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45
On Percent Armor Pen
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With 30% armor pen versus no armor pen, we get the following damage boost at the following armor amounts:

50 armor - take 66.6% damage   35 armor -take 74.2% damage   11% more damage

100 armor - take 50% damage   70 armor - take 59% damage   17.5% more damage

400 armor - take 20% damage   280 armor - take 26.3% damage   31.5% more damage

1000 armor - take 9.1% damage   700 armor - take 12.5% damage   37% more damage

2000 armor - take 4.75% damage   1400 armor - take 6.66% damage   Take 40.2% more damage

This approaches 42.85% bonus damage at infinity, and realistically caps at 40% for hypertanks (rammus, malphite, etc), with a minimum 11% damage if rushed against hypermages by level 6 or 7 (orianna, kassadin, etc).

If rushing lethality, which is a 60% 2.22% per level of lethality conversion to flat armor pen, completing a lethality item at level 6 for hypermages provides slightly more damage (2-3% more) but is equal or less against any other opponent with naturally more armor or has built armor. This only worsens as the game progresses.

Maths:

Limit x»infinity (100/100 .7x - 100/100 x) / 100/100 x

Lim. x»inf 100 x/100 .7x - 1
100s become negligible

Lim. x»inf x/.7x - 1 = 42.857

Let's compare this with general scaling and alternative items. We're assuming rushing armor penetration as a primary item, which gives us two options: serylda's grudge (SG) and Lord Dominik's Regard (LDR) which have the stats below:

SG:   45 AD   20 haste   30% armor pen   Abilities slow (no damage change)

LDR:   30 AD   20% crit   30% armor pen   0-15% bonus damage (with 1 item at level 6 it's reasonably max 6% with 800hp difference, averaging 3%. At 10 resonably 12% with 1200hp difference, averaging 6%)

The average AD champion has between 70 and 100 AD at level 6, the ADCs at the lower end and top lane bruisers at the upper end. We'll average this to 85 base AD (bAD) for the sake of simple maths.

Let's compare this to a couple alternative options, namely meta items The Collector (C) and Blade of the Ruined king (BoRK) to keep the price bracket the same and avoid Mythics.

C:   55 AD   20% crit   12 lethality (9 pen at 6/7, 10 pen at 10/11)   -5% max health (~5% more damage with minimal stats)

BoRK:   40 AD   25% AS   8% lifesteal (no damage change)   4%/6% max health per hit (on average)     At 1600 health this averages 80 damage a hit     At 800 health this averages 40 damage a hit     Taking 60 as reasonable average @ level 6, 90 at level 10   One flat 75 magic damage at level 6/7, 100 damage at 10   Slow (no damage change)

Assumptions moving forward:   Bonus attack speed is not a 1:1 damage increase, nor is ability haste, but we can consider both about a 1:.5 damage increase as raw abilities scale 1:1 with haste, raw attacks scale 1:~1 with attack speed at these low levels, and we'll assume you're maximizing dps by squeezing in autos between abilities and utilizing auto resets. This varies by champion, as base AD does, we're just getting a feel for the items as a whole and how they stack up. Utilizing this equation, below, we'll calculate the approximate boost of each item:

((AD bAD) * (100 AH/2)/100 * (1 AS/2) * (1 .75 crit/2) * (1 pen/lethality boost) * other boosts)/bAD and note extra damage.

SG = ((85 45) * 110/100 * 1 * 1 * (1 .1425) * null) / 85 = 192.25% damage
LDR = ((85 30) * 1 * 1 * (1.15) * (1.1425) * (1.03)) / 85 = 183.09% damage
C = ((85 55) * 1 * 1 * (1.15) * (1.04) * (1.05)) / 85 = 206.8% damage
BoRK = ((85 40) * 1 * (1.125) * 1 * null 60) / 85 = 229.42% damage 75 magic damage

This implies building % pen as a first item is not cost effective (BoRK and Collector win this round). However, let's look at level 10/11 with pen as a secondary item. Below is a table formulated with the same equation as above, but pairing common Mythics as a core item with the previous 4 items as a secondary item (or vise versa). Base AD has gone up by 15 points to 100, %pen has increased from 14.25% (average of 50 and 100 armor) to 18% (average between 150 and 70 armor), and we'll still consider attack speed growth as negligible for simplification.

Mythic options - chosen on populatrity and AD base:   Kraken Slayer - 55AD, 15%as, 20% crit, 50 .4(mAD sAD)/2.5, 10%as   Immortal Shieldbow - 50ad, 20%as, 20%crit, 7% lifesteal (null), 5ad   Galeforce - 60ad, 20%as, 20%crit, bonus (195 .45(mAD sAD))*1.4, 2%ms (null)   Eclipse - 60AD, 12 lethality (9 pen), -4.5% max health (~4% damage with stats), 4% armor pen (3% damage)   Goredrinker - 55ad, 20ah, 175�D for 175 burst, 7AH  

Plugging these into the equation above we get the following table for damage boost:  

X Serylda’s Grudge Lord Dominiks Regard Collector Blase of the Ruined King
Kraken Slayer 285.91520625 292.12003125 299.89546875 263.29125
Immortal Shieldbow 279.209535 285.276475 292.879125 257.690625
Galeforce 286.189773375 292.98665 299.8524375 264.275
Eclipse 266.63325 274.701544 282.67512 251.28
Goredrinker 236.3186 242.63468933125 249.10093096875 220.46146875

In summary, BoRK is a best first-rush item for damage output but not a very viable second item. For second, LDR and Collector are about even, keeping in mind that LDR gets better against more armor AND health, while Collector is better against damage builds, this should advise your build options moving forward.

TL;DR: Dont sleep on building LDR as a second item as percent armor pen scales hella well due to natural armor growth, you practically lose no damage immediately but scale better later. Bork is only good before armor gets built, but provides survivability later on so if you are planning on building it build it first.

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