Ezreal: Trinity Force vs Infinity Edge

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.
 
It's important to be clear that the more bonus AD (damage on top of the IE or TF) Ezreal has, the more it favours the Infinity Edge as the critical damage multiplier will boost the bonus AD. Many of you will be saying that Ezreal lands more than one Mystic Shot (Q) in one trade and you would be right. However, the more Q's he lands, the more it favours the Infinity Edge due to the 1.0 AD ratio. On with the graphs.
 

The Results

The results take into account sheen procs (the 150% damage bonus from Trinity proc - referred to as Sheen proc from here on), number of critical strikes and the various AD/AP ratios according to each item.
To help you understand the following graphs, I've made a video on how to read contour plots (aka rainbow graphs) to help prevent confusion. The video can be seen below:
 
 
 
 
 
 
Firstly let's take a look at the increased damage when every one of your five basic attacks procs Sheen.
 
 
As you can see - you effectively have to crit at least two times in this scenario to out do the damage of a Trinity Force since having 200 bonus damage on top of an Infinity Edge only happens at very late game when you have ~100 base AD and a fully stacked Bloodthirster. However this is an unrealistic situation as you will never proc Sheen five times out of five basic attacks.
 
What if you proc Sheen zero times?
 
 
Regardless of how many times you crit or how much AD you have, if you do not proc Sheen - an Ezreal with an Infinity Edge will always outdamage an Ezreal with a Trinity Force. Once again this is unrealistic as after you have used your QWER, you will at least proc sheen once. So let's take a look at a more realistic graph.
 
 
 
 Here we can see the damage output difference when you proc sheen 3/5 times - a much more realistic situation. In this situation, you will never outdamage someone with an Infinity Edge as well. As you can see, the trend is very clear, Infinity Edge outdoes Trinity Force in terms of damage output very very significantly. However for the readers who want to see one extra Mystic Shot in the mix, I'll include the following graph:
 
 
This is nearly identical to the graph above, with a narrower margin between Trinity Force and Infinity Edge. Once again, in a realistic situation, you will critical strike once out of five times and therefore still out damage Trinity Force.
 

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!
 
 

If you guys have any questions, feedback, suggestions, propositions or anything else you'd like to say:
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Cheers,
DiffTheEnder

Comments

  • #12 Play2pvp

    Yeeeeeeeeeey. This makes me wonder if Trinity Force rushing is good on Corki and for how long.

  • #13 OddSquad

    No its not. Because the Sheen proc does not benefit from his passive or armor shred. As a support I want to kill any AD carry of mine who tries and rush Triforce.

  • #14 eagLeaf

    Sheen (as well as Lich Bane and Triforce) does physical damage, it does benefit from the armor shred.

  • #17 Zero000x000

    Sheen proc benefits from both his passive and armor shred. Corki has the greatest synergy with Trinity Force of any champion in the game.  He requires mana to exchange, doesn't need to stack Doran's for health instead of a Phage because he doesn't need the life steal as he doesn't autoattack quite as much, he has low cooldown spells that time well with procs, he has great autoattack animation, he has armor penetration, he has hybrid damage.

    That said, Trinity Force doesn't have to be core every game, but it's amazing depending on playstyle.

     

    The entire strength of Trinity Force isn't damage per second, it's burst and poke in trades.  It's not used to make you autoattack like a monster, it's there so you can time attacks with spells to trade and essentially make every trade a guaranteed crit.  However, that's just the Sheen part, the rest of the Trinity Force is largely useless for trading, as Phage+Zeal's goal is to allow you to chase down people after out-trading them.  The AD carries that focus on trading and can use the stats of the Trinity Force are Ezreal and Corki, and Corki benefits from the entire Trinity Force while Ezreal does not (built-in AS steroid instead of ArPen steroid stacks this difference even farther).

  • #28 Nightvving

    Armor shred yes, passive no, try it yourself if you don't believe me.

    Both Tri-force Corki and IE Corki are both pretty good. Although nowadays I see more pros going IE (then again, pros also farm close to twice as fast as an average player... so they can get the items needed to make the IE build more damaging faster).

    That said I'd say Ezreal synergies even better with sheen/triforce than Corki. Corki still needs to get within 550 range to auto attack for the proc while Ezreal's mystic shot applies the proc.

  • #11 pooplord

    Excuse me good sir, but allow me to retort your findings with a few graphs of science. 

    http://imgur.com/GYsSb

    http://imgur.com/JE94L

     

  • #19 DiffTheEnder

    Easily the best math around. If anyone is reading this - please start a petition to get this guy his own blog.

     

    :P

     

    I lol'd

  • #6 Emperata

    I think Triforce on Ez will always be the best option, not only for the mana/MS/slow utility you get, but the fact that you're not going to be an all out auto attack mode with Ez... Q is the foundation of his kit and I think Triforce is the perfect item to compliment it.

  • #5 7alon

    I never get tri force on carries. Only ever on bruisers. Didn't even have to do the math to know the large diff of damage between the two items on ez. 

    Last edited by 7alon: 6/19/2012 9:58:46 PM
  • #3 Tunemi

    "It is widely known that Ezreal (along with Corki/Urgot) is one of the best users of Trinity Force" *record scratch* uhhh tri force is a common item on urgot? Haha but seriously, this article broke my heart. </3

  • #4 Addictedztje

    Quote from Tunemi »

    "It is widely known that Ezreal (along with Corki/Urgot) is one of the best users of Trinity Force" *record scratch* uhhh tri force is a common item on urgot? Haha but seriously, this article broke my heart. </3

    Imaqtpie is looking at you. And he's laughing. Feel his laugh. Observe it.

    Thanks.

  • #9 Tunemi

    Cuz qtpie is totally known for his wide array of ad carry experience especially Urgot and isn't just building what he builds everytime  I.E. tri-force, black cleaver >.> Honestly, try and cite someone else with credibility that builds it on him. 

     

  • #7 TheMagicStik

    Urgot is more of a bruiser than a carry and bruisers love Triforce especially bruisers with a 1.5 second cool down on a spell.

  • #2 Gahlo

    I've never had an issue reading these plots from your articles in the past, but I have no idea where you got any conclusions from these. =X

  • #10 DiffTheEnder

    :(

    Take a look at the mauve coloured zero on the colour bar on the right. Only two of the graphs have it even show up. In the rest, it's just infinity edge clearly outweighing the trinity force. I'm not sure what you're confused on x_x

    What can I help with?

  • #29 Gahlo

    Oh, it's comparing I-Edges extra damage over Triforce? My mistake then, I thought it was the other way around. That solves that then, I get it now. Thanks. =D

  • #1 ryokoseigo

    First time commenting, but I'd like to point something out:

    Sheen is what you rush, not TF.  You get a sheen instead of a BF sword as it will give you the greatest results in lane.  You can spam Q more, which is the only skill you will use in lane realistically, and you also deal more damage because of it.  A sheen +2 dorans, makes killing minions a joke, and allows you to spike the enemy for a good deal of damage often.

    After sheen+dorans, you'd still go for a AD item over the TF if possible.  You might want to considering calculating the damage increase of owning a sheen+ IE, vs owning a IE+ some other item you'd buy that's around sheen's value.

    Anyways, that is just the way I do it.

  • #8 TheMagicStik

    Most people go phage before sheen and many rush Triforce which isn't better than an Infinity Edge for dps and thats what an AD Carry needs.

  • #16 xepel

    If you are going to just get the same item build as any other AD Carry, why would you play Ezreal over a different AD Carry who has better steroids and synergies?

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