Few "FUN" facts about Armor and Armor Penetration.
I. For some reason Armor Reduction from different sources stacks multiplicatively.
II. List of champions with armor reduction build in thier kits (at max lvl):
E -> 25% armor reduction,
Q -> 26% armor reduction,
passive -> 25% armor reduction,
Q -> 20% armor reduction,
Q -> 28% armor reduction,
E -> 35% armor reduction,
E -> 35% armor reduction,
E -> 20% armor reduction,
R -> 40% armor reduction,
W -> 20% armor reduction,
Q -> 30% armor reduction,
 E -> flat 20 armor reduction,
 R -> flat 24 armor reduction,
III. It is possible to reach over 1000 armor on certain champions. (it's not even such a troll build) https://i.imgur.com/eDbH23u.png
IV. A team of (top), (jungle), (mid), (adc) and (sup) can reduce said 1000 armor down to around 123 armor... 12% of the initial value.
**Math: **
1000 x (1 - 0.35) x (1 - 0.26) x (1 - 0.3) x (1 - 0.2) x (1 - 0.4) x (1 - 0.24) (for 
) = 122,83
which can be further reduced by 
down to 80 and even further by lethality down to around 20 armor.
Glorious 2% of the initial value.
V. One point of armor is worth around 20 gold. Our 1000 armor tank just wasted 17 540 gold from armor reduction alone and 19 600 gold if we consider further penetration.
VI. Single + offers your team a teamwide effect of 43% armor reduction thanks to his spin.
Throw in any other champion with armor reduction, lets say in the jungle and you have a potential 58% armor reduction for your entire team.
Most tanks reach around 250 - 300 armor in average game. This means that often thier actual armor can be lower than 150... It's hard to call that a tank.
VII. Additionaly Armor Reduction also reduces damage of abilities and items that scale with armor. Isn't it great that one stat can destroy both your defense and your offense at the same time?
VIII. It's probably impossible to balance a game where one of it's core stats is so volatile that it can change form 1000 to 20 in few seconds.
IX. We are in a League of Black Cleavers again and we aren't even aware of this. I just hope some lost Riotter will read this.
Edit Just to clarify few things.
I dont think that Armor Reduction is to blame for all evil things on this world.
It's quite the opposite in fact.
We need those ridiculous amounts of Armor Reduction to keep in check tanks who can stack tones of resistances since the Tank Update.
Imagine landing in a game where your entire team is AD, there is 1k armor tank in enemy team and all you can do against it is to build + . For those of your teammastes who rely just on Black Cleaver's reduction it's still a 750 armor walking wall. For those who go for its 500 armor beast... It still ignores 80% of your damage.
Thats why if we want a balanced game we need to look at things from all angles and maybe sacrifice something for greater good.
Just preventing Armor Reduction from stacking would risk at casting us into a unhealthy tank meta. What should be done on top of that is to nerf those extereme cases of resistance stacking as well.
Here is a list of steps that Rito should make in my opinion to bring tanks back to the game and maybe even reduce some of current damage creep:
- Make % Armor Reduction unstackable.
- Standardize % Armor Reduction in champions kits to 25% (except for Trundle, thats his ult after all).
- Reduce % Armor Reduction on down to 15% at 5 stacks or remove it from BC and create new item because having an item that is both core and counter item at the same time is a bit wierd.
- Tone average Armor and MR of tanks down(or up in some cases) to 300 and 200 respectively at full build.
- Reduce the power of defensive cooldowns so that tanks can't go far above 400 armor and 300 mr.
- Add some utility to defensive CDs - armor aura for your team, slow around you, cdr whenever something hits you... just some examples.
- Add some health back to the tank items.
- Profit.
Now lets do some math after those changes:
A tank player decided to play a tank in a game with one (or more) of the champions that can Reduce Armor by 25%:
300 x (1 - 0.25) = 225 armor - thats the armor that most of the enemy team whould have to deal with (still quite tanky but nothing crazy).
For an adc who went extra mile and bought this gets reduced down to 146,25 armor.
Now for a tank who is agains only team.
300 x (1 - 0.15) = 255 armor - BC reduces 45 armor, almost entire item of armor.
For an adc who went extra mile and bought this gets reduced down to 165,75 armor.
Ofcourse all this is just a rough math but im quite sure that balancing a game where resistances are somewhat set in stone would be much, much easier that now, when everthing is a variable that can go from 20 to 1000 :D.
Tanks For Reading.
in your example would stack HP rather than pure armor against an enemy team with that much armor pen?
= 390 Armor, the most feasible without extra bonus % armor, add a tanks' base armor around 110 for 500 armor
on even a level 1 
with the lowest base AD in the game, grants 40+80+80+40 AD = 240 AD, dps then gets multiplied by the attack speed and crit modifiers +95% AS, +75% crit, +25% IE = 1023.75 AD, then divided by the ninja tabi, frozen heart, cold steel, and randuin's crit reduction *.88, *.85 *.85, *(0.75 *0.8 (randuin's only mitigates the crits that actually occur) = 390 AD
and 
or any other adc with much higher base AD values to feed in.
+ conditioning will leave you at 500 armor and 82% dmg reduction and this is without probably the most important thing about armor items, their effects
this seems like a pretty hard thing to kill i mean when you factor in all of the actives your opponent is left feeling like he has 2 items less than he does, omen cancels Infinity's passive, thornmail cuts your healing in half, frozen heart and tabi lower your damage even further and you have essentially one less attack speed item.
