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BUILD GUIDE: Health and Resistances. An Optimization Guide by Cormag

by Cormag (last updated over a year ago)

227,376 Views 67 Comments

Runes

Unknown Section mastery

Introduction

Ever wondered if you should be buying health, or continue buying resistance? Then this guide is for YOU!

This is a mathematical guide on how to optimize your defenses. It should be useful for people who play tanks mostly, but hopefully lots of people will find it helpful.

Check out my other guide!!: http://www.solomid.net/guides.php?g=4844

Some people have asked where my xin guide is.. I removed it since it was outdated, will release a new one sometime in the future.

The Formula

Incoming damage is reduces by a factor, according to the formula below:



100/(100+Armor)



Examples:

1. Having 50 armor will multiply incoming physical damage by 2/3 (Blocks 1/3 of the damage)

2. Having 100 armor will multiply incoming physical damage by 1/2 (Blocks 1/2 of the damage)

3. Having 200 armor will multiply incoming physical damage by 1/3 (Blocks 2/3 of the damage)

Health

Lets start of by calculating the gold value of Health




AVERAGE cost of 1 Health: 2.6 gold

or

1 Gold buys you: 0.385 Health

Resistances



AVERAGE cost of 1 Armor: 15.9 gold

or

1 Gold buys you 0.063 Armor



AVERAGE cost of 1 Magic Resist: 15.8 gold

or

1 Gold buys you 0.0633 MR

As you can see these values are very close,so we can just round off:

Average cost of 1 Resistance = 15.85 gold

1 Gold buys you 0.062 Resistances

Effective Hp

I will introduce a new terminology "Effective HP"

Armor can be viewed as a sort of "bonus hp shield".


Then

EFFECTIVE HP = Health X (100 + Armor)/100


Example:

1. Having 50 armor and 1000 Health means you have 1500 EH

2. Having 100 armor and 1000 Health means you have 2000 EH

3. Having 200 Armor and 1000 Health means you have 3000 EH

A simple way to think of it is that every 1 Armor increases you EH by 1%

Optimization 1. (vs single type damage)

Here now comes the slightly tricky part:

1hp gives you 1+(AR/100) Effective HP

Examples:

1. Purchasing 1hp when you have 100 armor gives you 2 EHP
2. Purchasing 1hp when you have 200 armor gives you 3 EHP



1Armor gives you 0.01hp Effective Health

Examples:

1. Purchasing 1 armor when you have 1000 health gives you 10EHP
2. Purchasing 1 armor when you have 2000 health gives you 20EHP


BUT armor and Health have different gold values!! Which is why we calculated it early so we substitute them:


1 Gold of Hp gives you (0.385 + 0.00385AR)EHP

and

1 Gold of Armor gives you (0.00062HP) EHP


We then equate these value to find a SWEET SPOT

(0.00062HP) = (0.385 + 0.00385AR)

HP = 6.2AR + 620


This equation tells us when HP and armor are of Equal Value

Basically you always want your health to equal 620+6.2AR. If your health is greater than this purchase armor, if lower purchase health.

A simple way to think of it is a graph in which we try to follow the plotted line as closely as possible:

If above the plotted line... purchase Armor

If below the plotted line purchase Health


[http://i39.tinypic.com/30nf5hl.png]


Sweet Spot Values




At 620 hp....0 Armor


At 1000 hp...61 Armor


At 1500 hp...141 Armor


At 2000 hp...222 Armor


At 2500 hp...303 Armor


At 3000 hp...383 Armor


Optimization 2. (vs split damage)

The above is calculations are all good when facing a team that does only Physical damage. Now lets consider a team that does split Physical AND magical damage, then health becomes better valued since it blocks both types of damage, where as purchasing armor only blocks one type.

So as before:


1 Gold of Hp gives you (0.385 + 0.00385AR)EHP


1 Gold of Armor gives you (0.00031HP) EHP


We then equate these value to find a SWEET SPOT

(0.00031HP) = (0.385 + 0.00385AR)

HP = 12.41AR + 1241


This equation tells us when HP and armor are of Equal Value

Basically you always want your health to equal 12.41AR + 1241. If your health is greater than this purchase armor, if lower purchase health.

A simple way to think of it is a graph in which we try to follow the plotted line as closely as possible:

If above the plotted line... purchase Resistances

If below the plotted line purchase Health

[http://i41.tinypic.com/20tgw8k.png]


Sweet Spot Values




At 1241 hp....0 Armor and MR


At 1500 hp...21 Armor and MR


At 2000 hp...61 Armor and MR


At 2500 hp...101 Armor and MR


At 3000 hp... 141.7 Armor and MR


At 3500 hp...182 Armor and MR


At 4000 hp...222 Armor and MR



TLDR

Ideally we would like to follow the line increasing our hp and armor bit by bit following the "Sweet spot" line. Sadly this is not possible in game, so I have made a list of "checkpoints" for people to follow.

Important: Due to enemy penetration, it is always better to overshoot on the resistance side rather then health.



Against single type damage


Aim for 60 Armor/MR then get 1000 Health

Then 150 Armor/MR then get 1500 Health

Then 220 Armor/MR then get 2000 Health

Then 300 Armor/MR then get 2500 Health

Then 380 Armor/MR then get 3000 Health



Against a balanced team (Physical and Magical)


Get 1500 Health

Aim for 60 Armor and Magic Resist then 2000 Health

Then 100 Armor and Magic Resist then 2500 Health

Then 150 Armor and Magic Resist then 3000 Health

Finish of with 200 Armor and Magic Resist.

Factors to Consider

This theory crafting is all good, but the game is very complex and we have to take some factors into consideration. That being said... THIS GUIDE SHOULD BE TAKEN AS A GENERAL GUIDELINE, AND YOU SHOULD USE YOUR OWN COMMON SENSE WHEN MAKING JUDGEMENT CALLS.



FACTORS TO CONSIDER




1.Enemy Penetration should be taken into account. Most AD carries have roughly 30 Armor pen. Most AP carries have roughly 15 Magic pen, or 40 with


2. Some Champs have ACTIVATED resistant bonuses e.g ultimate, shroud and ball curl.. Therefore increasing the value of Health on them.


3. Some Champs have some form of life leach/regen or Health boost. e.g. W and passive or , and ultimate. Therefore increasing the value of Resistances on them.


4. Many champions have mixed damage. It is unlikely that you will face a team that does exactly 50% magic damage and 50% physical. It may be split 25%-75% or vice versa.


5. A team may have 4 Physical damage carries, so you stack armor, but their 1 AP carry focuses you with all his spells and bursts you down! Not much you can do about that : (


6. Armor also reduces damage from towers


7. Armor also reduces damage from minions and monsters


8.The META GAME of stacking HP and MR and the AD Carry is very feasible and should not be ignored.


9. Some champs have better growth of health per level e.g. Nunu with 2380 base health at level 18. Other have good resistance growths e.g Shen 91 base armor at level 18.

Making Decisions 1. Armor Items

RECOMMENDED ITEMS


+25 Armor Only boots that offer armor.

+75 Armor and +350 Health The ultimate physical defensive item. The health, armor and active all combine to make you very robust.


SITUATIONAL ITEMS


+99 Armor Great on champions who can make use of the CDR and mana.

+100 Armor Good vs autoattackers and ok vs physical casters.

+45 Armor Great on Tanky dps champs.

+50 Armor For casters. Active is useful to avoid AOE burst and to wait for Cooldowns to come up again.

+45 Armor and +450 Health Useful on champs that need to raise their threat level, or have trouble clearing waves.


MINIMAL ARMOR ITEMS


+25 Armor vs health stacking teams, or if you have a nice attack speed steroid.

+30 Armor For junglers and autoattackers

Making Decisions 2. Magic Resist Items

RECOMMENDED ITEMS


+25 MR Only boots that offer MR.

+48 MR This item by itself is also good. Upgrading it can be expensive so dont hesitate to buy it, and upgrade it much later.

+50 MR and +375 Health The ultimate magical defense item. The potential of the passive to block a high damaging spell is also great. One of the only 2 items that combine HP and MR.


SITUATIONAL ITEMS


+76 MR Great on champs that will not make use of the mana on and on high health champions

+56 MRGood on carries as it is much cheaper than and can cleanse

+30 MR and +250 Health Mid game item. Usually sold later on.

+57 MR An anti-casters item for casters.

+30 / 50 MR Very useful item. On hit effect makes it very cost-effective.

+30 MR and +300 Magical Shield This item is prefered over if you champion has abilities scaling of AD.



MINIMAL MR ITEMS


+30 MR Purchased for other reasons, never its MR

+30 MR. Meh

Making Decisions 3. Mixed Items and Health

RECOMMENDED ITEMS


+68 Armor and +38 Mr

+270 Health and +30 Armor and +39 MR




SITUATIONAL ITEMS

+1270 Health If your champion has some massive resistant boost like rammus, or abilities that scale of health then its good. Otherwise it provides to much health when resistances would be better.

+700 Health Good amount of health. This by itself is usually enough.

+630 Health Same as above.

+500 Health Same as above.

+520 Health Health item for supports.

+330 Health Health item for supports.

+250 HealthWill need to combine it with another low health item.


MINIMAL ITEMS


+200 Health err...

Case study 1- Xin Zhao



Assume we are facing a team of Split damage


LEVELS 1-5


Level 5 xin has base stats of 880 Health, and 53 Armor and 56 Mr(runes and masteries)

Our goal is to reach 1500 hp...To do this we can get: and


LEVELS 6-11

Level 11 with

Will have 2350 Health.
Then with an Armor and MR boost of 40 (assuming he hits 2 champions) he will have 115 Armor and 130 MR


Level 18


Level 18 with

Will have 3336 Health

Then with an Armor and Mr boost of 50 (Assuming he hits 2.5 champions), he will have 197 Armor and 197 Mr

Can then be sold for a situational item.

This build gives him a good mix of Health, Damage, Attack speed, Armor pen, and of course resistances.

Case Study 2 - Warwick



A rather complex hero to mathcraft about but lets give it a shot!

Assume we are facing a team of Split damage

Unlike , Warwick has no resistance bonuses, but he can gain health 3 ways: through his passive, Q and Ultimate.

LEVELS 6

Level 6 WW has base stats of 1050 Health, and 56 Armor and 57 Magic Resist (runes and masteries)

Now lets analyze and make assumptions on what happens when he gets into a early team fight at dragon.

He Q's someone for 10%(assume they have mr) of their health (roughly 1000) so his Q does 100 damage and heals him for 80.

He then autoattacks 3 times to gain 76 health.

He takes alot of damage and decides to ultimate someone hitting them 5 times. During this time he is considered to have full stacks of his passive, and 30% lifesteal... so he will gain roughly 180 + 80 health for a total of 260 health

Immediately after his ult he Q's them again and heals for 80 again, before dieing.

So far he has gained a total of 496 Health.

With this in-mind we can then assume that he effectively has roughly 1500 Health and 60 Armor and 60 MR... with no items. Pretty good

Our next goal will be 2000 hp, so we grab a

LEVEL 11

Level 11 with

Will have 1850 Health
With 118 Armor and 123 Mr

Another team fight at dragon...
He Q's for 20% of max health (2000) 400 damage which is reduced by mr to 200. He heals for 80% of this
160.

He then autoattacks 3 times again healing for 108

He Q's a second time healing 160 again

Then he ults Healing for 270 + 120 = 390 Health

He Q's again 160

So effectively he has roughly 1000 bonus health from QX3, 3 autoattacks, and his ultimate.

So now we are sitting at 2850 Health and 118 Armor and 123 Mr

Our next goal will be 200 Armor and Mr

Level 18



Will have 2580 Health
and 265 Armor and 270 MR

A teamfight at Baron this time: in which he will heal for 1000+ (see above calculations)

Giving us a total of roughly 3500+ Health and 270 Resistances

Nicely balanced out.

Acknowledgements

Solomid.net for the nice interface.


FYA UMASHI for feedback.

Change log

2 December, 2011: Guide released to Public

6 Decemeber, 2011: Tweaked the TLDR values to account for enemy penetration. Added case study examples.

13 December, 2011: Updated Warmogs Health value.

Comments

May 22, 2014 - 02:40 AM #1

Outdated but still very helpful, thanks :)

October 29, 2013 - 09:04 PM #2

Mundo with level 16 ga and visage has 202% of this actually hp that can be protected by resists making it very hard to actually reach even resists with the amount of hp you build on him :D.

May 21, 2012 - 08:20 AM #3

very good guide ty .

March 28, 2012 - 10:53 PM #4

enough maths for one day... integration homework can be done later - cba xD

January 30, 2012 - 04:38 PM #5

@McWut You are wrong. Leagucraft calculates the average of E(physicaldmg)HP and E(magicaldmg)HP; this isnt the EHP against split damage; Also isnt this guide about getting the highest possible EHP but about getting high EHP in relation to cost-efficiency.

January 17, 2012 - 01:14 PM #6

that is amazing.... finally someone posted this calculating stuff in good-player-compatible way ^^

January 14, 2012 - 10:10 AM #7

On leaguecraft.com/builder, I tried to get the maximum possible EHP on rammus.



The optimal build I found was Warmog's x3 and Guardian Angel x2 + Mercury's treads. This gives him 6,000 health, 244 armor and 150 magic resist for 15,400 gold. That's 17,800 EHP against balanced damage. That is the highest EHP I could build and I tried a lot of different things. So it seems that your guide is a little off.

December 30, 2011 - 05:21 AM #8

额。。很多都看不懂 =。= 求翻译。~

December 25, 2011 - 12:04 PM #9

Does exist a similar guide for attackspeed/crit/ad/lifesteal ?

December 24, 2011 - 08:25 PM #10

@Zero74: Not sure where you're coming from with that. Both armour and % damage reduction increase your EH by 1%. The only difference between them is that they can't reduce damage reduction with armour/magic penetration, but that's not relevant at all unless you have % penetration (Last Whisper) or have more ArPen than they have armor, and in case is not a "pretty big" difference.

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