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### Interesting Derivative Analysis of Armor's Diminishing Returns

TheUnburned

Senior Member

Was just doing some calculations on the effectiveness of armor, and I came across an interesting realization

Using the derivative:
d/dx 10000 / (100 + x)

Representing the damage multiplication of armor on physical damage.

Each additional point of Armor is half as effective after 41 armor, as it was at 0 armor.
Armor becomes 25% as effective by 100 armor
Armor becomes 10% as effective by 216 armor

Essentially meaning that after 200 armor, additional armor becomes increasingly worthless. Hence why an attack-speed slow is much more potent at this point.

Drakkar

Senior Member

why do you think randuin's is so crucial?

MickeyTheFiasco

Senior Member

Quote:
TwistedVampire:
why do you think randuin's is so crucial?

Indeed it is.

Steelflame

Senior Member

armor is supposed to scale in a way that every point of armor gives you 1% more effective health vs physical damage.

Private Riem

Senior Member

Quote:
Steelflame:
armor is supposed to scale in a way that every point of armor gives you 1% more effective health vs physical damage.

And it does.

SummonerMan Matt

Senior Member

lets say your oppnt does 100 phy. damage per attack and you have 0 armor with 1000 HP
It takes 10 hits to kill you

Now you have 100 armor
100*(100/200)=50 damage per hit
it takes 20 hits to kill you

Now you have 200 armor
100*(100/300)= 33.3333333
it now takes 30 hits to kill you.

Now you have 300 armor
100*(100/400)=25
it now takes 40 hit to kill you.

Each 100 armor = another 10 hits to kill you. Even with the diminishing returns.
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Lets try this agian with 2000 Hp to show why its not that simple tho.

lets say your oppnt does 100 phy. damage per attack and you have 0 armor with 2000 HP
It takes 20 hits to kill you

Now you have 100 armor
100*(100/200)=50 damage per hit
it takes 40 hits to kill you

Now you have 200 armor
100*(100/300)= 33.3333333
it now takes 60 hits to kill you.

Now you have 300 armor
100*(100/400)=25
it now takes 80 hit to kill you.

Now 100 armor = 20 more attacks because your base HP is higher. This is why balancing out HP and armor is helpful

Kirthalion

Senior Member

Quote:
SummonerMan Matt:
lets say your oppnt does 100 phy. damage per attack and you have 0 armor with 1000 HP
It takes 10 hits to kill you

Now you have 100 armor
100*(100/200)=50 damage per hit
it takes 20 hits to kill you

Now you have 200 armor
100*(100/300)= 33.3333333
it now takes 30 hits to kill you.

Now you have 300 armor
100*(100/400)=25
it now takes 40 hit to kill you.

Each 100 armor = another 10 hits to kill you. Even with the diminishing returns.
So its not as bad as people make it out to be.

Without diminishing returns killing champs would be close to impossible.

What is cheaper to stack then? 300 armor or 3000 hps?

SummonerMan Matt

Senior Member

Quote:
Kirthalion:
What is cheaper to stack then? 300 armor or 3000 hps?

One sec looking into this now

What does your champs Max hp start out at? Irelia has 2k , jax has 2.3k, Lee has 1.9k
Assuming 2.1k

What does your champ Max armor start out at? Irelia has 82, jax has 84.2, lee has 82
Assuming 83

Are we talking about JUST buying HP and armor or do I need to use in game items?
Assuming Just HP and Armor

HP
Giants belt = 1000gold/380hp = 2.631 Gold/HP
Ruby crystal =475 gold/ 180hp = 2.638 Gold/HP

HP= ~2.63g Gold

3000hp - (assumed base) 2100 = 900 (you need from items)

900(hp from items)*2.63 Gold/Hp = 2367 gold

Armor
cloth armor = 300 gold/15 armor = 20 gold/ armor
Chain Vest = 720gold/40 armor = 18 gold/ armor

Armor = ~19Gold

300 Armor - (assumed 83 base) = 217(from items)
217(from items)*19 Gold/armor = 4123 Gold

but to be honest I am not sure why u wanted this information

thepr0owns

Senior Member

Quote:
Kirthalion:
What is cheaper to stack then? 300 armor or 3000 hps?

technically Armour is, but Armour can be shredded.

Teraxe

Senior Member

Quote:
SummonerMan Matt:
lets say your oppnt does 100 phy. damage per attack and you have 0 armor with 1000 HP
It takes 10 hits to kill you

Now you have 100 armor
100*(100/200)=50 damage per hit
it takes 20 hits to kill you

Now you have 200 armor
100*(100/300)= 33.3333333
it now takes 30 hits to kill you.

Now you have 300 armor
100*(100/400)=25
it now takes 40 hit to kill you.

Each 100 armor = another 10 hits to kill you. Even with the diminishing returns.
So its not as bad as people make it out to be.

Without diminishing returns killing champs would be close to impossible.

Exactly, each point of armor increases your TTL the same as the previous.