Wrong, Flat Reduction is applied before Percentage Reduction:

http://leagueoflegends.wikia.com/wiki/Armor_penetration#Order_of_calculations

WOW! I'm amazed, you took all that time to figure out this formula for all of us curious people. To be honest, at times when i was bored, I would wonder how this works. I was trying to figure out if Dagger was better than Long Sword . To this day, still haven't figured out -.-, and I'm a bit too lazy to find out right now. +1 For you.

to pwnengine, percentage reduction is given by void staff and last whisper, both a 40% reduction in addition to their flat ap or dps bonus.

Many ppl have some idea (=they hope, but dont know anything) how some stuff works, but this is perfect source of info how it is correctly. Thx!

+1

You forgot about blue buff in the cooldown reduction part :)

Great guide, ty for posting all the information in one easy location.... Only question is how does dodge work? is there a cap?

Armor/MR do have diminishing returns. I'll edit and add in all the math if you want. But it's true.

It says near the bottom "Percentage penetration" Is calculated first but their is no item or rune or mastery which has percentage pen. Is there a champ with a special ability no one else can get in that regard?

Ok, this **** is making me confused :/
But you argue a good point, so I'll assume that you're right for now.

Sorry Searz, your "WRONG" is... wrong. What you say after that is simply another way of looking at the same formula. You're talking about "Effective Health" while this guide shows it from the "Effective Damage" perspective.

Compare the following
"Effective damage"
Effective_Damage = Physical_Damage * 100 / (100 + Armor)
Health = Health - Effective_Damage

"Effective health"
Effective_Health = Heath * (100 + Armor) / 100
Effective_Health = Effective_Health - Physical_Damage
Health = Effective_Health * 100 / (100 + Armor)

They give the exact same results.

I wanted this guide to be as simple and easy to understand as possible. I didn't want to go into multiple ways of looking at the same thing, so I just picked one and added the LoL Wiki link if people wanted to learn more. Armor stopping damage is more intuitive than armor raising health, so I went with the more intuitive option.


Effective health can be useful when comparing the cost effectiveness of a resistance item to a health item.
In other cases, besides being intuitive, thinking of "Armor" as blocking damage can make things more elegant.

"Effective Health" perspective
Add Armor: Calculate effective health (2 variables: armor & health)
Add Health: Calculate effective health (2 variables: armor & health)

"Effective Damage" perspective
Add Armor: Calculate % of damage blocked (1 variable: armor)
Add Health: simply add health (1 variable: health)


If you want to argue the semantics of "less and less effective", go right ahead. However it's a pointless debate, because if you truly understand the math you can look at it in multiple ways.

For example:
Let's say a champion has 2000 health.
If he has 50 armor, you could say that he has 3000 effective health against physical damage. (Or that he has 2000 health but blocks 1/3 of all incoming physical damage. Both perspectives result in exactly the same thing.)

Now let's say he gains another 50 to get 100.
He now has 4000 effective health against physical damage (or 2000 health but blocks 1/2 of all incoming physical damage).

Here is where the misunderstanding of perspective lies. You are saying that each point of armor gave him an extra percent of effective health. This is a static comparison as you are always comparing to WHEN HE HAD NO ARMOR. With this perspective, you would compare the 3000 effective health to the original 2000 health. Then you would also compare the 4000 effective health to the original 2000 health.

I find it much more useful to think from the perspective of buying a new item. For example, when you're sitting at the shop with 50 or 100 armor already on you, how much more survivability will the next 50 armor give you? This is a dynamic comparison as you are always comparing the new armor to what you already have. With this perspective, you would compare the 3000 effective health to the original 2000 health (a 50% increase). Then you would compare the 4000 effective health to the 3000 effective health (a 33% increase).

From this perspective, adding more and more armor becomes less and less effective. (This is also the mathematical reason why mixing in actual health items, on a tank, is more cost effective than simply stacking armor/MR.) I see this as a more useful perspective, because people decide what to buy throughout the game instead of buying their whole set at once. Damage output increases throughout the game and 1000 effective health is not as helpful late game as it is early game. It's important to know the kind of survivability you're getting at that moment, compared to what you've already got.


Summary:
1. The math can be formulated multiple ways to get the same result.
2. "Armor" is more intuitively thought of as blocking damage then giving health.
3. It's usually more helpful to compare the effect of armor progressively throughout the game, based on the armor you already have, rather than always comparing it to 0 armor.

WRONG.
Armor and MR does not have diminishing returns. Each point of armor increases the amount of physical damage required to kill the champion by 1 percent of the champion's health. For example: 100 armor reduces physical damage by 50 percent, so 100 percent more damage is required to kill the champion.

You forgot summoner spells on WW.

I'll point out more stuff if I find any.