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:

AD - 390

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 from Manamune - 52AD

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?

Again thank you for your help and if you don't understand something leave a reply and ill try to fix my opening post. Thanks!

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.