General Guide by glizdka
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Introduction
So I've heard you want some detailed information how does armor penetration work,
what are exact benefits.
Here you will learn everything about this, also I will give you numbers for it.
And the last thing you will learn here: when is The Black Cleaver better than Last Whisper.
If you are experienced player and know game mechanics, you can skip first chapters,
and go to chapter "Benefits from shreeding armor"
To do
 Calculations when to build penetration over building more damage (altho it might be standalone guide)
Penetration priority
This is first thing you need to know: Firstly you shreed with your flat penetration,
and then percentage penetration.
Say, you have 31 flat penetration from runes and masteries,
and 40 percentage penetration from Last Whisper,
Your taget had 150 armor.
So firslty we shreed flat penetration:
150  31 = 119
Then our percentage penetration:
119  (40% of 119) = 71
So total armor penetration is 150  71 = 79
This is also why flat penetration is more efficent
with low percentage penetration and vice versa.
Adding percentage penetration
So I've heard you have problems how does it work.
Game mechanics will never allow you to reach 100% penetration,
This is because each next percentage penetration cuts from already penetrated defense.
If you, say, have:
 40% magic penetration from Void Staff,
 10% from Arcane Knowledge ,
 30% from Locus of Power.
Then it goes like this:
100%  40% = 60%
60%  (10% of 60%) = 60%  6% = 54%
54%  (30% of 54%) = 54%  16% = 38%
Total percentage penetration will be then: 40% + 6% + 16% = 72%
How does armor work?
So I've heard you want to know how does armor exactly work, you need to firstly learn:
What is effective health?
It means basically that each point of defense (armor/magic resistance) increases effective health by 1% So if you have very high armor and low health it's like having high health and low armor.
Now that you know the effective health term I can introduce the pattern for counting damage reduction:
100%  HP (without armor)/Effective HP (HP x armor)
100 armor is 200%EHP : 100%  (100%/200%) = 100%  50% = 50% damage reduction
200 armor is 300%EHP : 100%  (100%/300%) = 100%  33% = 67% damage reduction
300 armor is 400%EHP : 100%  (100%/400%) = 100%  25% = 75% damage reduction
At the same time:
50% damage reduction is 50% damage taken
67% damage reduction is 33% damage taken
75% damage reduction is 25% damage taken
Why do we want to operate on DAMAGE TAKEN not on DAMAGE REDUCED?
Because DAMAGE TAKEN is the thing that kills us, not DAMAGE REDUCED.
More informations about armor can be found in my guide where I beat the myth about armor efficency cap
Benefits from penetrating armor
The best way to understand the benefit is to count DAMAGE AMPLIFICATION.
DAMAGE AMPLIFICATION is the difference between:
Damage taken after penetration and damage taken before penetration.
For example:
Enemy had 100 armor, and we pierce 50.
He had 50% damage reduction = 50% damage taken before penetration
Now he has 33% damage reduction = 67% damage taken after penetration
With examplary 100AD we hit for 67 damage instead of 50 before penetration.
The difference is 67  50 = 17.
The best way to see the benefit is to count it in percents.
17 is 33% of 50 so our damage is amplified by 33%
Although this method is very long, and it's not applicable to count benefits ingame,
when you are to decide if to buy Last Whisper or not.
Let me show you simpler and faster way...
Pattern
DAMAGE AMPLIFIED can be counted also by:
comparing difference between effective health before and after penetration.
If enemy has 100 HP and 100 armor he has 200 EHP (effective health).
If we shreed 50 of that armor his EHP will be lowered by 50 to result in 150 EHP.
It's like if we took away 50 EHP from his pool,
Now we have to deal 150 damage instead of 200 to kill him,
so it's like adding 50 damage to your 150 damage.
In other words damage was amplified, in this case, by 50 of 150 = 33%
Can you see that the 33% amount is equal to 33% counted in previous method? But the way is quicker.
So basically we have the pattern to count DAMAGE AMPLIFICATION:
In practice:
Piercing 50 of 200 armor is: 50 / (100 + 200  50) = 50 / 250 = 20%
Piercing 30 of 50 armor is: 30 / (100 + 50  30) = 30 / 120 = 25%
Piercing 100 of 110 armor is: 100 / (100 + 110  100) = 100 / 110 = 91%
Now you can quickly count how much will you benefit from shreeding armor.
Cheap Sheet for lazies
So, I decided to give you table, where you can check most values.
Red color becomes more and more intensive along increasing damage amplification value.
Horizontal axis is armor penetration you have. (Including percentage penetration as well).
Vertical axis is armor your enemy has.
If you, say, want to check how much will give extra 15 penetration from The Brutalizer,
But you already have 30 penetration from masteries and runes. Enemy has 130 armor.
Then just check amplification for 15 penetration against 100 armor (130he has  30pen you already got).
Facts
We can clearly see several facts facts:
 More armor you shreed in percents, more damage amplified you get:
100 pierce of 100 armor is 100% damage amplification.
75 pierce of 100 armor is 60% damage amplification.
50 pierce of 100 armor is 33% damage amplification.
25 pierce of 100 armor is 14% damage amplification.
So it's best to cut all the enemy's armor
 More armor enemy has, less damage amplification you get for the same armor penetration,
(flat armor penetration works better against low armor targets):
100 pierce of 100 armor is 100% damage amplification.
100 pierce of 200 armor is 50% damage amplification.
100 pierce of 300 armor is 33% damage amplification.
100 pierce of 400 armor is 25% damage amplification.
 Percentage armor penetration doesn't only cut off more armor with higher target's armor,
but also provides more damage amplification along increasing target's armor:
50% of 100 armor is 33% damage amplification
50% of 200 armor is 50% damage amplification
50% of 300 armor is 60% damage amplification
50% of 400 armor is 67% damage amplification
The Black Cleaver vs. Last Whisper
The point which Last Whisper is better than The Black Cleaver in,
is when penetration from both equals against certain amount of armor.
Ofcourse if we look at penetration only,
because The Black Cleaver gives better stats besides penetration itself.
Keep in mind that you already have some flat and percentage penetration from runes/masteries.
Taking a look at penetration order (flat before percentage) i can tell,
that the point is somewhere around 140 armor depending on how much flat and percentage penetration
you already have from runes and masteries.
140 is the point for full penetration from runes and masteries,
for bare item's penetration the point is somewhere areound 130 armor
you will cut 82 armor with The Black Cleaver and 81 with Last Whisper against 140 armor enemy.
Against higher armor enemy Last Whisper has better penetration.
With 21 flat and 10% percentage penetration,
you will cut 73 armor with The Black Cleaver and 75 with Last Whisper against 140 armor enemy.
With 25 flat and 10% percentage penetration,
you will cut 77 armor with The Black Cleaver and 78 with Last Whisper against 140 armor enemy.
With 15 flat and 10% percentage penetration,
you will cut 68 armor with The Black Cleaver and 72 with Last Whisper against 140 armor enemy.
you will cut 70 armor with The Black Cleaver and 71 with Last Whisper against 140 armor enemy.
you will cut 63 armor with The Black Cleaver and 65 with Last Whisper against 140 armor enemy.
With penetration only from items,
you will cut 45 armor with The Black Cleaver and 56 with Last Whisper against 140 armor enemy.
Bye
I hope now you know everything about penetration and that you find it informative.
Remember that calculations for armor are same for magic resistance,
since game mechanics are the same for both.
Please don't forget to vote.
Little credit:
jhoihjoi's guide how to create a...guide  that helped me a lot


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