PSA: Armor and MR do not have diminishing returns.

WoonStruck··21 votes·2,831 views

**Diminishing returns is when you specifically receive less of a value for every instance of that value. **

In the case of armor/mr you are simply seeing the effect of scale. Just like 600 HP is +50% of 1200, but another 600 is only +33% of the 1800 you now have.


There is no soft cap or diminishing returns for resistances.

If you have 3000 HP, buying 180 doesn't seem significant. Its the same with armor.

If you have 3000 HP and you have 300 armor, you have 12000 Effective Health Points (EHP) vs physical. Buying another 100 armor gives you another 3000 EHP vs physical damage. Absolutely no diminishing returns involved.

Armor is the same as HP, just represented in a different light.

If you don't think you get diminishing returns from the flat HP you purchase, you do not get diminishing returns from armor either. You are buying flat 'EHP', where each point of armor supplies equal 'HP' to 1% of your actual HP in total health vs that damage type.

{quoted}

All reduction/division values can actually be pretty missleading and confusing with how they're written. It's easier to look at armor as fractions when considering what the OP is talking about:

100 armor is 50% damage reduction, 50% damage taken, or 1/2 damage taken. 200 armor is 66.67% damage reduction, 33% damage taken, or 1/3 damage taken. 300 armor is 75% damage reduction, 25% damage taken, or 1/4 damage taken. 400 armor is 80% damage reduction, 20% damage taken, or 1/5 damage taken.

If you have 1000 HP, getting another 1000, 1000, 1000, 1000 is going to do the same exact thing as taking 1/2, 1/3, 1/4, and 1/5 damage from armor.

This is very much linear scaling, not diminishing returns. Diminishing returns indicates you'd need more and more armor to go from 1/2, 1/3, 1/4, 1/5, etc. jumps rather than the same value (100) being between each increment.


The % damage reduced tooltip is very misleading and is causing way too many people to mistake efficiency with diminishing returns.

Buying health becomes more efficient at certain thresholds, just like armor/mr is more efficient than health at certain thresholds. This is efficiency of your purchases, not diminishing returns when you make an inefficient purchase.


TL;DR: You are not buying a % reduction vs that damage type. You are literally buying HP that is only effective vs that damage type. However, rather than the base unit being 1 HP, its 1% of your max HP.

58 Comments

Itankyou10 votes

They have diminishing returns. % values --> math, sorry but ur wrong.

WoonStruck3 votes

Pretty sure he's being facetious, for whoever downvoted it. haha

67chrome4 votes

All reduction/division values can actually be pretty missleading and confusing with how they're written. It's easier to look at armor as fractions when considering what the OP is talking about:

100 armor is 50% damage reduction, 50% damage taken, or 1/2 damage taken. 200 armor is 66.67% damage reduction, 33% damage taken, or 1/3 damage taken. 300 armor is 75% damage reduction, 25% damage taken, or 1/4 damage taken. 400 armor is 80% damage reduction, 20% damage taken, or 1/5 damage taken.

If you have 1000 HP, getting another 1000, 1000, 1000, 1000 is going to do the same exact thing as taking 1/2, 1/3, 1/4, and 1/5 damage from armor.

This is very much linear scaling, not diminishing returns. Diminishing returns indicates you'd need more and more armor to go from 1/2, 1/3, 1/4, 1/5, etc. jumps rather than the same value (100) being between each increment.

Penns3 votes

Jumping from 1/2 to 1/3 is still better than from 1/4 to 1/5 dmg taken tho ._.

67chrome3 votes

Linear scaling isn't the same thing as diminishing returns.

Diminishing returns implies that if going from 0 to 1 requires 1, going from 1 to 2 requires more than 1.

Penns1 votes

Isnt that kind of how it is? If you need x armor to go from 30% to 40% dmg reduction, you need more than x armor to go from 40% to 50%..

67chrome6 votes

20% damage reduction isn't twice as good as 10% damage reduction though, 20% damage reduction is more powerful than 10%. 10% damage reduction is actually an ~11.11% increase in overall defense, where 20% is a 25% increase in overall defense. Concerning CDR: 40% is the equivalent of a 66.67% increase in skill frequency, and 45% reduction is the equivalent of an 81.8181% increase in skill frequency. 50% reduction is the equivalent of a 100% boost as well, as double damage is countered by halving damage taken. %reduction and %increase in power aren't interchangeable integers.

Armor scales in a 50%, 66.67%, 75%, 80% way because each % point is not at all equal to all other % points.

Consider that 1% damage reduction from 98% damage reduction to 99% damage reduction isn't a 1% increase in overall survivability: as it's a massive jump from 2% damage taken to 1%, a doubling in overall survivability. Another way of saying this is that the last 1% damage reduction has the same exact power as the first 98%: which means all games with %damage reduction mechanics where you do go 10%, 20%, 30%, 40% damage reduction actually have exponential scaling (Fire Emblem is a good example here).

Also: 1% on 99% is obviously not a 1% boost in defense, as it causes a unit to go from being able to take 100 OHKO attacks to an infinite amount of damage.


What you're running into is perception vs. reality issues, where the misleading way %damage reduction is written is making it quite difficult to internalize how %damage reduction should progress.

This can be further illustrated by simply converting %damage reduction into %damage taken. 60% damage reduction and 80% damage reduction don't sound particularly far apart in power, but 40% damage taken vs. 20% damage taken clearly shows the latter is twice as powerful as the former.

Penns1 votes

Makes more sense now, but with 30 armor you take 780 dmg, withc 130 armor 430 and with 230 you take 300 dmg, so the first 100 armor were more efficient than the second one... or not?

WoonStruck2 votes

Getting armor when you have very little feels more efficient because the noticeable change is much greater. However, the actual effect is a linear scale in tankiness, much like HP.

Just like buying 500 health after you already have 5000 doesn't feel that effective, but adding in armor to that does.

Reikken1 votes

kind of. but a linear increase in % damage reduction is an asymptotic increase in durability. 0% to 10% damage reduction is relatively small, while 80% to 90% damage reduction is a 100% increase in durability, and 90% to 100% damage reduction is an infinite increase in durability---makes you literally invulnerable.

So really it just depends on how you're looking at it. You technically could say that 20% to 30% to 40% damage reduction is a linear increase, but I sure as hell wouldn't. In practical terms, it's not linear at all.

Effective health is a much more practical measure than damage reduction, for comparisons.

WoonStruck2 votes

You're mistaking relativity (relative to starting point) for actuality (actual effect).

But yes, effective health is far more practical than % damage reduction.

Reikken3 votes

{quoted}

You're mistaking relativity (relative to starting point) for actuality (actual effect).

not really actual effect of increasing damage reduction from 0% to 10%: live 1 second longer (1.1 actually) actual effect of increasing damage reduction from 80% to 90%: live 50 seconds longer (if it takes 10 seconds to kill you when you have 0% damage reduction, and dps is constant)

(and fwiw, it takes 11 armor to get 10% damage reduction, and it takes 400 armor to get 80%, and 900 armor to get 90%.)

TheSlogs5 votes

You need to look at it as effective health. When you have 1000 health and 100 armor, you have 2000 effective health when taking physical damage because you receive 1/2 damage. Then when add 100 armor for a total of 200, you have 3000 effective health when taking physical damage, because you receive 1/3 damage. And so on. You have your health times X effective health, where X is the number of the resistance you have in hundreds.

MohawkBird2 votes

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WoonStruck2 votes

That's not diminishing returns because you're talking about 0-100 representing 0 to infinity. Do you not know how scales work?

Each and every point of % damage reduction past 50% is worth VASTLY more than the last, and every point past 70% is worth vastly more than those past 50%.


Think about it this way: past 50%, you only have 50% potential damage remaining that you can take.

That means that increasing your damage reduction to 60% is worth around as much as 20% damage reduction was prior to 50%.

Going from 50% to 70% is effectively gaining 40% damage reduction.


This is why I keep saying you people don't understand the scope of infinity represented in a capped numerical scale.

Once you're at 70%, increasing your mitigation by another 1% is actually ~3%. It might be 3x harder to reach that extra 1%, but you're getting 3x as much out of it.

It is parallel. Not diminishing.

Armor/mr do not have diminishing returns.

**Only counter-itemization lowers the effectiveness of the investment in them. **

Dominick Destine8 votes

While everything stated by OP is technically true, in practical terms it's complete Hecarim Droppings.

We're playing in an era with the highest level of % armor penetration and flat armor pen we've ever had... and, by definition, the higher your armor , the higher the effect of said % effects, this goes double for "Bonus armor penetration" and is even more effective when you consider the fact that % penetration goes before flat penetration making it that much more effective.

Armor has massively diminishing returns in a practical scenario... in an isolated "Optimal" scenario, purely rhetorical math, no it does not have raw diminishing returns.

Remember; item 3147 item 3156 item 3036 item 3142 item 3071 item 1400

WoonStruck4 votes

That's not what was being argued, however.

People seem to think that the % damage reduction in the tool-tip not going up as quickly means more armor is not of equal value.

The classic "armor/mr have diminishing returns" is an age-old myth that's existed since season 1. That's what I'm trying to dispell because I have seen a LOT of it again lately.


The current state of armor counter-itemization is a whole other ball game.

I definitely agree that armor pen is far too strong right now, though.

Dominick Destine2 votes

{quoted}

That's not what was being argued, however.

Yes, I understand and I didn't contradict your calculations, I specifically said you were right... I guess I should have clarified that the people you're addressing ARE wrong and you ARE right, your calculations are spot-on... but again my argument specifically is that in the current iteration of the game, in practical terms they are expressing a sentiment which is backed up by empirical data (I.e. highest prevalence and superiority of armor pen of all seasons).

So yeah, you're not wrong and yes I know armor pen is a different argument... but it IS relevant because that's why people are buying into the myth, that's why people say "Armor has diminishing returns", etc.

WoonStruck2 votes

There's so much flat and % pen that you must have a certain threshold of armor for it to be effective, though. That's a factor as well.

However, I believe the best direction for the game right now would be to switch the penetration formula back to base (minus) flat (divided by) % reduction value. At the very least for physical damage.

All of the armor pen items they added made the current formula an extremely bad one to continue using.

TotalJerk4 votes

item 3147 item 3156 item 3142 are all bad examples as they get weaker the more armor you buy, and item 1400 doesn't give armor pen anymore.

Dominick Destine4 votes

{quoted}

item 3147 item 3156 item 3142 are all bad examples as they get weaker the more armor you buy

That's true if it's an individual purchase, but if you add the percentage based armor pen unto that, the effect is greatly magnified... it's specifically setup to be this way; 30 flat armor pen on its own is pretty meaningless... but 30 flat armor pen + item 3036 and/or item 3071 makes that 30 flat armor pen significantly more effective.

item 1400 doesn't give armor pen anymore.

Good point, that should show you how often I play AD junglers.

(I.e. never)

WoonStruck2 votes

FFS why would anyone downvote you for this. I really don't understand.

What you state is entirely true. There's no interpretation or opinion to take from it. Its straight facts presented and you accepting someone correcting you.

Boards, tho.

Dominick Destine2 votes

{quoted}

FFS why would anyone downvote you for this. I really don't understand.

I am somewhat of a semi-celebrity in these parts. In the old forums I was a straight up legend. I hope to achieve that level of fame here someday.

By the way, a semi-celebrity in a bad way, most people hate me.... but the vast majority, even the haters, find my content entertaining.

TyrekGoldenspear1 votes

Probably because your attitude towards others can easily be seen as condensending.

You're like a reality TV contestant. The snarky sarcastic one who always has something to say. :P

And just like reality TV it's entertaining to watch you engage in verbal fencing with somebody.

Dominick Destine1 votes

{quoted}

Probably because your attitude

Your "Hurt Feelings" are not an argument.

Facts, logic and reason are the only things that matter. Reality is not a popularity contest.

TyrekGoldenspear3 votes

Ya see? Verbal fencing.

You can't help but use fancy verbage and an air of superiority to either irritate people into replying back to you or ragequitting from the keyboard.

But you won't get me to respond. No sir....

Whoops.

Dominick Destine1 votes

{quoted}

Ya see? Verbal fencing.

No, more like reality. It's not complicated.

TyrekGoldenspear1 votes

And now I parry.

Theorchero1 votes

[{quoted}](name=Dominick Destine,realm=NA,application-id=3ErqAdtq,discussion-id=EE5JYxAm,comment-id=0003,timestamp=2016-07-30T20:18:55.639+0000)

While everything stated by OP is technically true, in practical terms it's complete Hecarim Droppings.

We're playing in an era with the highest level of % armor penetration and flat armor pen we've ever had... and, by definition, the higher your armor , the higher the effect of said % effects, this goes double for "Bonus armor penetration" and is even more effective when you consider the fact that % penetration goes before flat penetration making it that much more effective.

Armor has massively diminishing returns in a practical scenario... in an isolated "Optimal" scenario, purely rhetorical math, no it does not have raw diminishing returns.

Remember; item 3147 item 3156 item 3036 item 3142 item 3071 item 1400

worst build ever report hecarim

agbudar7 votes

buying armor is useless due to the sheer amounts of armor pen that we have item 3071 item 3036 alone shreds more then half the armor you buy

xWaters2 votes

So... like what the hell is the point of being a tank on the frontline? I can't take any hits despite building full resistances against the enemy team. And I do 0 damage because of my investment into defense. Like I don't know a lot about this game, you could call me a casual, but it's ridiculous to nearly be 100-0 in a team fight as a tank.

Dominick Destine2 votes

{quoted}

So... like what the hell is the point of being a tank on the frontline?

The idea is to disrupt the enemy team and survive as long as possible... right now (In my opinion) , pure tanks are underpowered.

Hybrid tanks are in a good position and arguably doing better than ever Zac MonkeyKing Amumu Volibear and even/especially Malphite etc. this is because armor is good up to a point and then damage becomes more valuable... when in the old days, stacking defense to an extreme was a solid plan because the enemy team was forced to either ignore the super-tank and take disruption or focus the super tank and get roasted by the enemy team (Classic EX: Rammus, or remember when Shen was a primary tank? )

A lot of tanks are going item 1402 rather than item 1401 for that reason.

WoonStruck2 votes

Armor penetration is in a pretty stupid state right now.

They added a ton of armor pen options without reverting to the base - flat / % reduction. Its currently base / % reduction - flat, which effectively invalidates armor.

Riot is extremely stupid sometimes, if that tells you anything. Very often they don't look at what realistic consequences will be.

WoonStruck4 votes

Why are people actually downvoting this thread of facts? lol

TyrekGoldenspear1 votes

Too much maths. It makes brains hurt. edit: up-voted your post to make it positive again. I am one of the few who bothers to read and try to comprehend lol.

TheOvermind3 votes

Resistsances might be flat values but they actually work in % damage reductions : Having 0 armor and then buying 10 armor => you went from 0 % physical damage reduction to 10%.

You essentially bought 10% physical damage reduction

Having 50 armor and again buying the same amount ( 10 armor) gives you only 4.2 % additional physical damage reduction

This amount only decreases the more armor you get getting closer and closer to 100% dmg reduction but will never be that much.

Armor has no diminishing returns in Starcraft where it is actually a flat amount subtracted from the damage dealt. The more armor you get in atarcraft the better. But not in league of legends . Well actually it is better, but it won't be cost efficient, because you will be buying something like 100 armor and only get 2% dmg reductio. Out of it, assuming you have something like 450 armor.

Penns2 votes

Idk, I never understood that ehp stuff but getting 20% physical damage reduction for 100 armor seems better than only getting 3% for the same amount of armor, doesnt it?

darkestkhan1 votes

Depends how much reduction you have. Percent values are not that intuitive - just experiment with calculator for a while to see what happens.

XIII Vanitas2 votes

Thanks, this is very informative.

Tobias Brackner2 votes

Thank you very much for posting this.

A lot of people are blind to the math involved in this game and having these things to break it down goes a long way to make sure we are all informed about the systems we are interacting with.

deadlychuck2 votes

In terms of the stat shown in game, it does have diminishing returns, but that change in growth rate of % physical damage reduction, correlates with a linear growth in effective health. I thought this was common knowledge.

That said, it still acts as a multiplier, not flat HP. The same calculations give different amounts of bonus health, calculated from the HP of the player. If you buy enough armor to double your effective health, 2k > 4k, then buying another 500 HP, effectively increases your health by 1k.

Defensive stats is pretty much how tanks scale, similar to abilities for AP champions, and what use to mainly be auto attacks for AD (now champions are given full AD scaling kits for some reason). Similar to how some champions increase their scaling of an ability with each rank, tanks increase their scaling of health based on how much gold they invest into the defensive stats. Though tanks aren't the only ones capable of benefiting from this, that's why you see stuff like tank ekko and such.

That said, the solution to those problems probably has more to do with the utility of champions who aren't tanks being played as tanks, more so than any raw # things like scaling or base damage.

The Deckowner2 votes

on a side note, armor and mr does somewhat diminish when enemy has %pen items, after they build that item the resistances you buy are basically all diminished.

higura2 votes

what makes armor and mr worthless is how easy it is for high dam dealer to just ignor it, the pen is way to high in the game so for most build is haveing pen on runes enough to burst a full tank down in no time at all, and even if your playing vs a tank who build specifik to counter you can you just buy one pen item in game and negate it all...

this means items like item 3075 item 3110 item 3742 are a complete waste of gold because item 3083 and item 3748 will not only make you just as tanky (if not more), give you more damage to help your team burst down tagets and are cheaper with less slot used...

i dont see it change anytime soon tho because riot seems to like the idea of high damage champs haveing all the fun while support is getting picked less by the season...

DunkinNoobs1 votes

While technically true, it does not account for penetration, nor does it account for the fact that each point of health is worth more for every point of armor or MR you have, and are thus better served investing in HP once you have decent amounts of Armor/MR.

Reikken2 votes

each point of health is worth more the more armor you have, AND each point of armor is worth more the more health you have

TyrekGoldenspear1 votes

So, how much armor do I buy before I should start buying straight health?

WoonStruck2 votes

It really depends. If you have 1000 HP and 50 armor, an item like Sunfire will give you perfect linear efficiency. The health you're purchasing is exactly as efficient as the armor on the item.

Basically, take the current max HP you have, and multiply it by the armor you're purchasing, then divide by 100. That is how much effective health you are gaining. If you can purchase an HP item that will give you the same or more, HP is more efficient.

Keep in mind that HP also applies vs all damage types.

Also, you must keep in mind enemy armor/mr penetration. Items like Black Cleaver, Last Whisper, Void Staff, etc all give you effective diminishing returns on your armor/MR; it becomes harder to make up the points that you lost vs the enemy attacking you. In Black Cleaver's case, it actually globally reduces your armor based on the stacks.

However, those 'diminishing returns' due to counter-itemization don't really matter as far as efficiency. If they lower your armor, it means you are very likely to gain more EHP by buying more armor than HP anyway. There are graphs from waaaaay back on reignofgaming, and I'm sure there are other sources as well that show the exact trends of defensive stat efficiency.


That said, currently, there's a heavy lean on HP itemization if you truly want to tank, not be a bruiser. Armor pen is that insanely strong at the moment, as long as a few of your HP items are armor items to nullify the flat reductions a little bit.

TyrekGoldenspear1 votes

Ack. So much math.

I'll just run item 3068 ,item 3065 , and item 3742 and item 3156/item 3110 , rounding off with flat health from item 3083.

Would that work? and grab a item 3512 for resistances and splitpushing?

iluvalar1 votes

Let me precise this however. Resistance have LINEAR return, much like everything except hp5 (and healing).

However, every stats are in pure multiplicative logic with each others. So as soon as you buy armor, everything ELSE takes more value. Not only HP to make efficient HP, but also everything that increase your DPS as your life span being the second in the "damage per second" have just increased.

You go from 30 armor to 130 armor. Your lifespan increase immensely by like 40%. Every other stats just increase their own value by 40% EXCEPT armor. Proportionally to any other stats, armor is then in diminishing return. Assuming that you had another viable option beside armor at your first buy, it became an obvious better choice then another 100 armor for the second item.

It's true for armor, but it's also true for any other stats; If you build AD anything but AD take value, if you build AS anything but AS takes value, etc...

ZT Xperimentor1 votes

*Only when looking at effective health.

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