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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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