Hi summoners!
Some games ago my friends in LoL discussed what would be better on AD carries early on. Armor Penetration or flat Damage.
Therefore is decided to study this in detail:

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ASSUMPTIONS:
Basic assumptions:
I've used the stats for most AD carries but only show numbers from Ashe:

We assume that the attacker has a base damage = 50 and increases by 3 every level
Base Armor = 11,5
Armor per Lvl = +3,4


3 Builds were tested: I only take red Runes and Quintessences into account!!!
a.) Pure ArPen: 25 ArPen (runes) +6 (Masteries), BaseDamage=50+3(Masteries)
b.) Pure Damage: 6 ArPen (Masteries), BaseDamage=50+3(Masteries)+15(runes)
c.) Balanced: 15 ArPen (red-runes) + 6(Masteries), BaseDamage = 50 +3(Masteries) + 7(quints)

I also included the 10% armor Pen passive in damage calculation.
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EQUATIONS:

REAL_ARMOR = Base_Armor - (Base_Armor*0,1)-ArPen
REAL_DAMAGE = [1-(REAL_ARMOR/(100+REAL_ARMOR))]*Base_Damage
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RESULTS:
I've attached the diagram for the results for better understanding
ArPen Build 56,7 58,0 59,2 60,4 61,5 62,5 63,5 64,4 65,3 66,1 66,9 67,6 68,4 69,0 69,7 70,3 70,9 71,5
Damage Build 57,4 58,4 59,4 60,3 61,2 62,0 62,8 63,6 64,4 65,1 65,7 66,4 67,0 67,6 68,2 68,7 69,3 69,8
Balanced 58,0 59,1 60,2 61,2 62,2 63,1 64,0 64,9 65,6 66,4 67,1 67,8 68,5 69,1 69,7 70,3 70,8 71,4



Since you cant reduce Armor less then 0 with ArPen build a.) seems weaker at the first levels.
ArPen build: reaches same damage as other builds at lvl 6. Once lvl 8 it starts to deal more damage.
The balanced build wins over all levels slighty over the pure damage build (on average dealing 2 damage more)
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CONCLUSION:
Taking ArPen reds and damage Quints does most damage compared to other rune combinations.


Hope that helps

Enjoy to bring Havok as AD Carry to the fields of justice

Cheers
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Changes:
a.) I actually calculated with 7 Ad from quints just wrote it wrong in post. Fixed
b.) Included Armor Seals. means Base_Armor + 9*1,41(Seals) + 3 (Masteries)

On average:
Pure damage build falls of compared to other builds (equal till lvl 2!)
Balanced build wins over all levels compared to other builds with roughly 1-2 damage
ArPen build is only strongest at lvl 18...

CONCLUSION:
Balanced build does most damage over all (i mean 1-2 damage is not much but hey)
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Concerning the question of ShakeNBakeUK: When do Damage Quint/lvl dominate the flat damage:

Ok here i attached the new calculation tab.


Considering the question: when does Ad/lvl dominate flat Ad

Not really sure if i understood correct what you want to know but here is one answer:

Flat Ad: 15 (reds+quints)
AD/lvl: 3*(0,25per lvl) + 9*(0,13 per lvl)

You get equal damage once you hit lvl 7, then AD/lvl is better
at lvl 18: Flat AD = 15, ADperLvL = 34,6 (almost double)
reds quints sum
1 0,75 1,17 1,92
2 1,5 2,34 3,84
3 2,25 3,51 5,76
4 3 4,68 7,68
5 3,75 5,85 9,6
6 4,5 7,02 11,52
7 5,25 8,19 13,44
8 6 9,36 15,36
9 6,75 10,53 17,28
10 7,5 11,7 19,2
11 8,25 12,87 21,12
12 9 14,04 23,04
13 9,75 15,21 24,96
14 10,5 16,38 26,88
15 11,25 17,55 28,8
16 12 18,72 30,72
17 12,75 19,89 32,64
18 13,5 21,06 34,56
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comparison with Balanced build:
Where you have ArPen reds (dont change over level)
Quints: 6,8
As you can see in the table above: Once you hit lvl 10 Damage/lvl Quints do more damage.

CONCLUSION:
For laning phase the flat damage quints are sure the better choice.

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Had to change the formular:
Real_Armor = Base_Armor-ArPen - (Base_Armor-ArPen*0.1) (since i forgot that ArPen happens before %based Armor pen)

I will only give a short comparison of Full AD, Balanced and full ArPen

ArPen
1 53
6 63,5
11 67,6
18 72

Balanced
1 56,8
6 64,5
11 68,29
18 72,3

Damage
1 57,1
6 64
11 67,8
18 71,3

Conclusion Till lvl 6 Flat damage is minor better (not even 1 damage though)

Attached Thumbnails

 

nice calculations.
is armor pen worth the 2-3 extra dmg at late game, over the 10 higher dmg earlier game and FAR easier last hitting that flat AD provides?

NOPE.JPG

edit: the above was when the values showed AD having a huge advantage vs. low armor targets, i.e. not taking armor seals & masteries into account.



please can you do a comparison of ArP marks and quints vs AD marks and quints vs AD/lvl marks and quints for me?

I would really like to know at what stage AD per level overtakes Flat AD or ArP.


edit2: how about if you use Flat AD Quints and AD per lvl Marks, at what level does that setup out-perform the Flat AD / ArP setup.
Basically I want to know if it is ever worth taking AD per lvl Marks at the moment.
Yes you sacrifice some of your very early game strength, but for the majority of the game length they should outperform the flat runes.

you may also wish to re-do the original calculations, taking flat armor seals into account, as every bot lane champ is currently taking those runes.
edit: and +6 armor from defensive masteries

3x AD quints give 7 AD (6.8), not 6 AD; so a mix between ArP/AD is even better than you make it seem.

gj

a.) ShakeNBakeUK: Hmm True i should include Armor Seals, will do soon
b.) ivo111: Will change that to
c.) ShakeNBakeUK: Will see if i have time for that to

will post soon

rlly gj, we need more people like you with facts instead opinions.

Now add crit chance + crit dmg(masteries early + IE later) & see which one does most dmg when you crit.

Flat AD is better because Sivir and Graves.

but it still confirms a 3AD 6ArPen Mark-setup