Attack Damage. 2 second cooldown. Does not stack with
Sheen or
Lich Bane.
That's a fairly straight forward description. An important note is the critical damage increase which will play a significant part in our calculations to come.
Assumptions
Now in producing the contour plot (rainbow graph), on the damage output increase that Infinity Edge gives over Trinity Force - a set ability combo is required. Having the advantage of foresight and being the author, I can tell you that Infinity Edge far outweighs Trinity Force in terms of damage output. So in the interest of showing data values where Trinity Force can hope to match up to Infinity Edge - these are the assumptions:
- Ezreal has no runes and masteries equipped.
- The only item he has built is a Trinity Force or a Infinity Edge.
- His spell rotation consists of QWER, i.e. he uses every spell once.
- He lands 5 basic attacks in one trade.
- The bonus damage axis is any damage that is not IE/TF.
Important Note: Since the bonus damage axis does not take into account any damage apart from the IE/TF, you would have to take into account Ezreal's base AD, runes and other items to read accurately. So at level 18, you would have to look at >101 bonus damage (assuming no extra items) and at level 1 >50 bonus damage due to your base AD as well as extra bonus damage due to runes/masteries. The graph has been designed this way so results can be read off for various points in the game. Bonus damage values from 0-50 are effectively impossible to hit values and should be ignored. They are in the graph simply to provide an axis starting from zero.
The Results
Conclusions
Even after trying to give the edge to Trinity Force by limiting the study to a small number of basic attacks, including a full QWER rotation and numerous sheen procs. It is painfully obvious that the Infinity Edge is significantly better damage wise than a Trinity Force. It is important to note that an Infinity Edge also scales any other AD you might have due to the critical damage increase. Having said this, I would strongly recommend not rushing a Trinity Force first for damage purposes unless you absolutely require a bigger mana pool or the utility from the slows and MS increase. However that is my opinion and you are free to disregard it if you wish.
I hope you guys enjoyed a return to some serious mathcrafting after a period of absence of rainbow graphs. Please do leave a comment below on anything that might have passed through your mind while reading this :) Cheers :D
If you enjoy reading the article - I'd really appreciate you clicking the up arrow - thank you in advance!

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Posted 6/23/2012 4:19:17 PMSecond best item after IE, pure damage-vise is actually equal between fully stacked BT and PD.... Though unstacked, the PD wins outright (after IE + 1-3 dorans that is).... unless enemies have so much armor that LW is the best choice.... Also PD gives movespeed == utility and speeds up farming.
Thats why the standard build is (Standard, because it gives the most damage increase overall):
1.1-3 Dorans + Berserkers greaves
2. IE+ Vamp scepter(optional)
3. Zeal. (sell dorans at some point)
4. Depending on enemy armor stacking, finish LW or PD, then finish the other one.
5. Choose 2 of these items in most suited order (very game dependent): BT, QSS, second PD, Guardian Angel, Banshees Veil
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Posted 6/23/2012 4:07:33 PMThis post is nice to ppl who did not know this already, great article for the new Ezreal players, however every seasoned Ez player/or theorycrafter knows that bought BT and IE outdamage trinety BYYY FAAAR.... So this post becomes kinda stupid after that, since the reason for trinity, is not the damage, but the extremely nice buildup and power you gain in lane, mutch the same as the triple dorans+wriggels-->PD build for other ADs:
- Ezreal has a low mana pool early and very high damage burst damage..... for only 1250 gold you can increse that burst (sheen proc) and that mana pool, making you win trades in lane.
- The Phage combined with 1-2 Dorans (1800-2200gold) gives you a Lot of damage and survivability for laning, making you win trades as well, and if you win trades the slow makes sure they have to blow summoners or you get a kill.
--> These two items makes you win certain match-ups for sure, making you stronger and ahead of the enemy AD.... at this point you can snowball -->
Depending on how long the game have lasted: 1. you build either straight for Trinity as you are still laning and this makes you stomp even harder in lane.
2. Build IE for maximum damage, and do a regular AD carry build, even though you have some nice options: phage+sheen --> Trinety after IE, or sell sheen+phage -->frozen mallet (makes you kite like a boaws).
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Posted 6/20/2012 1:39:39 PMNow if IE is the best first item, what is the next best? Phantom Dancer or Trinity Force?
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Posted 6/20/2012 12:10:36 PMget an intrinity edge problem solved
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Posted 6/20/2012 11:46:25 AMI'd be more interested in seeing a post on the Gold Efficiency/Value Added of going for Phantom Dancer vs Trinity Force as a second item for Ezreal assuming you rushed Infinity Edge first.
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Posted 6/20/2012 11:37:41 AMNow i might just happen to be a bit crazy in saying this because i personally love ezreal and play him loads and read up all the stuff on ezreal and tested all the stuff on him so im pretty sure that most of the time on ez unless u have mega sustain support or are destroying ur lane u rush a bloodthirster. NOT TO MENTION ezreal usually gets early game sheen unless when he b's he can buy straight up bf, the again after that unless he can get straight up IE/BT not trying to bash you thats just my personal opinion of what i like and believe is most common.
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Posted 6/20/2012 6:50:50 AMI've never been sure what to pick up first on Ez, and even with this information I think I may still get Phage or Sheen first, but likely finish IE before finishing Trinity Force. - just going to be very dependant on the situation I guess! Thanks for this Diff The Ender! I've added the link to my weekly eSports news roundup. :)
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Posted 6/20/2012 6:04:34 AMwould be way more interesting if its stronger to get pd or trinity on ez. Cause you cant rly compare utility against raw dmg. Its like Comparing the dmg of a Frozem mallet against Bt. There is no reason to do it. But as ezrael with full lategamebuild, u have to choose between pd and trinity, so it would be nice if some1 could compare them.
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Posted 6/20/2012 6:45:16 AMYou don't need utility as an AD Carry.
You need to be able to pew pew.
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Posted 6/20/2012 10:44:30 AMUtility = Positioning = Not dying = More damage?
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Posted 6/20/2012 10:23:16 PMtell ashe that. because ashe is the number 1 ad carry due to number 1 utility and not a certain void carry that has 0 escapes and no real utility except for a small slow, but deals RETARDED amounts of damage with any items at all.
tl;dr ->at end of day, ad just has to go pew pew.
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Posted 6/20/2012 6:02:26 AMI love reading these btw, keep it up :)
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Posted 6/20/2012 6:01:48 AMCould you do the math on when Infinity Edge + Last Whisper do more DPS than Infinity Edge + Phantom Dancer?
As an AD player, I've been wondering about this for a long time. I tend to buy Last Whisper immediately after Infinity Edge if the enemy team has 1 Chain Vest on their team. Or does anyone else know?
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Posted 6/20/2012 10:43:45 AMLook at the actual amount of armor that they have. If two to three are >100, then buy Last Whisper. Otherwise, Phantom Dancer is better. Generally, the PD is better because it offers better positioning and by late-mid game, you start relying on your auto-attacks more than your spells (except for using spells to proc your passive, letting you AA more).
Note: Some of the enemy champs might have taken armor runes and masteries and built smaller items that give them ample armor. i.e. Wriggle's.
This is what I remember from a while back, so it might be outdated. I'm not sure.
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Posted 6/20/2012 4:38:09 AMFirst of all you are looking at damage you get from Trinity Force rather then all the other stats for example Attackspeed and Health that TF offers that IE doesn't get. Secondly Trinity Force gives you more damage on your Q and more burst damage then TF offers.