Both flat damage and armor penetration are beneficial for champions who need to put out as much physical damage as they can. Here, we’re going to do some comparisons with a few different characters to figure out how you can dish out the pain on your opponents and why it works.

A Quick Review

As of the writing of this article, penetration behaves like this:

Reduction % Penetration Flat Penetration

So if you were attacking an opponent with 100 base armor and you debuffed them with Black Cleaver (25%), had Last Whisper and the Weapon Expertise mastery (40.2%), and 6 flat armor penetration, the armor calculation would look like this:

100 * (1-.25) * (1-.402) – 5 – 10 = 30 armor (Approximately. Credit to Khoral for catching this error.)

The damage calculation looks like this:

Damage Reduction = Armor/(100 + Armor).

So 100 armor would result in 100/200 = 50% damage reduction. Damage dealt is

Damage Dealt = Damage * (1 – Reduction).

Alright, now that we have that out of the way, let’s look at some examples.

Autoattacking

For all of our comparisons, we’ll be using a full set of Marks and Quintessences of either flat AD (15 AD) or flat armor penetration (19). We’ll also be assuming the autoattacker has an average damage stat for a marksman AD carry (48 + 3 per level), and that the defender has 35 armor. Also included are flat 3 AD, 8% and 6 armor penetration from masteries.

So right off the bat, flat AD has a noticeable advantage over ArPen. In addition to this trading advantage, it is much easier to last hit with flat damage. Let’s look at an endgame situation against a medium armor opponent.

This includes % pen from LW and mastery. Purchased AD is +210 from IE, LW, and BT. +12 from Deadliness Mastery. In an end-game scenario only examining autoattacks, ArPen comes out ahead. However, ArPen affects physical damage from abilities and on-hits, like Blade of the Ruined King. Let’s substitute Bloodthirster for BotRK.

Not visible in this chart is the active, which is 15% of your targets maximum HP. If the target’s maximum HP is their current HP, the numbers (and their differences) will triple. ArPen comes out ahead here as well. A note should be made for Jarvan IV: his passive is up to 10% of your target’s current HP, which also benefits from ArPen but not from flat AD.

So for now, ArPen is weak early game but stronger late game. This is only when we look at autoattacks, though. What about abilities? Let’s look at an example of a carry ability with a decent AD ratio, like

Graves and his Buckshot

This chart shows Buckshot’s damage at levels 1 and 18. Interestingly, it is essentially tied between rune types at level 1. At level 18, ArPen (unsurprisingly) pulls ahead. I’m only doing the math for one projectile from Buckshot, but doesn’t really matter in this math how many I use. Armor Penetration also affects physical on hits, like Sheen/Trinity Force/Frozen Fist and Muramana, so let’s look at…

Ezreal and his Mystic Shot

This is going to be a pretty big picture.

So this is a variant of Blue Build Ezreal. I like BT instead of BotRK, big deal. At level 1, with nothing, ArPen is already ahead! Looking good for those runes already. ArPen affects bonus damages from all sources that apply to Mystic Shot, which is why the difference is pretty decent at level 18.

One more case, the king of AD ratios is…

Pantheon and his Many Spears

Pantheon’s AD ratios are fat. Really fat. We’ll look at Spear Shot and Heartseeker Strike separately.





So here, Spear Shot is ahead by 7 damage at level 1 with flat AD. Obviously ArPen is going to pull ahead endgame, but Pantheon throws a lot of spears and his early game is where he shines, so flat AD is a serious contender so far.

Damn! Heartseeker does 30 more damage at level 1. A 3.6 bonus AD ratio does that. It still loses end game by 90 damage, but once again, Pantheon’s early and mid game are where he punishes, so getting ahead as fast as he can is generally advisable.

Conclusions

So why does this happen? Basically, armor penetration affects every aspect of physical damage a character puts out. This includes base damages from abilities, purchased damage, AD ratios, flat on-hit bonuses (Sheen-based), and percentage on-hits (BotRK). It even benefits the bonus AD from masteries. AD runes affect only autoattacks and AD ratios. Due to these effects, armor penetration wins out in the end-game damage. However, it must not be forgotten that flat AD is extremely useful for last hitting and early trades, and in the case of Pantheon, getting ahead as fast as you can. The decision of which runes to use is up to you; you just need to be prepared to play in a style your runes support.