Hi, I'm Matthew Knipfer, the guy who emailed Ross Boomsocks at 5am about a build borne from the depths of computation. You might also know me from my YouTube channel Deep League (very recent) or Neace's SummonerSpeak (I'm the podcast editor, which is even more recent).

That first build I sent him had a few small arithmetic errors which didn't matter, but the itemization path was quite a bit off from the optimal route. As such, there has been some confusion as to what's the true build. Even worse, some people like KingStix ignored both the old and new version and are taking things like Eclipse and Black Cleaver. That is not Mathematically Correct Pantheon.

This build is about leaning into the multiplication League offers for damage. It's about recognizing the opportunity for a champion that seems like a bruiser to actually be one of the highest damage ceiling assassins in the entire game.

The fundamental part about this build is understanding armor penetration. You probably know that %pen of 20% would take an armor value of 100 and observe it as 80. Easy. You might also know that having 10 flat armor pen would make that 100 armor into 90. Also easy.

What many people don't know is what happens when you have multiple instances of each. Suppose we have two instances of 20% pen. On the surface, you'd expect to see 40% armor pen, taking that 100 armor down to 60. That's not what happens. %pen is calculated multiplicatively, meaning that you multiply each together. Instead of having 100 - 20% - 20%, it's 100*0.8*0.8. The cumulative effect is that the observed armor becomes 64.

If you're wondering how that can be, think of it like this: every previous instance of %pen reduces the efficacy of the next instance by that much. If we have one instance of 20% pen already applied, it makes the next instance 20% less effective. In Pantheon's case, his passive would make the following %pen items 10/20/30% less effective, respectively, based on his ult level.

This leads into order of operations. League calculates reductions and penetrations in four steps:
1. Flat reductions
2. % reductions
3. % penetrations
4. Flat penetrations

Because 2 and 3 are both multiplicative and are adjacent to each other, we can bundle them together:
1. Flat reductions
2. All % changes
3. Flat penetrations

You will rarely ever run into flat reductions, so don't worry about them. Pantheon doesn't have them anyways.

Something special occurs when we have the % changes take place before the flat penetrations. Let's assume you have 30 lethality and you're level 18 (lethality scales from 0.6 to 1.0 efficacy across level 1-18); that's 30 flat armor pen. If you're Pantheon with your ult passive giving you 30% pen, you can take a target with 100 armor and view them as having (100*0.7 - 30) 40 armor. That's a solid change. Let's pan out, though, and view the extremities, since that's where you see why mixing lethality and %pen is so useful.

If we have a target starting with 50 armor and you built all %pen items, you could never get them to zero armor. Even with 90% armor pen, they'd have 5 armor left. And, to make matters worse, the first chunk of armor someone has is the most valuable (armor has diminishing returns). You cannot get to 90% pen because of the multiplicative stacking we detailed above, so a way cheaper and better way is to take lethality along with your %pen. If you have 30% pen and 30 lethality, you now view your target as having 5 armor as well. Notice that the stats of 30% pen and 30 lethality only require one item and levels whereas the 90% pen is an astronomical hypothetic outside of the bounds of the game. That shows just how crazy good of value you can get out of combining %pen and flat pen. If you bought even just one more serrated dirk, you are at zero armor.

I'm not going to bore you with the graph, but just understand that since your lower armor values are more marginally valuable, when you have a %pen getting you into those low values for lethality to take them out flatly, %pen is functionally amplifying your lethality.

Now suppose we are fighting someone with 400 armor. It should be easy to see that 90% pen would be absurdly helpful here, but we know that's not possible. The further out in armor value you go, the more valuable %pen becomes. But, we know two things:
1. Stacking %pen is inefficient
2. Your opponents are not all tanks
The more instances of %pen you have (passive, Eclipse, Black Cleaver), the more inefficient each one is. You'd rather take some mixture of lethality and %pen as you would get comparable damage against most tanks while having significantly more damage against all other units (as shown in the previous portion).

Now I recognize that no one has 50 armor while you're level 18, but the example was about only using one item and your passive. You'd have far more items at level 18 with more lethality.

There is something to be said though about too much pen. The game does not allow you go penetrate below zero armor. That's why I coined the term "Excess Lethality" to describe all penetration that pushes at the zero bound without affecting observed armor. Your goal should be seeing how far out in armor values you can get to the zero bound while minimize the space below it, as well as considering the scope of potential high armor units you encounter. That was a mouthful, but think of like this: you want to balance % and flat pen to hurt many units for a lot of damage.

If you want a graphical explanation, there exists a slope defining the relationship between input armor and observed armor. The slope is tilted down as you have more % pen. Lethality pushes the entire curve straight down. You want to have the curve close to zero for as many reasonable armor values as possible.

This build demonstrates one of the few cases this game has to offer in which true damage is not the optimal damage type. True damage cannot be modified up or down in nearly all cases. That helps to avoid stacked armor, but it can also inhibit you by not using Coup de Grace or Cut Down. Technically it is amplified by Prowler's Claw, but The Claw is used more often for mobility.

Physical damage, however, can be modified up and down. Now, suppose we somehow got our enemy to zero observed armor. If we can apply a modifier like Coup de Grace or Cut Down, we can still amplify the physical damage, making it do more than 100% of the input damage. This is how Mathematically Correct Pantheon does damage that doesn't make sense.

When you activate PTA from an empowered W, slap them silly to lower health, and then Q as they're in Coup de Grace zone, you are cranking out a level of damage the developers likely never intended.

Don't call this true damage. It's Beyond True.

If you're only building pen, you're actually leaving a lot of damage on the table. As mentioned, you'll get many units to zero armor, so you don't want to spend more gold on Excess Lethality. Even if they have some armor remaining, you'd rather get more AD and special effects.

Essence Reaver fixes all of Pantheon's mana problems, it gives him great stats in AD and ability haste, and it empowers his auto attack with a disgusting sheen hit that makes your empowered W engages powerful, while also taking down towers in ten or so hits. Pantheon typically isn't a split pusher, but with this pushing power, a response is required from the other team. Since you can 1v1 nearly any champion with some items from one shotting, they will realize they have to send additional players. This creates space on objectives, which you then ult towards.

Blade of the Ruined King is activated on all three hits of empowered W. The fact your BOTRK hits occur when your opponent is full health, means you get the max value from it before using Q and E. If your opponent is low enough Q is amplified, while Coup de Grace is also activating. You could not ask for better synergy.

Prowler's Claw is one of the best items in the game for stats alone. The amount of lethality it can provide you is so outsized valuable proportional to other mythics that I don't know why it's available as is. Consider Eclipse's mythic passive. 4% pen isn't even one fifth of other %pen items. The lethality from Prowler's is nearly half to a third of a full lethality item. You might argue that Eclipse's damage passive and shield are better, but they're not in this case. You do so much damage from the pen here that 6% of max health pool is practically useless, and the shield from it overlaps with your E having immunity to damage from one direction. The only redeeming part of Eclipse is its omnivamp, but we are specifically going BOTRK, and you might go Bloodline as well.

That's not even pointing out that Eclipse's %pen is 30% less efficient when it's overlapping with Pantheon's passive, while lethality damage is amplified by Pantheons passive instead. Go Prowler's.

Prowler's also gives you some much needed mobility. You might have a point and click leap stun, but anyone with eyes and a brain can generally gauge what standing too close to you is. Prowler's lets you slide through targets as an additional mobility spell. It can be used on minions to climb the wave and leap. It can be used on teammates of your opponent to then leap to the backline. It can even be used to dodge spells or keep someone on the correct side of your shield. Prowler's is also interesting because you can cast any ability during it. This means that if you buffer W at the right time as you're sliding with Prowler's, you will instantly stun them on contact, while also applying the Prowler's debuff. You do run the risk of cancelling the Prowler's dash altogether and its effects being wasted. Practice this first.

We already covered how stacking %pen is inefficient. Let's consider what else is wrong with Pantheon as is. Most people take conqueror because he can stack it easy, but does he? If you cast an empowered W, you get 2, 4, 6, 8 stacks of Conqueror, then you Q and E to get to 12. But wait, now that you're at full conqueror, what do you do? All that you have for reasonable cool downs is Q, which does work well here, but consider how other champions who rock conqueror like Fiora and Irelia have so much more continuous follow up. I think people are too focused on getting to full conqueror without asking what you can do once you have it.

Let's not forget if you're taking those extended trades, you will run out of mana quickly. Pantheon struggles greatly with mana in those circumstances, so Essence Reaver is a must. I don't know why it's not standard on him, even if you're going bruiser. Actually, you should be taking it especially if you're going bruiser since your AD stat will still be impressive.

Other than the wasted %pen and misunderstanding of conqueror, I can't say many bad things about bruiser Pantheon. Barring those problems, he actually suits the role well.

Trades in lane should be quick and use your PTA proc to the fullest. Start with empowered W. You'll have three passive stacks at the end. You then have two options. Either Q and E as you walk away or Q > auto > E. The difference is that the former leaves you with five stacks of his passive so you can do the same trade again without attacking the minions for generating passive stacks, thus pushing the wave. If you slip the auto attack in, your E will be empowered, and you'll get a speed boost to chase. You'll recognize which you need as you're laning.

You also have a surprisingly strong and unexpected level 1. Take W first, and either away from the wave or once the melee minions die, W onto your opponent and begin auto attacking them. Your PTA amp will nearly always guarantee you win this extended head bashing moment. Pantheon's exceptionally high base armor makes these level 1 trades easy and effective.

The rest of the laning phase is matchup dependent.

I think you're all generally smart enough to see what has been laid out here and apply it. I don't need to teach you the basics of ganks and waves. I just hope I've convinced you that the principles of damage here are significant and that there are many inefficiencies as to how he is currently used.

If you'd like to see me go in depth on the mechanics of League like this, go subscribe to my YouTube channel. I'll be releasing the first set of videos this week.