As a comment stated, Black Cleaver reduces armour on targets, and then the percentage from Last Whisper is subtracted from the amount after the black cleaver has reduced the armour.

This means, assuming full stacks of the debuff, that the targets armour will be reduced by 25% (or will be at 75%).

Armour=Armour*0.75

Then the 35% from Last Whisper and the 8% from Weapon Expertise can be taken off. These stack multiplicatively, so 1-(1-0.35)*(1-0.08)=0.402

This means that the armour becomes

Armour=((0.75*Armour)*(1-0.402))

This can further be simplified to

Armour=.75Armour*.598

And the final step; .75*.598

Armour=0.4485*Armour

And as such, to see how much is shredded, we can just say

1-0.4485=0.5515

or in percentage, 0.5752*100= 55.15%

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You may realise that there was brackets, but these were ignored. I will just state that multiplication, just like addition, is commutative, i.e. the order doesn't impact the result.

(2*3)*5=6*5=30
2*(3*5)=2*15=30

Section 1.

The only champions with Flat Armour Reduction are: Corki, Heimerdinger, Kog'Maw, Nasus, Taric and Rammus

Flat Armour Reduction is taken into account first. So really, you should account for this, but as it is not commutative and is dependant, you would need to know the exact armour value you wish to test, and just let the:

armour value = armour value - Flat Armour Reduction. Use the reduced value for specific examples.

For this example, Flat armour reduction is left at 0.

Section 2.

Next, you must account for the percentage of armour that will be reduced by items/abilities.

Black Cleaver debuff stacks additively, up to 25%, but any other %Armour Reduction stacks multiplicatively with that.

Let's say, for example, you apply 4 stacks of the debuff for 25% Armour Reduction, and you have an ability that further reduces 15%.

You may think that this means you reduce armour by 25%+15%=40%. This isn't quite correct, unfortunantly.

% Armour Reduction stacks multiplicatively and as such will actually reduce it by

(1-25/100)*(1-15/100)=0.6375-> This is their remaining armour (as a ratio to 1)

(1-((1-25/100)*(1-15/100))=0.3625 or 0.3625*100=36.25% -> this is how much you reduced their armour by

Where the '25' represents one percentage (in this case black cleaver armour reduction %) and '15' represents the other percentage (in this case the other ability that reduces armour by 15%)

You then need to let the armour = their armour * the ratio of their armour left.

In this example it will be-> Armour=Armour*0.6375

Section 3.

After this, % Armour Penetration is applied. This too stacks multiplicatively.

In this example, lets say we have 35% from Last Whisper, 8% from Weapon Expertise , and 15% from another ability.

So ((1-35/100)*(1-8/100)*(1-15/100))=0.5083

This means that the armour becomes what it was at the end of the previous step:
Armour=Armour*0.6375 but then you need to multiply it by 0.5083)

This means that in this example -> Armour=((0.6375*Armour)*(0.5083))

Or, for simplicity's sake Armour=0.6375Armour*0.5083

We can then multiply the 2 fractions, so to create a single co-efficient.
0.6375*0.5083=0.3240

Therefore, Armour=0.3240*(Armour - Flat Armour Reduction) (-Flat armour reduction accounts for armour being lowered before the others are stacked on)


Section 4.

Since S3, the final step is reducing the answer by the amount of flat armour penetration.

Therefore, Armour=((0.3240*(Armour - Flat Armour Reduction))- Flat Armour Penetration)

So effectively, if we have 25 armour penetration, it will just be ->

let fA=Final Armour and iA=Initial Armour which = 150

fA=(0.3240*(iA-0))-25

fA=(0.324*150)-25

fA=23.6 Armour

Note. This above formula is NOT universal. The % Armour Reduction and % Armour Penetration will change the co-efficient, and it must be worked out independantly for different values.

Just to prove its accurate, here is the same equation completed 2 different ways. Use your calculator and work it out if you want.

Let iA = 300

iA= Initial Armour
fA= Final Armour

Equation 1

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fA=((iA*0.75)*(1-0.402))

fA=((300*.75)*(1-0.402))

fA=((225)*(0.598))

fA=134.55

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Equation 2

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fA=0.4485*iA

fA=0.4485*300

fA=134.55

The above formula was simplified and not true to the initial values, nor were the order of operations dealt with in a disambiguous fashion.

35% ArPen from Last Whisper and 8% from Weapon Expertise are reduced multiplicatively, and thusly return the armour value ratio of (((1)-((35)/(100)))*((1)-((8)/(100))))=0.598; thusly 0.402/1 has been reduced, or 40.2%.

Abbreviations

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Armour Penetration = ArPen
Magic Penetration = Mpen
Attack Damage = AD
The Brutaliser = Brut
Sorceror's shoes = Sorcs
Ionian Boots of Lucidity = Ionians

All workings based on: MARKS/REDS AND BRUT/SORCS

WITH REFERENCE TO: LONGSWORD/KINDLEGEM/IONIAN BOOTS OF LUCIDITY

BEAR IN MIND, THESE RESULTS USE EXTRAPOLATION

ArPen Runes

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AD Runes

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MPen Runes

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Hybrid Runes

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Cost for runes

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