This guide is meant to understand the concepts of Effective Health, it's uses, and how it impacts gameplay.
There are two different "Resistance" stats: Armor and Magic Resistance. There are other forms of damage mitigation as well, mostly on special abilities or found in Masteries. For now we will focus on Armor and Magic Resistance. There will be a "Too Long; Didn't Read" at the end for a brief summary, if you only wish to know how the mechanics of Resistances might influence your play.
Also a few terms:
"Incoming Damage" for the purpose of this guide is the damage an ability or attack SAYS it will do. If you have 200 AD on a character, their "Incoming Damage" for each attack is 200 multiplied by Critical Damage when aplicable. If a Spell says it does 200 damage that is it's "Incoming Damage"
"Actual Damage" is what is dealt after mitigation. It is "Incoming Damage" modified by "Damage Reduction %" and other modifiers.
There are other modifiers as previously stated, but for simplification, and since most of them are either negligible outside the early game or abilities specific to champions, we're going to mostly ignore them.
What does Resistance do?
There are two ways of looking at how Resistance effects a champion, and two primary methods of looking at the v
You can mouse over your Armor and Magic Resistance on your Character Window (by default, to the bottom left of your screen) to find your Damage Reduction. Damage Reduction is taken from the following formula:
R = 1 - (1 / [1.0 + X(100)]) Where X is your Armor Value and R is the % Damage Reduction
50 Armor: 33.33~% Damage Reduction against Physical Attacks 1 - (1 / 1.5)
100 Armor: 50% Damage Reduction against Physical Attacks. 1 - (1 / 2)
200 Armor: 66.66~% Damage Reduction against Physical Attacks. 1 - (1 / 3)
400 Armor: 80% Damage Reduction 1 - (1 / 5)
As you can see, there are Diminishing Returns based on how much Damage Reduction you get for each point of Armor. While 50 Armor points from 50 to 100 provides an additional ~17% reduction, a similar amount requires another 100 points, or 200 altogether.
Calculating Damage Reduction is the most pure way of looking at a given Resistance stat. You know that with 400 Armor, you will take 80% less damage than you would have otherwise from physical sources of damage.
For many people, another way of looking at Resistances is more useful:
Effective Health, or Life Extension
"Effective Health" is a combination of two different stats. Health and a given Resistance stat. Armor and Magic Resist are calculated in such a way as to provide a "1 for 1" exchange on "Effective Health"
Every 1 Armor your character has, will effectively increase their current health by 1% against physical damage. Or, to put it another way, your character will live 1% longer than it would have otherwise against that type of damage. This can be shown with this formula:
E = H * (1 + X) Where H is Current Health, X is the Resistance Stat, and E is Effective Health
It is a simpler formula, but has more variables.
Character with 1000 Health and 100 Armor: 2000
Character with 1000 Health and 200 Armor: 3000
Character with 3000 Health and 100 Armor: 6000
Character with 500 Health and 1000 Armor: 5500
All against physical attacks.
Armor and Magic Resistance work with the same formulas, but against different types of damage. Armor only affects Physical Damage, and Magic Resistance only works against Magic Damage.
As such, even a character with 1000 armor and 500 health will still be treated as having only 500 health if they have no MR against Magic Attacks, or if the source of the damage is True Damage, which always ignores all mitigation.
Both of these ways of looking at Resistance are accurate.
The extension of "Effective Health" is also "Time" If you are consistently taking 100 Physical Damage (and no other damage) and have 500 Health, you would live 5 seconds.
For every point of Armor you have, that 5 seconds would be extended by 1%. So if you had 500 health, 200 Armor, and were recieving incoming damage of 100 physical each second, you would live for 15 second.
Likewise, if you calculated that you only took 33.33~ damage from each attack because your 200 Armor grants 66.66~% mitigation, you can also calculate that you will live for 15 seconds, since it would take 15 x 33.33~ to reach 500. If you wish to check it at other values, you will see it remains consistently the same.
Where It Gets Complicated
Damage Reduction gives you a direct and pure look at how Resistance is functioning. Effective Health gives you a look at how much Incoming Damage you can receive of a given type.
The part that complicates this is that there are 3 distinct types of damage:
Physical, which is only affected by Armor and special abilities.
Magical, which is only affected by Magic Resistance and special abilities.
True Damage, which can never be mitigated by any means.
Even when you have equal Armor and Magic Resistance (which is not that common, but not that uncommon either), the potential of True Damage can alter your Effective Health projection.
Furthermore, there are different itemization associated with each Resistance. While the Gold Efficiency of a Negatron Cloak might be just about close enough to that of Chain Mail, the items one can build with Armor values tend to have more Armor than that that you can get from Magic Resistance.
At their height:
Thornmail: 100 Armor
Force of Nature: 76
And each of those items have their own ancillary benefits as well that can also effect incoming damage. Thornmail discourages being attacked due to it's passive, and Force of Nature provides a large increase to Health Regeneration.
There are also more Armor items with an Armor value greater than 60, while most Magic Resist Items have less than 60. Also, there are more Armor Items with Health built into them, while Magic Resist tends to favor Mana or other similar stats that do not aid Effective Health.
Lastly, characters tend to have more MR than Armor at the beginning of a game, and less MR than Armor at the end from their Base Scaling and stats.
More important than difficulty finding balanced Resistance stats through Itemization however is the simple fact that more often than not, you want to focus more on a given Resistance than another, covered in the next segment.
All of this means that there are many variables which effect your characters survivability.
Knowing Which Resistance To Get
Knowing whether to get Armor, MR, an even mix of both, or not bothering all depends on your ability to recognize threats, your role in the game, and what abilities might effect your decisions.
If you are receiving a lot of damage, regardless of good positioning (or in the case of a tank, especially because of it) you need to identify what is killing you: Magic Damage, Physical Damage, True Damage, or a mix of all of the above.
Against Magic Damage you want a mixture of Health and MR.
Against Physical Damage you want Health and Armor.
And against True Damage you want Health, as that is the only thing that will help you live longer.
First let us examine a situation where you might take a lot of Magic Damage:
You are playing as Maokai, a Tank with strong spells. You are playing against a team composed of several champions, but the ones you're always getting the most damage from are Annie and an underfarmed Miss Fortune.
From this situation we have a few different variables:
1. You are playing Maokai. There are no listed allies that have a meaningful impact on your itemization decisions at this time, but your Passive encourages the building of Health, since you will heal yourself based on a % of your Maximum Health periodically in a fight. Also, Maokai has relatively high Base Health, Armor, and Health Regeneration.
2. The main sources of damage both deal magic damage. Miss Fortune also deals a lot of Physical damage from her attacks, but at present she is relatively weak, so while you want some Armor, you are more concerned about Annie.
3. Annie's damage is primarily Burst, or done all at once. As such, your Passive, which requires time and a melee attack, might not see much if any use if you die too quickly. Likewise, your regeneration will also play a minimal factor.
In this case, looking at EHP gives a very straightforward answer. You want to maximize your MR in relation to your Health. You already have decent Base Health, and you're more likely to live to punch something and heal yourself if you take less damage.
If you already bought a lot of MR of course, you would likely consider buying Health.
Here's a basic stat line:
Health: 2000 MR: 300 EHP: ~8000 vs. Magic
Armor: 150 EHP: ~5000 vs. Physical
You'll take physical damage from MF's attacks, which will lower your EHP against all the magic damage, but overall the vast majority of it is still magic damage. Say 70%/30%
With those stats, you could be taking 17.5% Magic Damage and 12% Physical, still mostly magic damage, or a 60/40 split of Actual Damage based on the disparity between Resistances.
To improve your survivability more, more health would be good, but so would more MR. Let's look at what is worth buying.
Base Item Values:
Health: ~2.6 Gold per Health (Giant's Belt)
Armor: ~15.6 Gold Per Armor (Chain Vest)
MR: ~15.4 Gold Per MR (Negatron Cloak)
Looking at Damage Reduction, each point of Armor beyond the first has less value, but it is still very much worth considering, since you take a % less from incoming damage.
Looking at EHP however, each point of armor gives 1% more EHP vs. Physical.
At 2000 Health, every 15.4 Gold into MR gives you 20 EHP, which means you'll get effectively get 1 Health for every 0.77 Gold.
However, since EHP is a function of two variables, it is important to look at what buying Health will give you. Every 2.6 gold into Health will improve your EHP vs. Magic by 4. Giving you 1 health for every 0.65 gold, better than that which you would get from buying MR. Buying Health also increases your survivability against the 40% of damage that is Physical, though at a reduced rate due to the lower armor (1.04 gold per Physical EHP)
On the flip side, if you have a different stat-line:
HP: 4000 MR: 100 EHP: ~8000
The values change.
The Incoming Damage split remains 70/30 so you're even more concerned about Magic than you are about Physical.
For every 2.6 you spend on health you get only 2 EHP.
On the other hand, for every 15.4 you spend on MR, you get 40 EHP vs. Magic or 0.39 gold for every EHP, even more gold efficient than buying health was in the previous statline example.
Likewise, due to the lower Resistances, buying more health is less efficient: getting 1 EHP for every 1.3 gold spent. It is still worth mentioning though that Health still helps against that 30% Physical damage that you're taking, but overall you're better off getting more MR (and armor for that matter, since you could get more EHP from getting both Resistances than from buying Health).
Things get even more complicated however, when more abilities come into effect, as well as mechanics, Resistance Penetration and Reduction, "other" mitigation such as from %-based mitigation from Maokai's Ult, "free" and often temporary stat increases to Health and Resistances from Shields, Heals, and defensive buffs.
All of these play into it as factors. Choosing what to buy will depend on knowledge and quick math. Eventually, you will know from familiarity and experience what to get instinctively, and at what value of Health you should focus more on Resistance, and what value of Resistance to focus more on Health, and why, and when.