Diminishing Returns: Fact or False (RP Contest)

There is a common myth among players that is prevalent among all skill ranges. This myth concerns the effectiveness of stacking resistances on champions and whether it is effective to stack them beyond a certain value. Today we'll be taking a look at whether there is such a thing as "too much armor". Can your knight in shining armor really be wearing so much armor as to weigh him down?

Firstly let's get the video version out of the way:

Today's video presentation is on a different style to the usual to compensate for the lack of an in-depth written version. Feedback on the style would be appreciated - would you prefer more presentations like above or the usual in-depth written version with a narration/commentary over it?

A Quick Summary of the Explanation in the Video

I don't expect everyone to sit through a six minute video so here's a quick summary of what I cover and what to take away as knowledge from this article.

Introduction to the Myth and Examples

 

 The above is your health bar at 1000 HP.
All damage to you is affected by the following formula:
 
 
 
 
Assume an enemy is hitting you for 1000 damage per attack.
If you had zero armor, you would be killed in one blow.
 
 
Now at 100 armor, the damage multiplier is 50%, hence after 1 blow, you would be left at 500 HP:
 
 
Similarly, the following health bars depict how much health you would have left after one blow if you had 200, 300, and 400 armor respectively.
 
At 200 armor:
 
At 300 armor:
 
At 400 armor:
 
 
 As you can see the amount of damage you take is reduced but at a lower rate. Why is this so? This is the point where players are hoaxed into believing that diminishing returns exist on stacking armor. Let's try to explain why it's not actually diminishing.
 

The Explanations

 
This can be explained due to the nature of a hidden mechanic in LoL. Each point of armor in the game increases your effective HP by 1%. Meaning that a bit of health when you have 400 armor is a lot more valuable than the same amount of health if you have 100 armor for example.
 
Another way to explain this is to view it as additional "health blocks". In the above examples, every 100 armor adds a "health block" to your life.
  • When you have 0 armor, it takes 1 hit to kill you.
  • When you have 100 armor, it takes 2 hits to kill you.
  • When you have 200 armor, it takes 3 hits to kill you.
  • When you have 300 armor, it takes 4 hits to kill you.
  • When you have 400 armor, it takes 5 hits to kill you.
As you can see, each 100 armor adds the same amount of effectiveness as the previous 100 armor when viewed this way.
So the key point to take away from this article is this: Do not be fooled by health and percentages as they will seem diminishing. Understand that each point of health is worth more when you have more armor which is why there appears to be a diminishing return. If you understand that, you should have no trouble with that concept and you can silence your teammates when they bring up arguments like these.
 
To conclude, I would like to say that this is quite a simple concept that is easy to explain yet easy to confuse. I know many of you may have found this obvious yet at the same time, a few of you would have had your eyes opened. I hope the presentation of the explanation in this way helped get across a point that you would not have normally understood. I highly suggest you watch the video version as it's much easier to understand the explanation when you have graphics and when I can talk about it :)
 

Next Steps and RP Contest

While this article only explains the truth about diminishing returns, it doesn't breach into the analysis of how this affects stacking resistances and health in your builds. This is a much more in depth analysis that I will leave to the ever-friendly and colourblind, Gentleman Gustaf, who will be taking a hard look at stat multiplicativity when it comes to health and resistances. I simply wanted to tackle this myth and and try to clear up any confusion players had about the issue! Once again, I recommend watching the video version for an easier to follow explanation.

As for the RP contest, you will see its details at the end of the video. The only requirement you must meet to be able to win the RP contest is be a subscriber of my channel. I will be picking a random YouTube subscriber some time in the next week and contacting them through YouTube, so remember to check your inboxes regularly :)

 Finally, I hope you enjoyed it and as always this is DiffTheEnder signing out!
 
   
 
 
 
Help support me and upvote this article if you enjoyed it! Thank you in advance :)
 
 
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You can find all my articles/posts from the old Reign of Gaming here
 
Cheers,
DiffTheEnder

Comments

  • #43 Arekk

    For anyone who played a tank in World of Warcraft for many years and was into theorycrafting also, this is clear by now. 

    No, there aren't diminishing returns on the resistances. But each point increases the value of Health. At some point it becomes cheaper to buy HP instead of more armor/mres. 

    Also, let's not forget about League of Legends and what you need to do. It's about not stacking 6 tank items, and having no dmg. What's the point of killing a guy with 6 tanks items if he is not a threat to me? Or at least focus first. 

  • #36 dualkeybladeroxas

    Although it isn't strictly dimishing returns on stacking armor/resistances/hp, because they are multiplicative with each other it has essentially the same effect. ie, continuing to stack armor or mres with little hp or vice versa is actually inferior compared to getting reasonable amounts of both because your EHP will not be as high in the first method.

    So no, there are no diminishing returns but in a way it acts similarly. Also against % armor penetration/% mres penetration it actually does have diminishing returns.

     

  • #37 Katrex

    Quote from dualkeybladeroxas »

    Although it isn't strictly dimishing returns on stacking armor/resistances/hp, because they are multiplicative with each other it has essentially the same effect. ie, continuing to stack armor or mres with little hp or vice versa is actually inferior compared to getting reasonable amounts of both because your EHP will not be as high in the first method.

    So no, there are no diminishing returns but in a way it acts similarly. Also against % armor penetration/% mres penetration it actually does have diminishing returns.

     

    Nope it doesn't it's just gives less ie .5 extra hits per hundred instead of 1 hit per hundred.

  • #35 JackInTheCox

    Subtracting 333 from 1000 results to 667.  Thanks for putting in the work to clear this myth in video format.

  • #33 Eggsellent

    I always say that it's not that resists give diminishing returns.  It's that the more resists you have - as well as the more percentage based penetration and flat true damage the enemy team has - the more cost effective buying health becomes.

    People who argue whether resists have "diminishing returns" mathematically or not are wasting their time - FatsXL's comment summarized it perfectly.  All we should care about is how we should be itemizing for defense - and stacking resists is not the best way to get maximum survivability.

  • #27 Katrex

    Its all about perspective.  If you have 0 armor and buy 100 it doubles your effective hp, now you buy another hundred, it no longer doubles your effective hp it increases it by 50%. Similarly health works the same way.

    People are used to armor working diferently. X armor makes you Y% tankier. Now it works in the same way stacking health does. Which means armor and health stack multiplicatively in terms of calculating your survivability.

    Say you have 1000 health and 0 armor. You could buy 1000 health, this doubles your survivability. Next  if you buy 1000 again you get a 50% bonus going from x2 to x3 survivability. If you buy the armor though you double again. Getting a total of 4x survivability.

    So how do we apply this to the game. Well we have roughly 2000 health and 100 armor. This puts us at that x4 survivability. To put you at 9 x you need 3000 health 200 armor. 16x 4000 health 300 armor etc.

    So what do we aim for against a balanced team? 3k health 200 armor 200 mr. And damage.

    Lets say.   mercs Maw wits end warmogs atmas GA That puts us at about 3300 hp and 230 resistances which is about twice as tanky as as an ad with a banshees. 

    The problem occurs with last whipser. This skews everything. Istead of being twice as tanky you're only 1.5 times as tanky. Does this mean you shouldn't bui.d armor? Yes and no. It aproximately makes stacking armor and health the same as stacking health. If their entire team has last whispers and void staffs, then stacking health health and more health is technicaly correct. However they wont have those items till later in the game. And building for late game and being useless all early game is not an option.

    What can we learn from this? Well your last item should be health or lifesteal or damage, not resists. Other than that it probably depends on the game.

     

  • #26 TiKD

    The whole diminishing returns thing is kinda bullshit. It depends on team comp and changes from a game to game basis. This is useful in some aspects but in others it just doesn't matter. Sometime the the diminished returns is better.

    As for saying things like last whisper is more effective it's true that the more you stack the better those items are, but depending on the champ who wields it and the role you are playing it's practicality can differ immensely.

  • #32 ChemClub

    This post is the most logical I've seen in quite a while. Talking about whether diminishing returns truly exist is not worthwhile. They either exist for every stat in question (in the sense that each stat increases the benefit of the other stats, lowering the value of the purchased stat), or they don't exist at all. It really is worthless to argue which side of that discussion is right. Not to mention that all of this talk has little application in game, as there is seldom an option just to stack one resistance and do well in game. 

    This is the best line in the article for that matter:
    This is a much more in depth analysis that I will leave to the ever-friendly and colourblind, Gentleman Gustaf, who will be taking a hard look at stat multiplicativity when it comes to health and resistances.  

  • #25 Brontobeuf

    Is this AIR that we can listen at the very end of the video? If it is, awesome choice. :]

  • #24 EuWGasgano

    On almost every top and jungler champ with more utility then dmg i get really beefy and it works great for me. Most times i get Mercs, a big HP item, a big armor item and one big MR item... thats overall really nice, leaving you with ~3000+ HP, ~200 armor and 150-200 MR. You can now opt for two damage items, best would be some hybrid stuff which synergizes well with your tankiness, like atmas or maw.

    Of course i change things for the different champions like i feel its good but overall you can get a well rounded, tanky build including everything and still be a big threat.

    Last edited by EuWGasgano: 7/26/2012 6:03:26 AM
  • #18 gitndachoppa

    Well, hopefully someone with at least a basic understanding of LoL mechanics and competent in math will be covering this topic this time. As the last post on the subject by Prant was one of the most trash pieces of "theory crafting" I've ever witnessed. It left me with the opinion that Prant is not qualified and should not post on RoG on any topic where math and game mechanics are involved.

  • #21 DiffTheEnder

    Couple of questions regarding your comment.

    1) Hopefully someone with........... covering this topic this time? - Are you saying my one was bad and the next one will be good or are you saying mine was good?

    2) That's a bit harsh on Prant. He made a mistake and has since learned. The main point of his post was that the more resistances you have, the more effective items like Last Whisper were. It's taking it a bit too far to say he isn't qualified to make any post ever. We all make mistakes.

  • #23 MerryLane

    Anyway, Prant wasn't wrong.
    Diminishing return means that "every extra point you get worths less than the previous one".

    That's exactly appliable to armor and mag res, but "in game". Here you had defined precisely mathematically and out of reality, but in game, if you stack armor, it's not as effective because you would lack : damages, health, mag res, ... And of course %penetration that are so often run nowadays truly make diminishing returns even "mathematically".

    So I'd be really pleased gitndachoppa, and others that have a similar language, to try and understand my "buddy" Prant's point of view.

  • #38 gitndachoppa

    Quote from DiffTheEnder »

    Couple of questions regarding your comment.

    1) Hopefully someone with........... covering this topic this time? - Are you saying my one was bad and the next one will be good or are you saying mine was good?

    2) That's a bit harsh on Prant. He made a mistake and has since learned. The main point of his post was that the more resistances you have, the more effective items like Last Whisper were. It's taking it a bit too far to say he isn't qualified to make any post ever. We all make mistakes.

    1.) Your post was correct. But I was referring to you mentioning that someone will be covering "stat multiplicativity when it comes to health and resistances" next time. 

    2.) Not to belabor the point, but going through his posts, there is a history of lack of actual numerical analysis. With regard to his post on stacking hp, Prant concludes (wrongly) that stacking resist is inefficient, his whole argument was people buy lw and vs to counter resist and nobody buys bloodrazer, that and the whole diminishing returns deal. And some where along the way, he pulls the number 200 as the threshold out of his ass. With no math, it is hard to justify his point, especially since he doesn't look at specific itemization options. More than anything, I simply don't think someone should post with the implicit status of being an expert on theorycrafting when he is clearly not.

    Last edited by gitndachoppa: 7/27/2012 8:44:57 AM
  • #39 gitndachoppa

    Quote from MerryLane »

    Anyway, Prant wasn't wrong.
    Diminishing return means that "every extra point you get worths less than the previous one".

    That's exactly appliable to armor and mag res, but "in game". Here you had defined precisely mathematically and out of reality, but in game, if you stack armor, it's not as effective because you would lack : damages, health, mag res, ... And of course %penetration that are so often run nowadays truly make diminishing returns even "mathematically".

    So I'd be really pleased gitndachoppa, and others that have a similar language, to try and understand my "buddy" Prant's point of view.

    Prant was wrong. He completely ignores why people buy resist, which is power during mid game and tanking of the the frontline in addition to the carries. Your definition of diminishing returns is not what Prant was invoking, and it wasn't just armor he was talking about, please reread his post. In addition, you are incorrect in your conclusions, seeing as you ignore the point of actually buying resists and actual analysis of resist items.

    It is kind of hard to understand your buddy's point of view when he is obviously wrong. 

    Last edited by gitndachoppa: 7/27/2012 8:43:43 AM
  • #40 MerryLane

    Sorry but the real definition of Diminishing Return is :
    "every extra point you get worths less than the previous one". (go check on the internet if you don't trust me)

    It is totally true in this game. I will give you some sort of example. Let's say that you have 0 armor and that you buy one, two, three, four thornmail (let's forget the passive) to get 100>200>300>400 armor.
    Obviously, you tank once, twice, three times and four times better to physical damages.
    BUT they are less and less efficient than the previous one, if you consider that an ennemy can grab a last whisper, or because you can't get stats that you also need (damages, mana, health, resists, ...).

    I never said resists and armor were useless, far away from that. But if you have to calculate your best choice to buy, between hp and resist/armor following the "mathematical" formulas, you'd better favorise a bit more the health.

    And please re-read the part before " if you stack armor, it's not as effective [...] " because I never meant Prant only talked about armor. I was stating as an example, "if you stack armor, you will miss damages, resists, or sth".

  • #41 ChemClub

    What you seem to be ignoring is that, in your definition, 'worth' is a key word. Worth is a term related to the cost-effectiveness of an item. With each point that is placed into a resistance, the benefit of buying another point of health goes up. Assuming that you can not buy an item that contains both HP and armor in every slot, you will have to chose between the two. Which one is 'worth more' at increasing amounts of armor deals with the true essence of diminishing returns.

    Otherwise, its all about perspective. Each point in armor does have diminishing returns, but so does everything else. Doubling the effect of your armor at 40 armor is easy, but is not achieved by getting 40 more armor. http://www.reignofgaming.net/blogs/a-different-view/diff-the-ender/21061-diminishing-returns-fact-or-false-rp-contest?comment=27 addresses the issue of discussing diminishing returns well.

  • #42 gitndachoppa

    Quote from MerryLane »

    Sorry but the real definition of Diminishing Return is :
    "every extra point you get worths less than the previous one". (go check on the internet if you don't trust me)

    It is totally true in this game. I will give you some sort of example. Let's say that you have 0 armor and that you buy one, two, three, four thornmail (let's forget the passive) to get 100>200>300>400 armor.
    Obviously, you tank once, twice, three times and four times better to physical damages.
    BUT they are less and less efficient than the previous one, if you consider that an ennemy can grab a last whisper, or because you can't get stats that you also need (damages, mana, health, resists, ...).

    I never said resists and armor were useless, far away from that. But if you have to calculate your best choice to buy, between hp and resist/armor following the "mathematical" formulas, you'd better favorise a bit more the health.

    And please re-read the part before " if you stack armor, it's not as effective [...] " because I never meant Prant only talked about armor. I was stating as an example, "if you stack armor, you will miss damages, resists, or sth".

    Let me state this as simply as I can: resist does NOT suffer from diminishing returns. Saying that it does is flat out wrong, as was prant. And if you insist that is the case, then so are you.

  • #44 MerryLane

    As you say, worth is a key word and you don't seem to understand the point in here.

    Let's make it simple. You go to Wallmart or IDK, and you see Iphone6 for only 1000 dollars (half price).
    So as you do want the Iphone, you will buy one. As long as you are there you will buy a second for your mother (coz you have no gf). Buying a third would still be cool, because it's worth the same price than the two firsts, rite?
    But you don't need it as much as a new car, so basically, the third and fourth would still worth the same, but it's still not worth buying them ...

    Damn. Gosh. Seriously.
    And again, sorry but the real definition of Diminishing Return is :
    "every extra point you get worths less than the previous one".
    These extra points would worth the same, but it's still not worth the same. KAY?

    Last edited by MerryLane: 7/27/2012 11:13:16 PM
  • #45 ChemClub

    Well, you seem to ignore the fact that each additional iPhone is 'worth' less to you, as you no longer need a phone. The COST of the phone does not change. The BENEFIT of the phone is drastically lowered. In terms of cost-efficiency (WORTH), each additional iPhone is diminished in VALUE. However, the benefit (and thus worth,value) of buying headphones and iTunes gift cards (both COMPLIMENTARY GOODS) increases. Replace iPhone with resistance and headphones with health, and you have an easy explanation of the law of diminishing returns.

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