TEH - Total Effective Health, or; a guide on how to build a tank properly.

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Warrition

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Adjudicator

11-28-2011

Quote:
Originally Posted by Stimraug View Post
Warrition, diversity in perspectives in general is a positive thing, but are we not talking about the one and only perspective of increasing our survivability here? Your example has been given many times already, in the light of showing that the logic behind diminishing returns is flawed; if it was not, then AD, AS and every stat Tryndamere ever came up with had diminishing returns!

What I'd like to point out is that the perspective rickless is giving here, and which you are "supporting", is not a perspective from a realistic/meaningful viewpoint.
AS and AD do in fact have diminishing returns, from this perspective -- and there's nothing incorrect about that; Tryndamere players know this, which is why you don't see good Tryndameres with 5 bloodthirsters, despite it having the highest AD in the game.

rickless' perspective is both realistic and meaningful in the context of League of Legends. To put it simply, as you purchase more and more armor, there comes a point where your survivability would be more benefited by purchasing health; this is inarguable. Even though each point in armor increases your EHP by the same amount, it eventually becomes a better investment to purchase health. Health suffers from the same diminishing returns -- but again, there are two ways to look at it.

In the end, both sides are "correct" from a certain perspective, and both sides agree that a balance of armor and health is most effective.


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caydi

Member

11-28-2011

What is the point of arguing about this? It's an argument over semantics. Depending on how you choose to look at it, you could argue that Morello is right. You can also argue he's wrong, depending on how you look at it. In the end though, everyone is coming to the same conclusion, so who the hell cares whether it's called diminishing returns or not?

You don't argue semantics by showing mathematical proofs. Define the terms you use, then work from there. If you want to say there are no diminishing returns, define "diminishing returns" first. Your definition of it is clearly different from others' definition. But that's how language goes - it's ambiguous.

Armor, health, attack damage, attack speed, etc. have diminishing returns if you look at it from the perspective of percents. They don't have diminishing returns if you look at it from the other. (What is your frame of reference?)

Stimraug, you argue that rickless's and Warrition's perspective is not "meaningful." It's incredibly meaningful to me, though. Why would I buy another 10 AD if I already have 1 million AD? That's the point. Clearly, you understand that. Clearly every one else does. So why argue over it? You're arguing over semantics.


Quote:
Originally Posted by chumbler View Post
After checking the actual definition of diminishing returns (it has been a while since I've had an economics class), it apparently refers specifically to diminishing marginal returns, in which case yes, it is true that armor/MR (and health) have diminishing (marginal) returns, simply because they do not scale exponentially. However the real returns of armor/MR (and health) do not diminish and depend only on the other stat (by which I mean the real return of armor/MR depends only on health, and the real return of health depends only on armor/MR.) There are no artificial diminishing return mechanics imposed on armor/MR and health, unlike move speed, for example.

In conclusion, diminishing marginal returns: Yes. Diminishing real returns: No. The real returns are the more important one and the easier one to evaluate and compare. Armor/MR and health are an economy of scale, but they have natural diminishing marginal returns as a result of not scaling exponentially.
This is what I'm talking about. Define the word you're arguing over first.


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Eledhan

Senior Member

11-28-2011

Quote:
Originally Posted by Stimraug View Post
EDIT: Also. please refrain from upvoting reds just because of their color. If their facts are wrong, downvote to set things straight.
EDIT2: I just re-read the thread... It's kind of sad how ricklessa tries to appear media-sexy by using the words "kitten" and "cookie". Don't they give PR-training there at Riot's
If you think this is bad...you should have seen him back in the day before he was a red...

Trollin like a BAWS!!!

rick and I are on good terms now, though. He can be a bit difficult to talk with, but because he looks at things differently than I do, I appreciate the conversations since I always learn areas in which I am wrong, or I learn better ways to show how I am right.

Anyway, try not to let it frustrate you and just stick with the facts. I learned a while back to keep an open mind and not get upset if others don't see things the same way I do.

______________________________________________

As an on-topic note...

EHP is best calculated as a % increase from base HP for the relevant damage type. The best example I can think of is using 100 Armor and 1,000 HP.

There are a few different ways to arrive at the 2k EHP, but my favorite is as follows:

100 Armor = 100% increase in EHP * 1k = 1k more HP = 2k EHP for physical damage

That's about as simple as it gets...

_________________________________________

Regarding the diminishing returns...

Diminishing returns wikipedia definition is here...

http://en.wikipedia.org/wiki/Diminishing_returns

Basically, the proper use of the term "diminishing returns" is exactly as you described it. It's a term that comes from Economics, and has been misused in gaming.

Honestly, the only way to really look at this whole thing is to look at it from a cost-effective standpoint, which I believe is where rick is coming from. Unfortunately, he hasn't quite explained it using the correct terminology, since the phrase "diminishing returns" is technically incorrect.

His explanation is valid, but it's not an example of diminishing returns of the EFFECT of purchasing armor since that would only be true if buying one armor increased EHP by less than 1% of base HP.

HOWEVER!!!

His explanation IS an example of "diminishing marginal utility" for armor. Each point becomes less cost-effective (and thus, less desirable) than the point prior to it. However, this is true for ALL purchases in League of Legends. For example, going from 100 AD to 145 AD is the same flat distance as going from 145 to 190, but the % increase to DPS is less, therefore meaning the second BF Sword purchased is less marginally useful than the first one.

http://en.wikipedia.org/wiki/Diminishing_marginal_utility#Marginal_utility

This simply indicates that the issue here is one of different uses of the terminology.

I have found this to be the case even in the professional world where people say things like "gross profit" when in actuality they aren't talking about gross profit, but instead are explaining a "markup" from cost. To demonstrate my point, a brief example...

A 5% markup of a $100 cost item generates a $105 sales price. However, this is NOT going to generate a 5% gross profit, because 105 - 100 = 5 gross profit, which is actually 4.7619% Gross Profit.

This is a simple exercise that we should all learn from (myself included) regarding EHP and its applications. We must be very careful as a community (and even Riot Games staff) to make sure we aren't saying things that are misleading to newer players.

I wish it were possible for EVERYONE to understand the proper use of the two terms, but that's simply not possible. All we can do is try to help people with questions to follow the logic for themselves and answer any questions they may have.


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Eledhan

Senior Member

11-28-2011

Quote:
Originally Posted by chumbler View Post
After checking the actual definition of diminishing returns (it has been a while since I've had an economics class), it apparently refers specifically to diminishing marginal returns, in which case yes, it is true that armor/MR (and health) have diminishing (marginal) returns, simply because they do not scale exponentially. However the real returns of armor/MR (and health) do not diminish and depend only on the other stat (by which I mean the real return of armor/MR depends only on health, and the real return of health depends only on armor/MR.) There are no artificial diminishing return mechanics imposed on armor/MR and health, unlike move speed, for example.

In conclusion, diminishing marginal returns: Yes. Diminishing real returns: No. The real returns are the more important one and the easier one to evaluate and compare. Armor/MR and health are an economy of scale, but they have natural diminishing marginal returns as a result of not scaling exponentially.
This is largely correct. However, the word "return" is misleading, and it would be better to use the proper terminology of "utility" when talking about diminishing marginals. This is because the word "utility" refers to the utilization of resources (in this case, gold) and indicates proper understanding of the terminology and concepts.

I realize that this is an impossible request...but I figured since people in this thread would want to be properly informed, I'd just tag my little two cents onto your post.


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Eledhan

Senior Member

11-28-2011

Quote:
Originally Posted by caydi View Post
What is the point of arguing about this? It's an argument over semantics. Depending on how you choose to look at it, you could argue that Morello is right. You can also argue he's wrong, depending on how you look at it. In the end though, everyone is coming to the same conclusion, so who the hell cares whether it's called diminishing returns or not?

You don't argue semantics by showing mathematical proofs. Define the terms you use, then work from there. If you want to say there are no diminishing returns, define "diminishing returns" first. Your definition of it is clearly different from others' definition. But that's how language goes - it's ambiguous.
The term "diminishing returns" already has a proper definition. People shouldn't be using the term incorrectly.

I realize that this never happens in the real world, but honestly? A red posting about game mechanics should get his facts straight before using phrases like "diminishing returns" without understanding what it means.

Quote:
Armor, health, attack damage, attack speed, etc. have diminishing returns if you look at it from the perspective of percents. They don't have diminishing returns if you look at it from the other. (What is your frame of reference?)
Only certain stats have diminishing returns...but they ALL have diminishing marginal utility.

Stats such as Move Speed actually do have diminishing returns, since after a certain point, every MS point you buy is reduced in actual effectiveness, not just a reduction in the percentage increase received.

Quote:
Stimraug, you argue that rickless's and Warrition's perspective is not "meaningful." It's incredibly meaningful to me, though. Why would I buy another 10 AD if I already have 1 million AD? That's the point. Clearly, you understand that. Clearly every one else does. So why argue over it? You're arguing over semantics.
He's arguing over it because the terminology is WRONG. The concept is right, sure, but the words are wrong. It's like saying that ricklessabandon is an orange forum member when in actuality he is a red forum member.

I'm not holding the fact he used the wrong term against him, because our culture is terrible about using the wrong word for the right concepts, and I'm sure he just picked it up that way. I happen to be a business analyst who MUST use the right terms or people think I'm talking about something completely opposite than what I intend, so I picked up on it very quickly.

Other less-informed (from an economics standpoint) players may not have picked up on it, and that's probably why the guys you are addressing called rick out on it. It's nothing personal, but getting the right data and terminology is so, so important.

Quote:
This is what I'm talking about. Define the word you're arguing over first.
The problem arose when rickless started using the phrase "diminishing returns" to explain the "diminishing marginal utility" phenomena. A simple issue, really, but for those who don't understand BOTH phrases, it can seem like a personal attack.

Everyone in this thread just needs to take a deep breath and chill...


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fomenta

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Senior Member

11-28-2011

ricklessabandon,

Three props for you:
1. for understanding the math and seeing through "no diminishing returns" urban legend.
2. for spending the time explaining the system and trying to point out where people err, despite a almost religious devotion to the no diminishing returns mantra.
3. for keeping both your name and your job title in the same case -- lower case is for ballers bro.


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Arrlaari

Senior Member

11-28-2011

Quote:
Originally Posted by ricklessabandon View Post
...
in this example, our first purchase option looks like:
10 health = 10 ehp
1 armor = 20 ehp
1 armor = 2 cookies
...
let's look at our 101st purchase option with 2000 health and 100 armor:
10 health = 20 ehp
1 armor = 20 ehp
1 armor = 1 cookie
....
let's look at our 201st purchase option with 2000 health and 200 armor:
10 health = 30 ehp
1 armor = 20 ehp
1 armor = 0.66 cookies

and look at that--armor is worth even less after stacking more of it! 'ehp' why have you failed us?!
Because you have confounded returns and costs. The armor is not worth less, it costs more. To be more explicit, when value of the hit points you gave up by applying gold to armor instead of hit points has increased, the opportunity cost of not applying that same gold to hit points has increased.

Your cookies are a ratio: return/opportunity cost. When the denominator increases the fraction decreases, therefore when hit points become more valuable armor is worth fewer cookies.

The difference between diminishing returns and increasing opportunity costs becomes significant when you move on from planning your gold allocation to estimating how tanky you will grow as your total gold income for the game increases.

If armor has "diminishing returns" one expects the EHP per gold function f(g) of a player who puts all their gold into armor to be o(g), i.e. strictly dominated by the linear functions. But in fact it will be Θ(g) - i.e. armor has linear returns on gold invested. A player who perfectly divides their gold between hit points and armor, however, will have an EHP per gold function F(g) which is Θ(g^2), i.e. quadratic returns on gold. Foolish indeed is the man who takes linear returns when quadratic returns are on the table! When allowing for unavoidably imperfect allocation, one reasonably weakens the prediction to O(g^2) EHP growth.

A carry putting gold into their auto-attack chooses between 3 synergistic stats that offer Θ(g) returns: AD, aspd, and crit chance. They also benefit from a single chance to put some gold towards a fourth synergistic Θ(g) stat in the unique passive on Infinity Edge, and so intelligent gold allocation we predict O(g^3) auto-attack growth, increasing to o(g^4) with IEdge.


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ricklessabandon

qa analyst

11-28-2011
4 of 5 Riot Posts

first off and most importantly, nothing in this thread should be considered a personal attack--i haven't taken anything personally, nor was anything i said meant to be taken as such (apologies if anyone feels otherwise). i'm certainly all for being passionate in discussion, but i think this thread might be headed in a heated and non-productive direction.

Quote:
Originally Posted by Eledhan View Post
He's arguing over it because the terminology is WRONG.
again, it looks like people are getting quite agitated over the subject, so i'll make this my last post in this thread since fervor tends to go up to 'dangerous levels' when there's red involved.
disregarding everything previously posted in this thread (by everyone), i'm going to ask/answer some questions in hopes to make my stance clear--make of it what you will.

briefly:
1) assuming 0 armor, how much damage reduction do you gain from purchasing 45 armor?
2) assuming 45 armor, how much damage reduction do you gain from purchasing 45 armor?
3) is the above an example of diminishing returns?
4) why or why not?


here are my answers:
1) ~31%
2) ~17%
3) yes.
4) my understanding of the term 'diminishing returns' is aligned with this quote from wikipedia:
"In economics, diminishing returns (also called diminishing marginal returns) is the decrease in the marginal (per-unit) output of a production process as the amount of a single factor of production is increased, ceteris paribus."
the single factor i am increasing is armor, and its per-unit output (damage reduction in this case) is decreasing.

my assumption about people that use effective health as a system for evaluating defensive purchases is that they would change the first two questions to ask about 'effective health' instead of 'damage reduction' and answer as following:
1) 45%
2) 45%
3) no.
4) using the same definition of diminishing returns, 'no' because the per-unit output (effective health in this case) is the same.

this is why i've said repeatedly that the topic is silly, and that it's a wording issue.
if i'm mistaken, and people that use 'ehp' would not alter the questions (giving the same answers to 1 and 2, but would answer 'no' to number 3) i'd actually be interested to read the explanation for number 4.

(apologies for any typos--posted during lunch)


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ricklessabandon

qa analyst

11-28-2011
5 of 5 Riot Posts

Quote:
Originally Posted by Arrlaari View Post
Your cookies are a ratio: return/opportunity cost. When the denominator increases the fraction decreases, therefore when hit points become more valuable armor is worth fewer cookies.
i certainly concede this point--the cookie example was misleading.
when discussing 'effective health gains' there aren't legitimate diminishing returns on mitigation.

whenever talking about mitigation in general though, there are diminishing returns--my stance on which is explained in the post above.


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Stimraug

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Senior Member

11-28-2011

Quote:
Originally Posted by Warrition View Post
AS and AD do in fact have diminishing returns, from this perspective -- and there's nothing incorrect about that; Tryndamere players know this, which is why you don't see good Tryndameres with 5 bloodthirsters, despite it having the highest AD in the game.
AS and AD do not have diminishing returns, not in *ANY* perspective. A completely different subject are the economical terms such as marginal diminishing returns etc. Contrary to what someone posted above, this is NOT a question of semantics. This all started (to me) when Morello stated in a patch preview some weeks ago that the more armor you remove from an enemy, the more effective the penetration/reduction is. THAT is incorrect, THAT is a lie, THAT is confusing everyone and THAT is creating these threads of nonsense where sheep follow red posts and upvote them and hop on the lick-a-red-train. He never corrected it, even if I bumped my thread for weeks.

When I was talking about "Tryndamere", I was referring to the Riot president. The reason why you do not see Tryndameres using 5 bloodthirsters is because AS, ArPen, Crit Chance, and Crit Damage bolster his DPS more than just pure damage at some point. And the *REASONS* behind that are NOT some imaginary diminishing returns but rather the gold optimization, as a competent, educated Arrlaari said. Judging by the continuous rehashing and arguing over things that have been proven and settled time and time again, I'm not sure if many here can actually understand those simple functions.

Quote:
Originally Posted by Warrition View Post
rickless' perspective is both realistic and meaningful in the context of League of Legends. To put it simply, as you purchase more and more armor, there comes a point where your survivability would be more benefited by purchasing health; this is inarguable. Even though each point in armor increases your EHP by the same amount, it eventually becomes a better investment to purchase health.
No. The perspective is not meaningful, in any respect or context of LoL. Have you not read *anything* that has been said here? "To put it simply"??? PLEASE. *Of course* you have to balance the purchasing of resistances and HP, but it is NOT because of any diminishing returns, but rather, AGAIN, the gold optimization issue, which has been explained several times! So many posters in this thread just continue to mix gold optimization with mathematical formulas again and again and again.

Quote:
Originally Posted by Warrition View Post
In the end, both sides are "correct" from a certain perspective, and both sides agree that a balance of armor and health is most effective.
No, this is not a stalemate. There was never an argument about a balance of armor and HP not being most effective. I even gave a simple easily memorized formula in my own post to optimize your resistances / HP ratio, in regards to gold optimization. It is wrong to say that resistances have diminishing returns.

Arrlaari, I appreciate that you brought your educated facts into the discussion. I do not have a degree in economics, and so I could only bring my own calculations and reasoning with me. I'm sure that in America professional talk is more convincing than pure sense.

I also want to add that while it is important to define the term, I'm sure it was very clearly defined when we were talking about the subject of penetrating/reducing someone's resistances, and whether more pen/reduct is increasingly more valuable to the attacker, as Morello incorrectly stated.

Rickless.
Quote:
Originally Posted by ricklessabandon View Post
the cookie example was misleading.
when discussing 'effective health gains' there aren't legitimate diminishing returns on mitigation.
What a surprise, I guess you beat Morello to it.

Quote:
Originally Posted by ricklessabandon View Post
i'm certainly all for being passionate in discussion, but i think this thread might be headed in a heated and non-productive direction.

--

again, it looks like people are getting quite agitated over the subject, so i'll make this my last post in this thread since fervor tends to go up to 'dangerous levels' when there's red involved.
This thread is conveniently heated to inspire productive discussion. But then again, we all have our ways of backing away from a discussion with dignity, whatever floats your boat.

I'd answer your questions, just for fun, if it wasn't the fifteenth time I would have to do it. You can play with terms and definitions as much as you wish, but we were clearly talking about whether buying additional resistances has diminishing returns. No, you cannot evade the facts by digging up different definitions from the wikipedia, the definition was already included in the context of these threads and posts. Also, you are *Still* talking about the dmg reduction percentage, which you *Still* confuse with survivability.

The topic is not silly,
the topic is not a wording question. This becomes clear if someone actually read all that has been written and proven.

EDIT: Downvotes for me? Heck, now I understand better how Bush got to presidency. You guys don't know what to vote.