Can someone explain Armour and MR to me please

Speedy59·May 8, 2016·17 votes·4,186 views

If I have 100 attack damage and the enemy has 50 armour how much damage do I deal? How much damage do I deal if have 200 AD?

Also is the same formula used for AP and MR?

Thanks

54 Comments

dangopeeMay 8, 201613 votes

Actual Damage = Unmitigated Damage * 100 / ( 100 + Resist Amount )

It is the same for both armor and magic resist.

WeatheredMay 8, 20163 votes

So... 100 of a resistance is 50% damage reduction? But 200 is 66.6...% reduction?

I guess it makes sense not to have resistances have a flat reduction so you can't have 100% damage reduction, but that's a pretty steep diminish.

TehNACHOMay 8, 201625 votes

Between you and the other guy, you're going to give me a stereotype that anyone with your icon doesn't understand how mathematics actually work.

There is no steep diminish. It makes more sense if you work the problem backwards and start off with Effective Health. For example, if you have 2000 Health and no resistances, you effectively have 2000 Health. Build 100 Armor and you negate 50% of the enemy's damage, or in other words your Health effectively doubles; 4000 Effective Health. Build 200 Armor and you negate 66% of the enemy's damage, or in other words your health effectively triples; 6000 Effective Health. It's not that there's a diminishing return in how much you decrease the enemy's damage, you're getting a linear bonus to the amount of Health you essentially have against opponents.

DarkSunSovereignMay 8, 20168 votes

Actually there are no diminishing returns, it just looks like it. Imagine the enemy has 1000 hp and you have 1000 ad cuz this is an example. If the enemy has 100 armor, in 1 AA, you'll deal 1000100/(100+100)=500 dmg. Thus, the enemy has 2000 effective HP. Every 100 armor gave him 1000 hp. Now imagine the same as above, but the enemy has 200 armor. 1000100/(100+200)=333,333333333 damage. Thus, the enemy has 3000 effective HP. Every 100 armor, again, gave him 1000 HP. Every hundred units of a single type of resistance offer 100% of your HP as effective HP. There are no diminishing returns.

MunchCrunchLunchMay 8, 20161 votes

yes there are. at some point your better off building hp factually than stacking resistances

TehNACHOMay 8, 20163 votes

That is not a diminishing return however. That is what happens when you have two linear equations (building HP and Armor) and multiplying them together. All you're talking about is maximizing the exponential effect created by multiplying the two together, not avoiding any diminishing returns from focusing on only one.

MunchCrunchLunchMay 8, 20162 votes

forget about math and focus on a 6 item slot video game.

TehNACHOMay 9, 20163 votes

By that logic, don't comment in this thread. OP is literally asking about the mathematics of the game.

CubedJusticeMay 9, 20166 votes

No man, clearly you need to stop using mathematics in a mathematics discussion.

AstôlfoMay 8, 20161 votes

So what would be the most efficient amount of resistance? Like, sure, the more you get, the more it increases, but the rate at which it increases slows down. So what would be the best point for having a good bit of resistance while still having a good resistance-to-damage rate?

TehNACHOMay 8, 20169 votes

Like, sure, the more you get, the more it increases, but the rate at which it increases slows down.

That is not how the mathematics work.

Another way to rephrase it is 1 Armor=1% health. For example, if you have 2000 health and 100 Armor, you have 4000 Effective Health. If you add 100 armor to that (200 armor), you will have 6000 Effective Health. 100 more armor (300 Armor) and that's 8000 Effective Health. There is no slowing down, there is no fall off. Increasing Armor is a linear bonus to your Effective Health.

The main worry about buying too much armor is that, as a multiplier, you want to make sure that the thing it's multiplying is also solid. To use an analogy, 3X3 is 9, where as 2X4 is 8. Properly balance the things you are multiplying together and you get a higher number. Don't balance them and that's where the inefficiencies appear. Again though I want to reiterate, buying Armor does not make the next set of Armor you buy any less efficient from a mathematical standpoint.

WolfeurMay 8, 20162 votes

What we should be asking is how to balance your stats between resistance and health.

LankPantsMay 9, 20161 votes

That depends entirely on your champion and generally isn't that relevant.

Some champs just benefit from stacking HP, even if that Ruby gives less durability than a Cloth armour it still may be worth it if you gain some damage from it and vies versa.

If you're stacking a lot of either you're going to be tanky, as a rule of thumb I think you want around 3.5K to 250 armour. That's what you should be shooting for.

It's also worth noting that perfectly balancing armour, HP and MR is expensive, hard and generally quite inefficient. It tends to work out better to have a little bit of MR and spike your HP up to make up for the loss in durability VS APs.

A Basic IslandMay 9, 20161 votes

I'm curious, if that is not a diminishing return, what is? In terms of how much dmg each pt of armor reduces each point reduces slightly less if looking at it from a pure 1/2/3 type perspective.

Ex 1 armor reduces 1 damage but 2 armor reduces only 1.8

TehNACHOMay 9, 20161 votes

It's not a diminishing return because of its application. If the goal of reducing enemy damage is for you to survive longer, then the far more accurate model to the application is to look at it from an EHP standpoint. In this case, we don't see the diminishing returns even as we look at things point for point.

ex. If you have 2000 HP, add 1 armor and you have 2020 EHP, 2 armor 2040 EHP, 3 armor 2060 EHP.

For a terrible analogy, I'd compare this to cooking steak. Watching you guys call damage reduction a diminishing return is like the people who think cooking with a higher temperature cooks your steak more thoroughly. What they think should not happen does not accurately model what actually happens because the method it should work is completely different.

A Basic IslandMay 9, 20161 votes

so then, what IS a diminishing return?

because, to the average math illiterate person (such as myself) explaining it as a diminishing return is a much more simple concept to grasp than each mitigation=1 effective health vs that damage type even tho it may technically be wrong to people who know math .

TehNACHOMay 9, 20161 votes

because, to the average math illiterate person (such as myself) explaining it as a diminishing return is a much more simple concept to grasp than each mitigation=1 effective health vs that damage type even tho it may technically be wrong to people who know math .

This is dangerous ass teaching that breeds misconceptions.

I'm refusing to answer your diminishing return question to avoid you ever justifying using it to explain the concept to other players. Don't try to utilize it; if you don't know how to answer a topic then don't answer it instead of trying to input something incorrect.

Hullabaloo907May 8, 20161 votes

The items that give you health+resistances are the ones that make you the most tanky. Items with just resistances make you almost as tanky against one source of damage. Items that just give you health make you somewhat tanky but are applied to both damage types.

I usually aim for have a randuins or frozen heart+another armor item+a top tier Mr item+ at least 4000 health when I play a tank. I find this is a good baseline goal, but it changes from game to game

WolfBVMay 8, 20161 votes

{quoted}

So what would be the most efficient amount of resistance? Like, sure, the more you get, the more it increases, but the rate at which it increases slows down. So what would be the best point for having a good bit of resistance while still having a good resistance-to-damage rate?

100-150 armor/mr is good

ninjaIRL May 8, 20166 votes

Incoming physical damage is multiplied by a factor based on the unit's armor:

Examples:

25 armor → ×0.8 incoming physical damage (20% reduction, +25% effective health). 100 armor → ×0.5 incoming physical damage (50% reduction, +100% effective health). −25 armor → ×1.20 incoming physical damage (20% increase, −16.67% effective health).

Every point of armor requires a unit to take 1% more of its maximum health in physical damage to be killed. This is called effective health.

Example: A unit with 60 armor has 60% more of its maximum health in effective health, so if the unit has 1000 maximum health, it will take 1600 physical damage to kill it.

All copy pasted from League of Legends WIKI

ninjaIRL May 8, 20165 votes

Someone keeps automatically downvoting posts.

WolfeurMay 8, 20162 votes

AD and AP have no diminishing return, unlike Armor and MR. As you get more resistance, the bonus resistance becomes less and less efficient.

The formula is damage * 100 / (100+resistance) and is the same for both physical et magical damage.

So, if you have 100 resistance, the corresponding damage will be multiplied by 100/(100+100), leading to 50% reduced damage. At 200, you get 100/300, leading to 66,6% reduced damage. Your first 100 points reduce by 50% while the other 100 reduced only by 16,6%.

Resistance reduction and penetration respectively reduces your resistance and negates a part of the resistance. The first one affects every damage you take while the second only works for the damage dealt by the source that has the penetration. They are calculated in that specific order:

flat resistance reduction
percentage resistance reduction
percentage resistance penetration
flat resistance penetration

Considering that the first points of resistance are the most impactful, flat penetration/reduction works best against those who have the least resistance. For people who build a lot of defenses, percentage is obviously better. That's why it's advised to buy sorcerer's shoes quickly, since your opponent doesn't have the time to build a lot of defenses.

Penetration is good for damage dealers, since they need to deal a maximum of damage. Resistance reduction is usually less powerful in numbers, but works for your allies. That's why it's advised to build them on tankier champions so they can survive long enough to allow the reduction to be effective.

TehNACHOMay 8, 20167 votes

You, stop putting this idea in people's heads. There are no diminishing returns; the mathematics of how it works reveals itself if you look at how Armor and MR apply defensively.

To...well, quote myself:

Between you and the other guy, you're going to give me a stereotype that anyone with your icon doesn't understand how mathematics actually work.

There is no steep diminish. It makes more sense if you work the problem backwards and start off with Effective Health. For example, if you have 2000 Health and no resistances, you effectively have 2000 Health. Build 100 Armor and you negate 50% of the enemy's damage, or in other words your Health effectively doubles; 4000 Effective Health. Build 200 Armor and you negate 66% of the enemy's damage, or in other words your health effectively triples; 6000 Effective Health. It's not that there's a diminishing return in how much you decrease the enemy's damage, you're getting a linear bonus to the amount of Health you essentially have against opponents.

and

That is not how the mathematics work.

Another way to rephrase it is 1 Armor=1% health. For example, if you have 2000 health and 100 Armor, you have 4000 Effective Health. If you add 100 armor to that (200 armor), you will have 6000 Effective Health. 100 more armor (300 Armor) and that's 8000 Effective Health. There is no slowing down, there is no fall off. Increasing Armor is a linear bonus to your Effective Health.

The main worry about buying too much armor is that, as a multiplier, you want to make sure that the thing it's multiplying is also solid. To use an analogy, 33 is 9, where as 24 is 8. Properly balance the things you are multiplying together and you get a higher number. Don't balance them and that's where the inefficiencies appear. Again though I want to reiterate, buying Armor does not make the next set of Armor you buy any less efficient from a mathematical standpoint.

WolfeurMay 8, 20163 votes

I understand your point, and you're right, but what I was saying was only about the mathematics of the Armor itself to make the OP understand that the damage reduction is not linear with resistance.

Effective health may be but not the reduction itself. It's just so people realize that doubling armor won't double the reduction.

TehNACHOMay 8, 20166 votes

Fair enough, but you need to be super duper 100% careful about your phrasing on that, because this misconception has been around foreeeeeeeeeeeeeever and its super annoying how much this is screwing over the people who honestly don't know better out of, say, inexperience.

WolfeurMay 8, 20163 votes

Sure, but you can't deny that at some point, buying health is more effective than the same amount of gold as resistance. You should be careful as well because your phrasing, on the other hand, makes it look like you can buy only resistance and be ok with that. If 1 Armor = 1% health, you should buy health so that your armor increases its effectiveness.

TehNACHOMay 8, 20163 votes

Yeah, but that's a different issue that can't really be used to excuse any "diminishing returns" argument towards Armor/MR and its relationship to Effective Health.

PB4UAMEMay 9, 20162 votes

The amount of incoming damaged reduced does have diminishing returns. He is not at all wrong for saying that.

However, the effective health formula has constant returns, aye, but that doesn't mean armor ALWAYS has constant returns.

Think of it like multivariate calculus, if you have a function f(x,y): x^.3y^.7 than f(x,y) has constant returns, however neither x nor y do.

TehNACHOMay 9, 20161 votes

It's not that he's wrong, it's that this is this and that is that.

He can stick to that sort of argument. That's fine if you make sure to phrase it super carefully so that anybody here that doesn't understand the mathematics doesn't misunderstand it (which I assume is the source of the misconception I'm slapping down all over this thread). What I was saying however is that that logic should not therefore justify not correctly siting the EHP argument where it would be so much more appropriate to this thread.

Also, this:

However, the effective health formula has constant returns, aye, but that doesn't mean armor ALWAYS has constant returns.

Is exactly the opposite of the super careful phrasing I worry about.

PB4UAMEMay 9, 20161 votes

The EHP formula is a multivariate function.

The damage reduction formula is not.

They have different returns as such; Given that the formula f(x) where x is your armor value, and f is the damage reduction, is in the form of a/(b+x), it does indeed experience decreasing returns.

However, as the EHP formula is also a function of health, the resulting value is one that does experience constant returns with respect to armor.

Armor, without regard to context can therefore not be said to experience constant returns to scale. As I said earlier, that one example doesn't mean armor will always have constant returns. It all depends on what you are looking at and trying to calculate.

TehNACHOMay 9, 20161 votes

I'm going to assume you wrote all that specifically towards my worries about not being careful about your phrasing.

Great, now go back and replace the second line of your last post with that, since you went out of your way to cover yourself so well.

Even though I've said, both directly to you and to the other guy, that that's a perfectly fine train of thought to have so long as you're just careful to phrase it so you don't breed the misconception that is plaguing this thread and other threads like this.

InsanitysTheNameMay 8, 20161 votes

There is only one truly armor only item in the game. The rest give hp as well. item 3075

AckelopeMay 9, 20161 votes

How about item 3110 ?

ProtestantCaesarMay 9, 20161 votes

That gives health. Singed

InsanitysTheNameMay 9, 20161 votes

Well Played Sir.

AckelopeMay 9, 20161 votes

Heh, nice one. Yielded a sensible chuckle from me.

DarkSunSovereignMay 9, 20161 votes

item 3157

InsanitysTheNameMay 9, 20161 votes

True. Was kinda in the mindset of tank items. :P Well Played Sir.

Average BardMay 8, 20162 votes

You need to Forrest Gump your way to knowledge. Basically, Buy MR items if you're going against champs who are AP. Build Armor against champs who are AD. Build Health for True Dmg and better sustain.

ZelisMay 8, 20161 votes

simple answer put mouse over armor and mr value in game and it will tell you the % of dmg that is reduced

Irelia BotMay 8, 20161 votes

The simple answer is that 1 armor or 1 MR is an effective 1% more health when taking that type of damage.

The equation for damage taken is damage before reduction X (100/(100 + base armor + (bonus MR*(1-% armor penetration) - flat armor penetration)))* (1-% damage reduction) = % of damage taken You can put number in this and get the % of damage being taken. most champs do not have the % damage reduction but it is there if you are contending with Maokai, Alistar, Annie or someone with phantom dancer.

AuroramancerMay 8, 20161 votes

To put it simply without using actual in-game math formulas...

Armor reduces all physical damage taken, from spells and auto attacks, by a % MR reduces all magic damage taken, from spells and auto attacks, by a %

The % of damage that is reduced will increase with your armor and MR values. However, the % damage reduced does not increase as the same rate as your armor and MR increases. Just to fudge up some numbers...

Suppose the following: 30 armor = 13% physical damage reduction 100 armor = 45% physical damage reduction 200 armor = 60% physical damage reduction 500 armor = 80% physical damage reduction

The increase in % damage reduced is lowered as you go higher in those stats. You get the most effective increase of damage reduction at lower values of armor/MR.

TehNACHOMay 8, 20164 votes

You, stop putting this idea in people's heads. There are no diminishing returns; the mathematics of how it works reveals itself if you look at how Armor and MR apply defensively.

To...well, quote myself:

Between you and the other guy, you're going to give me a stereotype that anyone with your icon doesn't understand how mathematics actually work.

There is no steep diminish. It makes more sense if you work the problem backwards and start off with Effective Health. For example, if you have 2000 Health and no resistances, you effectively have 2000 Health. Build 100 Armor and you negate 50% of the enemy's damage, or in other words your Health effectively doubles; 4000 Effective Health. Build 200 Armor and you negate 66% of the enemy's damage, or in other words your health effectively triples; 6000 Effective Health. It's not that there's a diminishing return in how much you decrease the enemy's damage, you're getting a linear bonus to the amount of Health you essentially have against opponents.

and

That is not how the mathematics work.

Another way to rephrase it is 1 Armor=1% health. For example, if you have 2000 health and 100 Armor, you have 4000 Effective Health. If you add 100 armor to that (200 armor), you will have 6000 Effective Health. 100 more armor (300 Armor) and that's 8000 Effective Health. There is no slowing down, there is no fall off. Increasing Armor is a linear bonus to your Effective Health.

The main worry about buying too much armor is that, as a multiplier, you want to make sure that the thing it's multiplying is also solid. To use an analogy, 33 is 9, where as 24 is 8. Properly balance the things you are multiplying together and you get a higher number. Don't balance them and that's where the inefficiencies appear. Again though I want to reiterate, buying Armor does not make the next set of Armor you buy any less efficient from a mathematical standpoint.

AuroramancerMay 8, 20161 votes

You're not wrong, but neither am I.

In terms of increased damage reduction, there are diminishing returns, no questions asked. In terms of increased effective HP, it is a linear function, no questions asked.

There are multiple, yet valid, ways of looking at this, and just because your stance is different than mine, does not mean that I am wrong. It is not misinformation to say "defensive stats yield diminishing returns on the damage reduction"

Holyfrost SubMay 8, 20161 votes

I am not really good at math - but from my experience playing games - no matter how much armor or magic resist and health you get, there is always items that will help ad carries and mages "out scale" your tankiness.

But that doesn't mean armor and mr are useless. It just depends on whether the enemy has enough common sense to counter build against your tanky builds.

Also i find that as a tank - you only build mr armor and health to back dive the ad carries and ap mages - yes - but CC is just as important. I usually do cc and - then die.

SO if you want to be invincible - it's probably not going to happen. But it will make you harder to kill. Not invincible no - but definitely harder to kill.

AnnoxisMay 8, 20161 votes

The formula to calculate the damage reduction of a particular value of Armor of MR is 100/(100+X) where X is the value in question. If your opponent has 50 armor, you will 66% of your physical damage to him.