### Armor pen, Critical, Attackspeed, Damage

Achendach

Member

Ok, because the search function is down, i am unable to find a solid example on the effectiveness of Armor penetration, critical and attack speed. therefore i decided to do a little maths craft myself.

bear in mind that as you read this, there are certain mathematical rule i would need to bend.

Quote:
Critical chance comparison with Armor penetration
where
AP=armor penetration
AS= attack speed
CC= critical chance
A= armor (where A - AP cannot reach less then 0)
D= damage
and ?/0 = 0 (yea. bending the rules here)

CC= 100AP / (100 + A - AP) i will explain how i get this later

using example, assuming A= 100 and AP= 50, you will get CC=33
meaning you will need 33% critical chance in order to reach the same efficiency as 50 armor pen over 100 armor

using example, assuming A= 500 and AP=50, you will get CC= 9.090909...
meaning you will only need 9.09% critical chance in order to reach the same efficiency as 50 Armor pen over 500 armor

using example, assuming A= 100 and AP = 80, you will get CC= 66.66..
meaning you will need 66.67% critical chance in order to reach the same efficiency as 80 armor pen over 100 armor

Raw formula assuming

Armor pen. Critical Chance
100 / (100 + A - AP) * D * AS = 100 / (100 + A) *CC *D *AS
Summary
after some formula revision, i realize that Critical chance can be as good as Armor penetration in the early armor level (1~100) before you mind is blow away by the complexity of the formula. i shall simplify things. if (100+ armor)/ 2 = AP then you will need max critical in order to reach the same efficiency. sorry for the wrong first formula

Quote:

Attack speed and damage has a rather complicated way of understanding.
(multiplicative)
as you stack AS and D, the more you stack, the lesser efficiency you get as you stack. this is the diminishing return rule.

e.g.
100 damage + 100 damage = 100% bonus
200 damage + 100 damage = 50% bonus
300 damage + 100 damage = 33% bonus

the same goes for attack speed as well

HOWEVER this only apply if your comparing to previous DPS
if you look at base DPS, stacking AS and D is additive. Therefore

100 base Damage + 100 Damage = 100% bonus
100 base Damage + 200 Damage = 200% bonus etc etc
BUT its important to remember that

1 base Damage + 100 damage = 10000% bonus
1 base damage + 100% attack speed = 100% bonus
150 base damage + 100 damage = 67% bonus
150 base damage + 100% attack speed = 100% bonus
Summary
as base damage gets higher, the return of getting more damage is reduced as compared to attack speed.

before you quote one of my sentence to flame, please read finish first

QQ.
1)but the price of 1 damage is different from 1% attack speed correct? so its wrong to compare them this way
yes I'm well aware of that, therefore for the sake of connivence, i would just assume that the value of Critical chance, Armor penetration, Damage and attack speed is the same.

2) why is your DPS formula so short? what happened to Critical damage increase?
for the sake of simplicity, i got lazy :P sorry bout that. but yea. Crt damage does increase your damage.

because its difficult to place a price on any in-game items, i would use IP instead,

AS = 241IP/ attack speed
AP = 209IP / armor pen
CC = 440IP/ critical chance.
with that being said, it would seem in terms of numeric value, armor pen wins

which stats being more advance effective would be base on you readers. ultimately there are so many factors that affect DPs. how would you build you hero?

the full formula of DPS would be
Attack speed * Damage * ( 1 + Critical chance( 1 + Critical damage / 100 ) / 100 ) + special damage modifier = DPS
DPS * Armor / (100 + Armor - Armor pen ) = output (i'm being easy on the armor pen and reduction.)

Quote:
Originally Posted by EnderA
So in general, 1 ArmPen will increase your DPS by between 1% and 0.5% if your target has between 1 and 101 effective armor. (Effective armor being the previous number "A - AP". This means every point of armor penetration makes the next point more effective.)

1% CC will increase your DPS by between 1% and 0.5% if you have between 0 and 100% CC, but increasing CritDmg slightly improves that DPS increase.

1% AS will increase your DPS by (1 / (1 + AS)) until you reach 2.5 attacks per second.

1 Damage will increase your DPS by (1 / D).

40% ArmPen will increase your DPS by a wildly variable amount. If they have no armor, it will not increase your damage at all, if they have infinite armor, it will increase your damage by 66.7%. If they have 200 armor, it will increase your damage by 36.4%. If they have 100 armor, it will increase your damage by 25%. Remember that percentage armor penetration is applied AFTER flat armor penetration now, so they stack fairly poorly.

EDIT

correct a basic formula error (thanks EnderA)
Added in more facts thanks to EnderA

Shawn Ogg

Member

hi, interesting post. One thing then: since you need to have AP>0.5A then Last Whisper + BCleaver/Star's Fervor is always a better choice than go crit, isnt it?

If you get LW alone you got AP=0.4A with according to your calcs is equivalent to CC=66%, Infinity Edge + Phantom Dancer gives 50%, so LW + Infinity Edge seems a better choice.

If you get LW + BCleaver then you have AP=60 + 0.4*(A-60)= 84 + 0.4A which is equivalent for an armor of 500 to aprox CC=89% hardly obtenaible during a course of the game. (For an armor of 100 i get a CC of infinity or cero following your rule, i dont know what exactly that means)

In short, according to your calcs and the stats obtainables by items it seems it is always better to go for AP than CC. Isnt it?

Achendach

Member

yes. that is if you were to go in moderation. you need as much CC as much as you need AP, the effect in focusing 1 is small but going in moderation for both direction, you can push your DPS to the limit.

But as games goes on, it is better to use flat armor pen and CC on low armor heros. But its better to go a combination of last whisper and CC to deal more damage to tanks whom stack armor.

EnderA

Senior Member

Quote:
Originally Posted by Achendach
AP=armor penetration
AS= attack speed
CC= critical chance
A= armor (where A - AP cannot reach less then 0)
D= damage
and ?/0 = 0 (yea. bending the rules here)

CC= 100AP / (A - AP)

100 / (A - AP) * D * AS = 100 / (A) *CC *D *AS
I believe you're making a mistake in how to calculate damage. On a hit, armor multiplies the damage amount by:

100 / (100 + A - ArmPen), where A - ArmPen cannot go below 0. Meaning, if you penetrate all their armor, you do 100 / 100 damage = 100% damage. (Makes sense.)

For DPS, you would get:

D * AS * (1 + CC * (Crit Damage - 1)) * (100 / (100 + A - AP))

So in general, 1 ArmPen will increase your DPS by between 1% and 0.5% if your target has between 1 and 101 effective armor. (Effective armor being the previous number "A - AP". This means every point of armor penetration makes the next point more effective.)

1% CC will increase your DPS by between 1% and 0.5% if you have between 0 and 100% CC, but increasing CritDmg slightly improves that DPS increase.

1% AS will increase your DPS by (1 / (1 + AS)) until you reach 2.5 attacks per second.

1 Damage will increase your DPS by (1 / D).

40% ArmPen will increase your DPS by a wildly variable amount. If they have no armor, it will not increase your damage at all, if they have infinite armor, it will increase your damage by 66.7%. If they have 200 armor, it will increase your damage by 36.4%. If they have 100 armor, it will increase your damage by 25%. Remember that percentage armor penetration is applied AFTER flat armor penetration now, so they stack fairly poorly.

Achendach

Member

oh my.

i cant believe i manage to messed up at such a basic level. thanks endera

Shawn Ogg

Member

After reading this topic and the one about crit damage vs AP id been playing with leaguecraft builder to get a nice build for Teemo (but i think thats is also a solid one for ashe or trist). Lets see:

First i considered what minimum stats to get from items:

-AS > 40%
-AP forces to include a Last Whisper or a Black Cleaver
-Damage-> all i can get.
-Life Steel: at least one item that grants this

Then i considered only 4 slots: 6 minus one for boots and one for a surv item. I have come to thse two:

-Last Whisper
-Stark Fervor / Phantom Dancer + Vampiric Scepter
-Infinity Edge

-Black Cleaver
-Stark Fervor / Phantom Dancer + Vampiric Scepter

(Those builds are expensive adding a fourth item would be unrealistic)

What do you think?
When would you choose one over the other?
What would you change?