### Welcome to the Forum Archive!

Years of conversation fill a ton of digital pages, and we've kept all of it accessible to browse or copy over. Whether you're looking for reveal articles for older champions, or the first time that Rammus rolled into an "OK" thread, or anything in between, you can find it here. When you're finished, check out the boards to join in the latest League of Legends discussions.

### Can someone explain ArP and how it calculates for me?

Rolia

Senior Member

So I recently picked up urgot as a champion that I really enjoy and personally think is underestimated atm. Now with that said, this isn't a thread to where I want to discuss that, but mainly to discuss exactly how much effectiveness ArP (my way of saying Armour Penetration) is. Obviously this is a champ that loves to have ArP so he can maximize his dmg potential. Now I tried to go and look up how ArP is supposed to work, finding the formula for it so I could do some math myself to see exactly how much effective ArP I actually have but I feel I have ran into a bit of trouble because I believe my calculations don't quite seem true.

So to my understanding, there are actualy two different types to get past armour (I actually just learned this when I tried to look it up). There is Armour Penetration and Armour Reduction, and is calculated first in this order:

Armour Reduction %
Armour Reduciton Flat
Armour Penetration %
Armour Penetration Flat

Now with that said, im trying to figure out effectively how much effective "Armour bypassing" (for lack of a better term) I actually have, as well as how it actually works (meaning if theres a cap or what not).

I went in a custom game to farm out all my items and wrote all my end game stats at level 18 with my full build, and they are here:

AS - 0.96
AR - 212
MR - 30
MS - 380
Hitpoints 2377
Mana - 2610
HP/5 16
MaR/5 28
ArP 34 Flat 40%
ArR - 55%
CDR 40%
Extra AD for spells is - 157
Dmg with my q 130+(390 x .85)
Cooldown of Q - 1.2

My build consists of Ninja Tabi, Muramana, Black Cleaver, Last Whisper, Bloodthirster, Frozen Heart.
My runes I run are ArP reds and quints (19), Armour yellows (13) and cdr blues (7.5).
http://www.lolking.net/summoner/na/32379986#masteries Here is my mastery page that I use for urgot.

Mainly from all that im mainly looking for someone to calculate specifically how much armour I bypass with someone having an example of 350 armour. MY current calculation has me bypassing a total of 73% of that total armour, and to me that seems very wrong, but ill do my my math here for someone to tell me what Im doing wrong:

350 x .2 (20% armour reduction from Urgot's E)= 70
350 - 70 = 280
280 x .05 (5% armour reduction from 1st BC stack) = 14
280 - 14 = 266
266 x .05 (5% armour reduction from 2nd BC stack) = 13.3
266 - 13.3 = 252.7
252.7 x .05 (5% armour reduction from 3rd BC stack) = 12.635
252.7 - 12.635 = 240.065
240.065 x .05 (5% armour reduction from 4th BC stack) = 12.00325
240.065 - 12.00325 = 228.06175
228.06175 x .05 (5% armour reduction from 5th BC stack) = 11.4030875
228.06175 - 11.4030875 = 216.6586625

Ok from this portion of the math, the seemingly 55% armour Reduction I have turns out to be 38%, so that tells me that ArP is mulitplicitive, and not additive, at least that's what I understand. Now to calculate the rest of my Armour Penetration:

217 x .4 (40% from Mastery and Last whisper together) = 86.8
217 - 86.8 = 130.2
130.2 - 34 (flat armour pen) = 96.2

So after all that with that I believe is correctly done math, this character has went from 350 armour to 96 armour with all those, meaning I effectively have 73% "Armour bypassing" (again for lack of a better term). Now that seems stupidly high, but it may just be me doing my math wrong or actually never realizing how much ArP does for you. So if someone could clarify my math that would be helpful

Also one last thing, how come I get 8% Armour Penetraion from masteris, and 35% from Last whisper, but only retain 40% total Armour Penetration? Why 40 instead of 43?

TLDR I need help calculating how ArP works with all my stats written above.

EDIT: Forgot to add my mastery page setup I have for him.

Rolia

Senior Member

bump

TrulyBland

Senior Member

First off: The Black Cleaver stacks stack additively, so you're removing a bit more armor there, I believe.

Secondly: Last Whisper and the mastery stack multiplicatively.
100%-35% = 65%
100%-8% = 92%
92% * 65% = 0.92*0.65 = 0.4 = 40%

Rolia

Senior Member

Quote:
TrulyBland:
First off: The Black Cleaver stacks stack additively, so you're removing a bit more armor there, I believe.

Secondly: Last Whisper and the mastery stack multiplicatively.
100%-35% = 65%
100%-8% = 92%
92% * 65% = 0.92*0.65 = 0.4 = 40%

Oh really, so that actually means I even have more armour I bypass from them.

So with that said after redoing the math, I end up with a total of 77% armour bypass. I get 82 armour in the end that they have left after all that reduction and penetration is applied.

Is that true?