Quote:

**g0dKratos**:

Well i read alot for this both runes and i saw alot of builds .. and they all just stack only armor penetration runes.Well for me this is not the best stats for carry.I mean physical damage runes give u more buffs than armor pen.They buff u basic atack + skills.Armor penetration buffs u only ur basic atack.. and if i read right armor pen runes + talant cant reach bellow 0 armor.Correct if i`m wrong but i think the best runes for melle carry or range... is physical runes not armor pen. (sorry for my bad english)

You are actually wrong - that's not my opinion, there is math (:O) and logic behind this claim.

First of all, most AD carry skills deal physical damage, which benefits from Armor Penetration the same way autoattacks do.

Armor can actually become negative, in which case it counts as damage amplification, not damage reduction.

Thus, the best runes are the Armor Penetration ones. With max ARPEN runes, you get ~26 ARPEN at lv1. With max AD, you get ~16 AD.

Even assuming that your spells have an AD ratio of 1.0 or higher (which is not the case more often than not), and taking into account that this extra AD is considered for skills that scale off of bonus AD, ARPEN is still better. Why?

Here is the reason:

Assume you are playing a champion with base 60 damage at lv1. You use AD runes, so that goes up to 76 at lv1. Your autoattack wants to deal 76 damage, but the enemy has 30 armor (typical value for NO armor runes on the enemy, with runes it's about 42). Thus, the formula that gives the final damage output is:

--

**Damage Multiplier = 100 / (100 + Armor) when armor ≥ 0 **
Thus, the damage taken in the end will be reduced by 23% (that's about one quarter), so the enemy will take 58 (58,46...) damage out of your 76 AD!

If you have 26 ARPEN though, the enemy is reduced to 4 armor. Thus, the damage is now reduced by a mere 4%, meaning the opponent takes 58 (57,69...) damage from your attack.

So the end result is the same, right? Nope! If you add more damage to a build with AD runes, the damage reduction by armor will remain the same - so you'll actually be dealing much less damage than your AD - if you use ARPEN runes though, your damage is decreased by a much smaller amount, thus

**your overall damage is higher with ARPEN**.

Example:

Say you have

*116 damage with AD* and

*100 with ARPEN*. Enemy has 30 armor:

AD: 89 damage

ARPEN:

**96 damage**
So with LESS damage, you deal MORE damage :O

As a bonus, let's see what happens when you have A LOT of ARPEN, say:

26 from runes

20 from Yomuu's Ghostblade

15 from Brutalizer

20 from Stark's Fervor

45 from Black Cleaver

-------------------------------- Total= 126 ARPEN.

Suppose the enemy had 60 armor, cause they had armor runes and bought cloth armor.

With -126, they now have -86 armor. NEGATIVE 86 armor.

The formula here is:

--

**Damage Multiplier = 2 − 100 / (100 − Armor) when armor ≤ 0 **
Thus, assuming you have 200 damage (with all those items you might actually have more), that means the damage multiplier is 1.46, or that your damage output is INCREASED by 46% !

So, an autoattack now deals (with 200 AD) 292 damage!!!!

Even if you had an AD user with some ARPEN (which brought enemy armor back to 30 from 60) with 300 damage (100 more than the ARPEN build, and you still get some ARPEN), the damage output would still be reduced by 23%, meaning you'd deal 230 damage! So with 100 more damage, and with 30 ARPEN, you deal 62

**less** than the full ARPEN build!

Hence, I think it is obvious that ARPEN > AD in every aspect.