Let's really compare armor penetrate to critical chance

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atlasgs

Junior Member

06-21-2010

I believe armor pen is still better.

CC = critical chance %
CD = critical damage %
AD = attack damage
AP = armor penetration
A = armor

Damage = AD * ( 1 + CC ( 1 + CD ) ) * ( 100 / (100 + a - ap) )

What we really want to know is the percentage change in damage from additional critical strike % or from armor penetration.

TCC = Change in critical chance percentage.
TAP = Change in armor pen.

For critical chance: ( new cc - old cc ) / old cc

( 1 + (CC + TCC) * ( 1 + CD) ) - ( 1 + CC ( 1 + CD ) )
-----------------------------------------------------------
1 + CC ( 1 + CD )

Simplifies to:
TCC ( 1 + CD )
------------------
1 + CC ( 1 + CD )

For armor pen: new - old / old
X = 100 + A - AP

( 100 / (X - TAP) ) - (100 / X)
-----------------------------
100 / X

Simplifies to:
( X / (X - TAP) ) - 1


So how much of a damage boost does 14% critical strike give us? I'll assume that you have the 10% critical damage bonus from masteries. And further assume that your base critical strike percentage is 0%. These are the most favorable conditions for critical chance.

%change in damage = .14 ( 1 + . 1) / (1 + 0 ( 1 + .1)) = .154 = 15.4% boost in damage.

So what armor must our opponent have in order for 29 AP to have the same effect? We will further assume that we have 6 armor pen from masteries.

(X / (X - 29)) - 1 = .154
X = 217
100 + A - AP = 217
A - AP = 117
A = 123

So in the best case scenario for critical chance runes, armor penetration is better up until 123 armor.


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Talking Socks

Senior Member

06-21-2010

I'm failing to understand the point the TC is making.

Let's assume the following.
-You buy last whisper
-You buy brutalizer
-You get EITHER armor pen runes OR crit chance runes
-You do not have any base crit or armor pen other than your items or runes
-Target has 75 armor

AP runes penetrate 29 armor
Brutalizer penetrates 15
Last whisper penetrates 40%
Crit chance runes increase chance by 12%

With armor pen runes, the damage increase will be :
(75 - 29 - 15)*0.6 = 18.6 armor after penetration, that's a damage bonus of 175/118.6 = 47.55%

With crit chance runes, bonus damage will be :
(75 - 15)*0.6 = 36 armor after penetration, that's a damage bonus of 175/136 = 28.68%
Then, because there's a 12% crit chance damage bonus will be 1.2868 * 1.12 = 44.12%

So armor penetration will provide slightly more damage.

Now what if they have 45 armor? In that case last whisper isn't needed on the armor pen build so I won't count it.

(45 - 29 - 15) = 1 armor, that's a 145/101 = 43.56% boost for armor pen
(45 - 15) = 30 armor, that's a 145/130 = 11.54% bonus, with crit chance this becomes 24.92%

So armor penetration is significantly better.


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Saysay

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Senior Member

06-21-2010

[QUOTE=Holypope;1659745]This has all been addressed before, but the OPS has oversimplied, which makes things a bit incorrect. Here's some better details:

Armor Pen: 29 armor pen with runes, 6 with masteries. 35 total. This can be pushed up to 50 with a brutalizer. that's about as high as it can go. period.

Crit chance: 32.7 crit chance from runes, 3 from masteries. 35.7 total. This can be maxed out to 100 easily, with any number of builds.





Actually it is 20% crit chance from runes.


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Lawful

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Senior Member

06-21-2010

Quote:
Originally Posted by XxKillMeFirstxX View Post
I disagree with the statement that crit% beats out armor pen because 99% of the time the early game laning and ganking is what decides the game. That being said I find armor pen WAY more useful than crit% and I also prefer attack speed over crit% too...

The thing is it's mostly about early game and making the best out of the little amount of gear you have during the early phases and that is where I feel rune/mastery choices really shine, but if we're playing for end game max build then crit% will probably trump all because you'll have everything you need and just be that much closer to 100% crit chance with a green elixor pop...
Disagree, crit rate is much better for earlier ganking for various reasons.

The most important is unexpected burst damage, when you deal 60,60,120,120,120 and he dies, he won't expect that.
While if you had PNR you would of been dealing 70-70-70-70 and the target just overpowers you or runs away without consequenes.

The key is the surprise factor and landing in as many bursts as you can while he is still in range, doing stable orthodoxal damage isn't going to give you that much of a chance to get that kill.

Plus PRN is a two handed blade, its useless if you have low AD and its also useless if the target has high Armor, so theres several ocassions where it can be neglected, while critical never is.


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Lawful

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Senior Member

06-21-2010

Quote:
Originally Posted by wildfire393 View Post
LW used to be an amazing item. Lategame, champs get up to 70-80 armor just from leveling, and when it applied before flat Penetration, that means that it'd give you 28-32 penetration. Since the recent change, where it applies after flat penetration, it's only generally applying to 30 or less, giving it only 12 penetration.
Is it me or did you never pass your math school exams?

80 AR

LW+17 PNR from Reds.

New formula: 80-17/1.4=45
Old formula: 80/1.4-17=40

A decrease in 35 AR , not by any means 12 like you stated and the difference isn't really that big to make a fuss over it.


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viscrom

Senior Member

06-21-2010

Quote:
Originally Posted by Talking Socks View Post
I'm failing to understand the point the TC is making.

Let's assume the following.
-You buy last whisper
-You buy brutalizer
-You get EITHER armor pen runes OR crit chance runes
-You do not have any base crit or armor pen other than your items or runes
-Target has 75 armor

AP runes penetrate 29 armor
Brutalizer penetrates 15
Last whisper penetrates 40%
Crit chance runes increase chance by 12%

With armor pen runes, the damage increase will be :
(75 - 29 - 15)*0.6 = 18.6 armor after penetration, that's a damage bonus of 175/118.6 = 47.55%

With crit chance runes, bonus damage will be :
(75 - 15)*0.6 = 36 armor after penetration, that's a damage bonus of 175/136 = 28.68%
Then, because there's a 12% crit chance damage bonus will be 1.2868 * 1.12 = 44.12%

So armor penetration will provide slightly more damage.

Now what if they have 45 armor? In that case last whisper isn't needed on the armor pen build so I won't count it.

(45 - 29 - 15) = 1 armor, that's a 145/101 = 43.56% boost for armor pen
(45 - 15) = 30 armor, that's a 145/130 = 11.54% bonus, with crit chance this becomes 24.92%

So armor penetration is significantly better.
Our numbers are so much different...

Why are you dividing 175 into the result, isn't that using the base armor in the end result when it's no longer the base? I'm failing to see why, although it's probably obvious to someone who knows math past the 3rd grade level, which I don't .

It makes no sense because with your math it's showing that armor penetration is so much better that it's a no brainer decision and picking critical strike is a huge mistake in any situation.

Btw with your method the hybrid red crit / penetrate quints route ends up being better than both.

(75 - 17 - 15)*0.6 = ~26 armor after penetration, that's a damage bonus of 175/126 = 38.9%
Then, because there's an 8.4% crit chance damage bonus will be 1.3888 * 1.084 = 50.6%

vs. 45 armor
(45 - 17 - 15)*0.6 = ~8 armor after penetration, that's a damage bonus of 34.3%
Then, because there's an 8.4% crit chance damage bonus will be 1.343 * 1.084 = 45.5%


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Lynxion

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Senior Member

06-21-2010

Quote:
Originally Posted by Holypope View Post

Crit chance: 32.7 crit chance from runes
What?


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Seaka

Member

06-21-2010

[QUOTE=wittywitt;1660211]

Quote:
Originally Posted by Holypope View Post
This has all been addressed before, but the OPS has oversimplied, which makes things a bit incorrect. Here's some better details:

Armor Pen: 29 armor pen with runes, 6 with masteries. 35 total. This can be pushed up to 50 with a brutalizer. that's about as high as it can go. period.

Crit chance: 32.7 crit chance from runes, 3 from masteries. 35.7 total. This can be maxed out to 100 easily, with any number of builds.





Actually it is 20% crit chance from runes.
Don't forget Starks and/or Black Cleaver to keep the theme going of armor pen/reduc.


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wildfire393

Senior Member

06-21-2010

Quote:
Originally Posted by Lawful View Post
Is it me or did you never pass your math school exams?

80 AR

LW+17 PNR from Reds.

New formula: 80-17/1.4=45
Old formula: 80/1.4-17=40

A decrease in 35 AR , not by any means 12 like you stated and the difference isn't really that big to make a fuss over it.
Okay. Let's say you have a fairly standard DPS Build - Armor Pen Marks and Ghostblade. This makes your armor Penetration 19 + 20 = 39. Now let's look at attacking your standard squishy target at level 18 - 80 armor.

Pre nerf: 80*.6 = 48 (Penetration of 32) - 39 = 9 net armor
Post Nerf: 80-39 = 41 * .6 = 24.6 (Penetration of 16) net armor.

In this scenario, it's lost half of its effectiveness, and is providing less Armor Penetration than a Stark's fervor (20 reduction) or a Sword of the Divine (30 Penetration while active). Combine this with the fact that it no longer gives increased damage over the parts and the item is significantly less effective now.


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R66Y

Senior Member

06-21-2010

I ran some initial calcs over my lunch, and will follow them up with with more thorough modeling later. I will post the finalized spreadsheets later when they are complete (likely this weekend, as there are a lot of different combinations you could build and I want to include item cost into the figures, as a brutalizer is not the same price as, say, IE).

Assuming you take the offensive masteries in either case to give you 6 AP, 2% crit, and +10% crit dmg, looking at only red runes (like I said, preliminary), you will do more damage to low armor opponents with the AP runes (I believe it was around 7% higher damage at 20 armor, 5% higher between 30-35 armor). The crossover point at which AP did less than crit% was around 110 armor. By 300 armor (tank type values), crit% yielded about 3% greater damage on average. A quick check with brutalizer did not shift the crossover point much (I think it was closer to 115 armor).

What this would indicate is that AP will give you higher sustained and reliable damage. Crit% would potentially land you a surprise burst of damage, but at 10%, the chances for landing 2 crits in a row is only 1%.