Views: 5418 Armor Penetration Runes Math
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GrandmasterD hasn't done the math yet and I'm an impatient ****abish, so I'll do the math for him. For the sake of simplifying things, only marks will be considered. 9x Greater Mark of Armor Penetration gives 1.28 * 9 = 11.52 armor penetration
Recall that:
The lowest possible base armor in the game belongs to
Sona at 9.3 armor at level 1. For the sake of making Armor Penetration runes be utilized at maximum effectiveness, we'll assume a hypothetical target which has exactly 11.52 armor. The math is as follows:
With armor penetration:
Without armor penetration:
Since 9x Greater Mark of Attack Damage gives 0.95 * 9 = 8.55 AD, if the AD scaling increases your damage by at least 11.52%, then AD marks > Armor Penetration marks.
Now, remember that this is the optimal case scenario where Armor Penetration marks are the most effective (on a low armor target). Let's take a real-world scenario: Darius at level 1 has 23.5 base armor. Add in 9x Greater Seal of Armor = 12.69 bonus armor and Cloth Armor = 15 bonus armor, plus 3x
Hardiness
= 5 bonus armor and this comes out to a total of 56.19 armor. Let's do the math again:
With armor penetration:
Without armor penetration:
Notice how this percentage is smaller than when the target had less armor? Now, I don't know about you, but last time I checked, 8.55 AD gave me a lot more than a 7.962% boost. Take Riven's level 1 BnB on a an average low-armor solo top laner who would prefer doing 21/9/0 instead of 9/21/0, Kha'Zix, with flat armor yellows and 3 points in
Hardiness
(18 + 12.69 + 5 = 35.69):
With AD quints, ArPen reds, and Elixir of Fortitude as well as 21/9/0 masteries:
With AD quints, AD reds, Elixir of Fortitude, as well as 21/9/0 masteries:
As you can see, even given optimal conditions (opponent did not run a full armor page or buy Cloth Armor, additional bonus AD which synergizes with armor penetration maximized with Elixir of Fortitude), usage of Armor Penetration runes still causes you to deal less damage. In a more conservative scenario where you don't have the elixir (which you won't after the nerf goes through):
With AD quints, ArPen reds, as well as 21/9/0 masteries:
With AD quints, AD reds, as well as 21/9/0 masteries:
As you can see, the gap widens. If the opponent bought armor, ran a more defensive runepage or mastery page, or had higher base armor like Garen, it only gets worse.
tl;dr: Armor Pen runes on Riven are dumb, makes you lose farm by making last-hitting harder, and doesn't even make you do more damage to champions even in the best case scenario.
Recall that:
- Damage multiplier = 100 / (100 + Armor - Armor Penetration)
- Therefore, raw damage needed to deal 100 physical damage to the target = 100 / (Damage multiplier) = 100 + Armor - Armor Penetration
The lowest possible base armor in the game belongs to
Sona at 9.3 armor at level 1. For the sake of making Armor Penetration runes be utilized at maximum effectiveness, we'll assume a hypothetical target which has exactly 11.52 armor. The math is as follows:With armor penetration:
- Damage multiplier = 100 / (100 + 11.52 - 11.52) = 1.0000
- Raw damage needed to deal 100 physical damage to the target = 100 + 11.52 - 11.52 = 100.00
- Therefore, 100 raw damage = 100 damage dealt, meaning you are dealing the equivalent of true damage.
Without armor penetration:
- Damage multiplier = 100 / (100 + 11.52) = 0.8967
- Raw damage needed to deal 100 physical damage to the target = 100 + 11.52 = 111.52
- 111.52 raw damage = 100 damage dealt. You need a 11.52% increase in raw damage to compensate for the lack of armor penetration.
Since 9x
Greater Mark of Attack Damage gives 0.95 * 9 = 8.55 AD, if the AD scaling increases your damage by at least 11.52%, then AD marks > Armor Penetration marks.Now, remember that this is the optimal case scenario where Armor Penetration marks are the most effective (on a low armor target). Let's take a real-world scenario:
Darius at level 1 has 23.5 base armor. Add in 9x Greater Seal of Armor = 12.69 bonus armor and Cloth Armor = 15 bonus armor, plus 3x
Hardiness
= 5 bonus armor and this comes out to a total of 56.19 armor. Let's do the math again:With armor penetration:
- Raw damage needed to deal 100 physical damage to the target = 100 + 56.19 - 11.52 = 144.67
Without armor penetration:
- Raw damage needed to deal 100 physical damage to the target = 100 + 56.19 = 156.19
- (156.19 - 144.67) / (144.67) = 0.07962. You need a 7.962% increase in raw damage to compensate for the lack of armor penetration.
Notice how this percentage is smaller than when the target had less armor? Now, I don't know about you, but last time I checked, 8.55 AD gave me a lot more than a 7.962% boost. Take
Riven's level 1 BnB on a an average low-armor solo top laner who would prefer doing 21/9/0 instead of 9/21/0, Kha'Zix, with flat armor yellows and 3 points in
Hardiness
(18 + 12.69 + 5 = 35.69):
With AD quints, ArPen reds, and
Elixir of Fortitude as well as 21/9/0 masteries:
- Base AD = 56.75
- Bonus AD = 2.25 * 3 + 15 + 0.67 + 3 = 25.42
- Total AD = 56.75 + 25.42 = 82.17
- Armor penetration = 8% + 11.52 + 5 = 8% + 16.52
- Damage multiplier = 100 / (100 + (35.69 * (1 - 0.08) - 16.52) = 0.8597
- Raw combo damage = 82.17 + (30 + 0.7 * 25.42) + (82.17 * 1.2) + (30 + 0.7 * 25.42) + (82.17 * 1.2) + (30 + 0.7 * 25.42) + (82.17 * 1.2) = 521.364
- Actual damage = 521.364 * 0.8597 = 448.22
With AD quints, AD reds,
Elixir of Fortitude, as well as 21/9/0 masteries:
- Base AD = 56.75
- Bonus AD = 0.95 * 9 + 2.25 * 3 + 15 + 0.67 + 3 = 33.97
- Total AD = 56.75 + 33.97 = 90.72
- Armor penetration = 8% + 11.52 + 5 = 8% + 5
- Damage multiplier = 100 / (100 + (35.69 * (1 - 0.08) - 5) = 0.7822
- Raw combo damage = 90.72 + (30 + 0.7 * 33.97) + (90.72 * 1.2) + (30 + 0.7 * 33.97) + (90.72 * 1.2) + (30 + 0.7 * 33.97) + (90.72 * 1.2) = 578.649
- Actual damage = 578.649 * 0.7822 = 452.62
As you can see, even given optimal conditions (opponent did not run a full armor page or buy
Cloth Armor, additional bonus AD which synergizes with armor penetration maximized with Elixir of Fortitude), usage of Armor Penetration runes still causes you to deal less damage. In a more conservative scenario where you don't have the elixir (which you won't after the nerf goes through):With AD quints, ArPen reds, as well as 21/9/0 masteries:
- Base AD = 56.75
- Bonus AD = 2.25 * 3 + 0.67 + 3 = 10.42
- Total AD = 56.75 + 10.42 = 67.17
- Raw combo damage = 67.17 + (30 + 0.7 * 10.42) + (67.17 * 1.2) + (30 + 0.7 * 10.42) + (67.17 * 1.2) + (30 + 0.7 * 10.42) + (67.17 * 1.2) = 420.864
- Actual damage = 420.864 * 0.8597 = 361.82
With AD quints, AD reds, as well as 21/9/0 masteries:
- Base AD = 56.75
- Bonus AD = 0.95 * 9 + 2.25 * 3 + 15 + 0.67 + 3 = 18.97
- Total AD = 56.75 + 18.97 = 75.72
- Armor penetration = 8% + 11.52 + 5 = 8% + 5
- Damage multiplier = 100 / (100 + (35.69 * (1 - 0.08) - 5) = 0.7822
- Raw combo damage = 75.72 + (30 + 0.7 * 18.97) + (75.72 * 1.2) + (30 + 0.7 * 18.97) + (75.72 * 1.2) + (30 + 0.7 * 18.97) + (75.72 * 1.2) = 478.15
- Actual damage = 478.15 * 0.7822 = 374.01
As you can see, the gap widens. If the opponent bought armor, ran a more defensive runepage or mastery page, or had higher base armor like
Garen, it only gets worse.tl;dr: Armor Pen runes on
Riven are dumb, makes you lose farm by making last-hitting harder, and doesn't even make you do more damage to champions even in the best case scenario.
That's not the point of the post at all bro. The conclusion you made out of it is also pretty bad.
The point of this thread: AD runes are better than Armor pen runes for Riven early game
Your conclusion: I will never get Armor pen against Rammus.
I am honestly not sure how you came to that conclusion lol. If an enemy like Rammus has super high Armor and you want to kill him, the best thing to do is to get Last Whisper, and that's not even related to Satella's post lol
You understood it wrong.
I mean that, when I go riven top, if I find out to be against a rammus, I wont get armor pen runes, and just build armor pen items instead.
Meh :D
Haha, I hadn't thought of it that way. Learning something new every day. Thanks!
xD :D
Armor Pen is not more effective against low armor targets. It is always equally effective no matter what your enemy's armor is. What makes Armor Pen more or less valuable is how much raw damage you are doing.
Haha, I hadn't thought of it that way. Learning something new every day. Thanks!
Read it all.
From now one, when I see a rammus in enemy team, I wont take armor pen with me. Full ad or critical damage is the way! (even if low damage difference)
+rep
That's not the point of the post at all bro. The conclusion you made out of it is also pretty bad.
The point of this thread: AD runes are better than Armor pen runes for Riven early game
Your conclusion: I will never get Armor pen against Rammus.
I am honestly not sure how you came to that conclusion lol. If an enemy like Rammus has super high Armor and you want to kill him, the best thing to do is to get Last Whisper, and that's not even related to Satella's post lol
From now one, when I see a rammus in enemy team, I wont take armor pen with me. Full ad or critical damage is the way! (even if low damage difference)
+rep
Oh I totally agree. Just want to know if AD runes could beat ArPen runes on Riven, even late game.
Hmm, no? The more AD you buy, the better Armor Pen is.
The more Armor Pen you buy, the better AD is yo. The stats love each other (and you know that already I'm sure)
So would
Oh and something that doesn't really have to do with what we're talking about:
What if we consider Effective HP instead?
Enemy has 36.69 Armor and you have 8% + 5 Armor pen so he has 28.7548 Armor. If he has 2000 HP he will have 2575.1 Effective HP and it'll take you (2575.1 / 521.364 =) 4.94 combos to kill him.
Enemy has 36.69 Armor and you have 8% + 16.52 armor pen so he has 2344.7 effective hp and it'll take you 2344.7 / 521.364 = 4.497 combos to kill him
Armor pen runes made you kill the enemy 4.94 - 4.497 = 0.443 combos faster.
Enemy has 100 armor and you have 8% + 5 armor pen so it'll take you 7.173 combos to kill him (too lazy to write all the math for this one LOL)
Enemy has 100 armor and you have 8% + 16.52 armor pen so 3509.6 Effective HP and it'll take you 3509.6 / 521.364 = 6.732 combos to kill him
Armor pen runes made you kill the enemy 7.173 - 6.731 = 0.442 (some numbers were rounded up)
If I didn't round up or down any number, in both cases, Armor Pen runes woulda made the enemy die ~0.4425 combos faster, no matter how armor he had. This would still be true if the enemy has 9000000000000000000000000 armor.
What I'm trying to say with numbers is:
Armor Pen is not more effective against low armor targets. It is always equally effective no matter what your enemy's armor is. What makes Armor Pen more or less valuable is how much raw damage you are doing.
But not for ArPen :O
When you are lvl 18, ArPen is better over AD overal :O
Better include those calculations aswell :P
Flat AD is better early for EVERYONE.
Not necessarily. Notice how to beat armor pen, the extra damage gained from the AD has to exceed a percentage of the base damage you do. This means if your base damage is godlike and your AD scalings are garbage or nonexistent (a-la
The real question is, since Riven has stupid AD ratios and will probably get at least one of those :
Armor pen runes will cause you to deal more damage to champions if you've got those two items, given that you also have a