AD Carry Itemization: Recap

Gentleman Gustaf here to talk about why AD Carry itemization can't be decided on just based off of dps numbers. But all of this information is useless in a void, so I'll be splashing in a summary of previous posts on RoG.

1st Item

So what should your first item be? In a previous post, I suggested that almost every champion, with possible exception of Tristana, Ashe, and Caitlyn should be getting Bloodthirster first. On those three champions, it wasn't so much that Bloodthirster was worse than IE as that they have naturally weak and auto-attack-based mid-game damage, and will be even weaker mid-game without the crit multiplicativity from IE. However, BT took a small cost nerf; has this changed much?

Note: My previous post was not considering any armor penetration items, and as such, armor was irrelevant for the relative damage values. This post will assume armor, and as such, dps numbers will be significantly lower. Consider the relative values to be more important than the flat values.

As a first item:
BT now costs 85.3/dps when unfilled, and 59.7/dps when filled.
IE now costs 51.7/dps. However, factoring Vamp Scepter in, it costs 56.7/dps.
PD now costs 65.9/dps. However, factoring Vamp Scepter in, it costs 69.4/dps.
SS now costs 62/dps. However, factoring Vamp Scepter in, it costs 68.2/dps.
LW now costs 60.8/dps. However, factoring Vamp Scepter in, it costs 70.1/dps.
BC now costs 67/dps. However, factoring Vamp Scepter in, it costs 74.1/dps.

So if you want to remain competitive in lane, you want BT or IE first. The nerf to BT, however, does help even BT and IE out, as IE does about 5% more sustained dps, or about 7 dps. However, the extra AD on BT still makes it best for AD Carries with significant AD scaling (most of them). The extra 30 AD will give you 30 damage or so after armor (let's use Graves as our example), not to mention the fact that it will hit multiple targets. As such, it will take 5 seconds for IE to beat out BT; sounds like a solid deal for BT. However, the cost nerf to BT will make things slightly easier for those few AD Carries who aren't loaded up on AD scaling (Tristana, for example).

Round 2

It may do to look at second-item scaling to really figure out which item is best. As a note for the rest of this post; any build which does not have BT is assumed to have a Vamp Scepter. As such, the actual damage efficiency of IE will be weighted downwards. However, this is only fair, because of the investment in lifesteal for Bloodthirster.

If you go BT first:
BT+PD costs 33.8/dps
BT+SS costs 35.5/dps (SS beats PD in dps once it hits 2 targets or more)
BT+LW costs 39.4/dps

If you go IE first:
IE + PD costs 30.4/dps
IE + SS costs 32/dps (SS equals PD in dps once it hits 2 targets or more)
IE + LW costs 35.5/dps

Here we see that IE pulls about a 10% advantage in dps, although it will lose the same 30 AD worth of up-front burst. Given that the difference in dps ranges from 20 (LW) to 25 (PD), it will take 2 seconds (after your second crit) or so to make up for the bonus damage your spells get from BT. At the second item, IE is starting to look like an even or better purchase. And what should your second purchase be? Well, SS seems to be as strong as PD, plus it's going to splash onto multiple targets. Sounds like a good deal to me.

But Gentleman Gustaf, what about armor? You haven't mentioned it at all!

It turns out that the armor doesn't actually matter much at this point. Those calculations are done with 100 Armor (and DPS is actually Gold/DPS):

So let's equalize damage and just look at ratios. Since PD is the most cost-efficient, we'll divide all cost/dps values by that of the PD option, and raise armor until SS or LW beats PD. Turns out that takes awhile:

SS passes PD at 300-ish armor:

And LW passes PD at 475-ish armor:

Obviously, this is not the whole picture. Remember those AD scaling abilities? Well, they'll also benefit from Last Whisper. So in general, the more a champion benefits from BT (think Graves' Buckshot; pure AD scaling), the more they'll like Last Whisper. As such, on champions who have both high AD scaling AND an AS steroid + mobility built into their kit (Graves, for example), I think Last Whisper first is a very good second buy. Although, I'd probably get Zeal first, because I like mobility and safe damage over more damage. So why would you get IE as a first item? It is weaker as a first item, and about even or slightly better after your second item.

Third's the Charm

Finally, you have your third item, and it is here where multiplicativity starts to shine:

BT + PD + LW - 30.1 gold/dps
BT + SS + LW - 32.4 gold/dps
IE + PD + LW - 25.8 gold/dps
IE + SS + LW - 27.8 gold/dps
IE + PD + BT - 26.2 gold/dps
IE + SS + BT - 28.3 gold/dps

Firstly, interestingly enough, PD beats SS by about 7%, but once you factor in two bounces (three targets), the damage is even.. So IE wins by about 15%, with either LW or BT. At this point, your dps is approaching 400. As such, the damage you gain from auto-attacks beats out the additional BT burst very quickly (on your first crit). And IE + LW already beats IE + BT out at 100 armor.

If we bring armor up to 200, we get the following numbers:

BT + PD + LW - 45.3 gold/dps
BT + SS + LW - 48.3 gold/dps
IE + PD + LW - 38 gold/dps
IE + SS + LW - 40.5 gold/dps
IE + PD + BT - 42.3 gold/dps
IE + SS + BT - 44.9 gold/dps

We can see three things from the three-item builds:

  1. IE beats BT out in dps pretty hard, and we can extrapolate that it only gets worse with a 4th damage item.
  2. PD barely beats SS in single-target dps late game, and always loses counting bounces. Plus it gives you strong wave clear. I reaffirm my previous statement that it's probably the item you want.
  3. If you don't get LW by your third item, your dps will start to suffer, (ratchet armor up to 300 and IEBT almost loses to BTLW, and loses by 20% to IELW).

Build Order

But Gentleman Gustaf, I didn't see very many IE rushes at IEM Katowice!

The reason we don't see IE rushes in Pre-Season/Season 3 where we did in Season 2 is all sorts of complicated, and hinges on a "flaw" of mathcrafting I've glossed over in the past; there's more to the game than math-

Aha! I knew it! Ultimately, you can't just turn the whole game into math and analyze it that way, Gentleman Gustaf!

Hold on, let me finish! There's more to the game than mathing out dps. Sometimes math needs context-

Aha! I knew it! Ultimately, you can't just turn the whole game into math and analyze it that way, Gentleman Gustaf!

Can we hold off on the interruptions until I'm done? As I was saying, sometimes math needs contextualization with other math. So, when you look at math for dps, you also have to look at math for stats that affect dps (defenses) and stats that those stats affect in turn.

In Season 2, the main form of tanking was resistances. It was not unusual to see a tank with Randuin's AND Frozen Heart as his first 2 items. Of course, this meant that Last Whisper was extremely important. But that was not the only result. Since lifesteal is calculated based off of post-reduction damage, AD Carries weren't really lifestealing all that much. As such, their best protection against tanks was to burst them as quickly as possible, making IE+PD+LW a very strong build. However, in Season 3, the name of the early game is health, and as such, the early Bloodthirster lets champions like Ezreal kite and sustain themselves through teamfights a little bit better. So let's say you're a less-kite/lifesteal heavy AD Carry, how does this affect you? Well, Ezreal (and he's in every game) is getting Bloodthirster, so you'd better get Bloodthirster yourself, or he'll out-poke and out-sustain you in lane, and have early-mid game dominance.

Gentleman Gustaf, who cares if you can't rush IE, it isn't better until late-game, why not just buy it third?

This is a bit trickier than it would seem. At first glance, it would seem simple: once you get your first item, you're set down a path you can't deviate from. You need to get AS/Crit, and then you need Penetration to kill tanks. However, IE BT does about the same damage as BT LW. So why not simply build BT -> SS -> IE -> LW? If I had to hazard a guess, it's because your 4th ADC item is typically a defensive item, which would put your armor pen off until too late.  Moreover, as it is currently, the main 3 AD Carries (MF/Ezreal/Caitlyn) all want builds which don't necessarily focus on those three items. MF wants BC, Ezreal wants any number of unusual items, including Frozen Fist, and Caitlyn starts IE often anyway. As such, if I have to make a prediction, it's that we will start seeing BT -> SS -> IE (on champions who want those three items) when we start seeing more AD Carries played consistently.


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