### Is this correct?

Ru3y

Junior Member

I couldn't change the title of this thread for some reason. basically this was a discussion about the hp:armor(or MR) ratio that gives best survivability agaisnt pure physical/magical attacks.

from page two

Quote:
Originally Posted by [B
DragonArmy[/b];414122]LOL, No one has figured out the math yet. I'll revise a post made on the MYM forumns by AKI

.....

H = 6.5625a + 656.25
(* a=armor H=health)

The important point is that Armor is not that helpful when you have low life and the other team is doing magic damage. However, armor becomes much more effective when you have a lot of life and there is less magical damage. Don't forget that your character also has a natural increase in armor and magic resistance as he or she levels.

Quote:
Originally Posted by [B
BeakOr[/b];323575]
hp = 600 + 6ar

So if hp is greater than 600 + 6ar, armour is better value. If it's less, hp is better value. Some examples:

At 1000 hp, the critical value is 65 armour
At 2000 hp, the critical value is 230 armour
At 3000 hp, the critical value is 400 armour

4) Case 2: Equal parts magic and physical

Given armour and magic resist are (nearly) the same price, in this scenario it's best to have equal armour and magic resist. This means that the price of each point of armour essentially doubles (think about it); it also means I can pretend that there's just one armour stat instead of two.

hp = 1200 + 12ar
----------------------------------------------------------------------------------------------------------
i also did some math on what is the attack:critical chance % for highest damage output (at consistant attack speed). this was the result:
Atk CC(%)
150 20
175 40
200 60
225 80
250 100

basically, you shouldn't get cc until you have at least 150 dmg (provided that you have decent AS)

i'm pretty sure that the maths behind this is wrong but the result looks pretty fair to me.

PREVIOUS POST (pretty useless):
----------------------------------------------------------------------------------------------------------
this is definitly wrong but i'm having a hard time finding which part of the math below is wrong

i've had no luck in finding what is the optimal HP:Armor ratio, all of my results came out pretty absurd. Does anyone know what it it?

thanks for the last post, i'll check that out.
btw, by using the ehp = hp + (arm*hp/100) formula, the optimum hp:armor ratio is 1.22222 : 1
...

---
Cloth armor 300G : 20armor
15G = 1 armor
Ru3y 475G : 200 HP
2.375 G = 1HP

(i know that hp and armor are cheaper with more expensive items. but let's just assume that the resistance: gold ratio is all the same)

1 armor = 6.3157 HP

(1-Arm/(Arm + 100))*Damage = actual Dmg
(Arm/(Arm + 100))*Dmg = Dmg reduced

armor is only effective (worth to purchase) when each armor reduces >7 dmg

substitute Arm with 1
(1/1+100)*Dmg > 7

Dmg > 7/0.00990099
Dmg > 707

-----
armor (or magic resistance) is only worth to be purchased when the enermy's dmg goes above 707

ShootTheBoot

Junior Member

No

Ru3y

Junior Member

why?

v3r175s

Member

You would need to compare each individual items, stats, and price, you cant just use two items to make the point for all of them.

Ru3y

Junior Member

i know that hp and armor are cheaper with more expensive items. but is this method correct?

v3r175s

Member

I didn't check the formulas, but what im trying to say is, for example you can't use the relationship between those two to apply to all items, yes in that case it would be better to buy the ruby than cloth armor, but for different items, the relationship would be different because the amount of armor you get for \$s would be different etc. and also another point is that there are virtually no only armor items, they all have other stats, so whilst practically your argument might make sense in a mathematical sense, there are no items to apply it to, for example guardian angel might not be worth the armor rather than health but its ability to revive makes the argument unmathematical.

Ru3y

Junior Member

Quote:
Originally Posted by v3r175s
so whilst practically your argument might make sense in a mathematical sense, there are no items to apply it to, for example guardian angel might not be worth the armor rather than health but its ability to revive makes the argument unmathematical.
you're right that the stat:gold ratio differs with different items, so i just want to know if my argument is correct in a mathematical sense

the reason im doubting is because i've read others arguments that says the amount of armor you purchase should be corresponding to the amount of hp you have, but i thought it should only be based on how much damage the enermy have

v3r175s

Member

I don't know what the formulas are, sorry so i cant say

Ksielvin

Senior Member

Quote:
Originally Posted by Ru3y
the reason im doubting is because i've read others arguments that says the amount of armor you purchase should be corresponding to the amount of hp you have, but i thought it should only be based on how much damage the enermy have
Here's why you need to include the health and armor you already have.

If you have 100 health, 1 armor is worth +1 effective health against physical damage. If you have 200 health, it's +2.

EDIT: Effective health means it takes that much damage to kill you from full health.

Let's say you're a lvl 18 Cho'gath with base stats of 1910 health and 84 armor. You have 1910*1.84 = 3514 effective health against physical damage, and you aren't worried about magical damage. If you get Ruby Crystal for 475g, it gives you 2110*1.84-3514 = 368 additional effective health, which is 0.775 per gold. If you get Cloth Armor for 300g, it gives you 1910*2.04-3514 = 382 additional effective health, which is 1.273 per gold.

So depending on your current stats, a new defensive item will have different value for you. If Cho'gath already had a Frozen Heart, health would become more valuable relative to armor. If he had a full Feast stack, armor would gain value. Same with health and magic resist of course.

Measuring effective health against damage type is a way of saying how much the stat improves your durability. You can arrive at similar valuation by starting with the damage reduction percentage. Only if you want the actual time in seconds it takes to kill you do you need the enemy dps.