# Season 3 Armor and Armor Penetration

So with the new season there will be new Items and changes to mechanics in the game. One that popped out at me, was the big change to Black Cleaver with its new stats:

- +45 Attack Damage
- +10% Cool-down Reduction
- +10 Armor Penetration
- Passive: Dealing physical damage to an enemy reduces their Armor by 5% for 6 seconds. This effect stacks up to 5 times on the same target.

Sounds pretty cool eh? Well even cooler the 5% armor reduction stacks additive instead of multiplicative. Meaning that it actually reduces armor by 25% instead of 22.6%.

Big whoop right? The example provided plays it down to loosing 100 armor if you have 400 at the start, leaving you with 300. That's not so bad. But what happens when you factor skills into the equation? Well, these do decrease multiplicative instead of additive, but lets look at some case by case champions. Starting off with the most alarming example I could find...

## Renekton

Renekton has the biggest reliable Armor Reduction under his hood. With 35% reduction he literally rips trough your armor. On top of that his Slice and Dice -> Ruthless Predator combination will allow him to put on 5 Black Cleaver stacks in 1-2 seconds. So what happens when you build Renekton to take advantage off the new mechanics and items? Well just for funzies let's give him the new Black Cleaver and a Last whisper some penetration runes and masteries and have him attack a target with 100, 200 and 400 armor.

### 100 armor

- 35% Armor Reduction from Dice will reduce 100 armor to 65 armor
- 25% Armor Reduction from Black Cleaver will reduce 65 armor to 49 (48,76)
- 50% Armor Penetration form Last whisper and Weapon Expertise will half that value to 24 (24,375)
- 15 Armor penetration from Marks will reduce that value down to 9 (9,375)
- 10 Armor penetration from Black Cleaver will reduce it down to -1 (-0,625)
- 10 Armor penetration from Quints will reduce that value down to -11 (-10,625)
- 6 Armor penetration from Sunder will reduce that value down to -17 (-16,625)

### 200 armor

- 35% Armor Reduction from Dice will reduce 200 armor to 130 armor
- 25% Armor Reduction from Black Cleaver will reduce 130 armor to 98 (97,5)
- 50% Armor Penetration form Last whisper and Weapon Expertise will half that value to 49 (48,75)
- 15 Armor penetration from Marks will reduce that value down to 34 (33,75)
- 10 Armor penetration from Black Cleaver will reduce it down to 24 (23,75)
- 10 Armor penetration from Quints will reduce that value down to 14 (13,75)
- 6 Armor penetration from Sunder will reduce that value down to 8 (7,75)

### 400 armor

- 35% Armor Reduction from Dice will reduce 400 armor to 260 armor
- 25% Armor Reduction from Black Cleaver will reduce 260 armor to 195
- 50% Armor Penetration form Last whisper and Weapon Expertise will half that value to 98 (97,5)
- 15 Armor penetration from Marks will reduce that value down to 83 (82,5)
- 10 Armor penetration from Black Cleaver will reduce it down to 73 (72,5)
- 10 Armor penetration from Quints will reduce that value down to 63 (62,5)
- 6 Armor penetration from Sunder will reduce that value down to 57 (56,5)

### Combination case

So with a single combination Renekton will bring a single target down to under 50% of their previous armor for his entire team. And for himself? Well against 100 armor targets he will do more then true damage. Continuing the Math a bit, when Renekton bursts any of these targets with his full skill combination damage with the following stats at level 18:

- 109 Base AD
- 95 Bonus AD (Last Whisper, Black Cleaver)
- 1,142 Attack speed
- 50% armor penetration (Last Whisper, Weapons Expertise)
- 41 flat penetration (Runes, Black Cleaver, Sunder)

### Damage Calculation

It will translate to the following damage calculations on 100 armor:

- Slice; 150+(95*0,9=85,5)=236 Damage, Multiplied by (100-5(BC)/2=47,5-41=6,5 Armor(100/106,5=0,938)) 0.94 = 222 Damage
- Dice; 225+(95*1,35=128,25)=353 Damage, Multiplied by (100-10(2bc)=90*0,65(Dice)=58,5/2=29,25-41= -11,75 armor(98/(100-11,75)) 1.11 = 392 Damage
- Ruthless predator (1st hit); 45+(109+95*0,75=153)=198 Damage, Multiplied by (100-15(3BC)=85*0,65=55/2=28-41= -13 armor(98/(100-13)) 1.13 = 223 Damage
- Ruthless predator (2nd hit); 45+(109+95*0,75=153)=198 Damage, Multiplied by (100-20(4BC)=80*0,65=52/2=26-41= -15 armor(98/100-15)) 1.15 = 227 Damage
- Ruthless predator (3rd hit); 45+(109+95*0,75=153)=198 Damage, Multiplied by (100-25(5BC)=75*0,65=49/2=24-41= -17 armor(98/100-17)) 1.18 = 230 Damage
- Cull the meek; 180+(95*0,8=76)=265 Damage, Multiplied by 1.18= 313 Damage

### Concluding Damage Output Reasoning=

In total it's 1607 Damage from the skills plus an additional 3 seconds of armor reduction and auto attacks resulting in 3 auto attacks at a 1.18 damage multiplier meaning 204*3*1.18=722+1607=2329 effective physical damage in about 5 seconds of time. Keep in mind that this is achieved by building nothing more but a Black Cleaver and a Last Whisper. Even more bonus damage scales things out of hand even more, dealing 914 extra damage for every 100 AD during that time span. That means if you get CDR boots, Black Cleaver, Last Whisper, Elixir of Fortitude, Elixir of Brilliance and three Bloodthirsters you will deal 5162 damage every 9 seconds starting with the highest Cool-down skill. The combination takes about 5 seconds to pull off, leaving you with 4 seconds of actual cool down.

## Other champions

Now I'm not about to take you to math wonderland for all of them. Just summing up that similar champions that have Armor Shred passives and physical damage combinations like: Jarvan, Jayce, Urgot and Wukong will get a heavy boost this new season. The most scary one in a dual might actually be Nidalee, with the ability to stack up the Black Cleaver shred from range waiting for you to step into her trap, reducing your armor by 55% for 12 seconds as long as she attacks you every 5 seconds... As for team fights, Wukong does a crazy job of diving in there with his dash into ulti and applying 5 stacks of Black Cleaver to the enemy easy, decreasing armor by 47% to the target of his choosing just by tagging them with Crushing Blow when he is done spinning. Jayce, Jarvan and Urgot get honorable mentions for using the new Black Cleaver to its fullest potential with Xin Zhao, Kayle and Trundle closing in behind due to lower Shred values and just plain dissynergy due to dealing magic damage on skills which doesn't proc the Black Cleaver on hit effect.

# Conclusion

In the end I like the new way penetration is calculated. But with the new percentage shred black cleaver I am worried that building armor will get quite insignificant indeed. Having a Nidalee, Renekton or Wukong decrease your armor by 55%, 49% and 47% respectively was not on my most wanted list.