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

Kalaveras

Senior Member

This helps a lot, since everytime I play tanks I don't feel like doing it properly, they are my last choice. Now I know what to do, thx

Stimraug

Senior Member

Quote:
Lorifel:
Exactly. Because 2 + 2 = 100 in bijective numeration. Or 11 in trijective numeration. It all depends on the numeral system, bro! =)

Yeah, you got me there. I don't even know what kind of numerical system some of these guys have in their heads.

Quote:
FORTRAN 77:

Say you have 1000 HP and 100 armor, then increasing HP by 1 is a .1% increase in EHP while increasing armor by 1 is a .5% increase in EHP. The 'diminishing returns' will be that increasing armor by 1 again will be a slightly smaller percent increase. By the time you have 150 armor, another point of armor would only be a .4% increase.
I have defined returns in a way that armor does have diminishing returns

Quote:
ricklessabandon:

there aren't legitimate diminishing returns on mitigation.

Oooh, you just contradicted a red, wuzzah.

Okay, on to the matter now, this time seriously...

You just defined that the damage resistance percentage has smaller returns with every additional point of resistance. Talking about missing the point, we've discussed for a long time about *survivability* here. For the hundreth time, when you buy resistances, you will gain as much survivability as you got from the last point of resistance. Getting more resistances or penetrating more of the enemy's resistance is equally powerful and valuable for every added/subtracted point of resistance. There is nothing meaningful gained in taking a number that increases slower and slower every time you add something to another number. Period.

Quote:
Asgrim:
Level 1. Buy a BF Sword or a Zeal, which gives a larger return? BF Sword.

No. The bigger return depends on the current AD, ASPD, Crit Chance and Crit Damage. With very high current AD and a low ASPD the Zeal might return more.

Quote:
Asgrim:
Just want to point out, no one brought gold optimization into this.
...
Mixing stats has absolutely nothing to do with gold optimization.
...
EDIT 3: WHOH! I thought of an even simpler way to explain it!
Now we have a BF Sword. What do we buy next? Well, mathematically it would still be a BF Sword, so let's go with that. Oh ****! Were above 125 AD! What do we buy next?

Oh wai- all of a sudden attack speed would give us more DPS then more damage. Mathematically, given NON-DIMINISHING returns, the return of a SINGLE STAT (in this case, AD) would remain most important.

But it doesn't! The return given from AS has suddenly increased, and the return for more damage, while metrically the same, has decreased!

First of all, the return given from AS increases as AD increases, yes, but the return from more AD does not decrease. It only decreases in respect to, for example, AS, AND when you factor in gold optimization. The stat itself gives the exact same benefit.

Quote:
Asgrim:

2. AD carry has 200 damage. Increase to 260, or attack 30% faster? 260 damage does more only if a fight lasts less then 6 seconds (assuming a starting 1.0 attack speed).

Even if the fight lasted for 10 seconds or 500 seconds the damage would stay the same.
6 second-long fight:
200 damage, 1.300 ASPD = 1.3 * 6 * 200 = 1560 damage
260 damage, 1.000 ASPD = 1.0 * 6 * 260 = 1560 damage

10 second-long fight:
200 damage, 1.300 ASPD = 1.3 * 10 * 200 = 2600 damage
260 damage, 1.000 ASPD = 1.0 * 10 * 260 = 2600 damage

500 second-long fight:
200 damage, 1.300 ASPD = 1.3 * 500 * 200 = 130 000 damage
260 damage, 1.000 ASPD = 1.0 * 500 * 260 = 130 000 damage

You seem to have difficulties even grasping such a simple term as DPS.

Quote:
Asgrim:

Just for a last, humiliating example for Stimraug:

"However, the ingame situation is far more complex of course, and because of this a much higher AD is many times more beneficial"

If this WAS the only thing that mattered, people would run 6 Bloodthirsters with 800-900 damage. They would also never get there, because they would move 60% slower then everyone else, have no survivability, and ultimately do MUCH LESS damage then a carry who built for crit, some damage, attack speed, AND pen.

Maybe you should read my whole sentence again, and better yet, quote it fully. I clearly meant, that when my calculations suggested that you should start buying Crit Chance after getting 125 AD, you should use discretion when following this, because ingame the situations are much more complex than just simple calculations, and there are a plethora of situations where a higher AD than 125 is more optimal than getting Crit Chance instead. I never meant anything your demeaning rant tries to communicate to the reader.

Quote:
Asgrim:

I don't know if I put that simply enough to prove people wrong, but I hope so.

Actually you put it quite ineffectively and with poor construct.

Quote:
Asgrim:

And I will calmly explain why gold optimization does not factor into this at all.
...
WHAT!? It's DIMINISHED!? AHHHHHHHH!!!! THE WORLD IS CRUMBLING!!!!!! AHHHHHHH!!!!!

Self-explanatory.

Silent Reaper

Senior Member

Quote:
asgrim:
the only exception here is again, if their carry has purchased penetration. Because no one likes to be penetrated.

LoL

Asgrim

Member

Quote:
Stimraug:
Yeah, you got me there. I don't even know what kind of numerical system some of these guys have in their heads.

Oooh, you just contradicted a red, wuzzah.

Okay, on to the matter now, this time seriously...

You just defined that the damage resistance percentage has smaller returns with every additional point of resistance. Talking about missing the point, we've discussed for a long time about *survivability* here. For the hundreth time, when you buy resistances, you will gain as much survivability as you got from the last point of resistance. Getting more resistances or penetrating more of the enemy's resistance is equally powerful and valuable for every added/subtracted point of resistance. There is nothing meaningful gained in taking a number that increases slower and slower every time you add something to another number. Period.

No. The bigger return depends on the current AD, ASPD, Crit Chance and Crit Damage. With very high current AD and a low ASPD the Zeal might return more.

First of all, the return given from AS increases as AD increases, yes, but the return from more AD does not decrease. It only decreases in respect to, for example, AS, AND when you factor in gold optimization. The stat itself gives the exact same benefit.

Even if the fight lasted for 10 seconds or 500 seconds the damage would stay the same.
6 second-long fight:
200 damage, 1.300 ASPD = 1.3 * 6 * 200 = 1560 damage
260 damage, 1.000 ASPD = 1.0 * 6 * 260 = 1560 damage

10 second-long fight:
200 damage, 1.300 ASPD = 1.3 * 10 * 200 = 2600 damage
260 damage, 1.000 ASPD = 1.0 * 10 * 260 = 2600 damage

500 second-long fight:
200 damage, 1.300 ASPD = 1.3 * 500 * 200 = 130 000 damage
260 damage, 1.000 ASPD = 1.0 * 500 * 260 = 130 000 damage

You seem to have difficulties even grasping such a simple term as DPS.

Maybe you should read my whole sentence again, and better yet, quote it fully. I clearly meant, that when my calculations suggested that you should start buying Crit Chance after getting 125 AD, you should use discretion when following this, because ingame the situations are much more complex than just simple calculations, and there are a plethora of situations where a higher AD than 125 is more optimal than getting Crit Chance instead. I never meant anything your demeaning rant tries to communicate to the reader.

Actually you put it quite ineffectively and with poor construct.

Self-explanatory.

You just ignored one of the strongest arguments I made entirely. If you are agreeing that it becomes more effective to diversify your items into different items, you are agreeing that there are diminishing returns.

The entire point of a carry is to deal damage. Anything that does that, is their goal. According to you, there are no diminishing returns on ANY stat. Which means, it behooves AD carries to purchase ONLY damage, as it will continually give the largest increase of total DPS to a carry.

Except that's not true. Again, while the metric value increase stays the same, the end result is NOT an increase to DPS in comparison to purchasing attack speed and other such stats along with damage.

That means damage, along with all stats in the game, provide diminishing returns. That's why it's important to diversify, in order to keep the cap on the returns climbing. All the stats have a correlation to each for this to happen, and they all have diminished returns without it.

Look, your mixing up the target of your argument and invalidating it. You agree stats need to be diversified, you agree that mixing stats to keep the return cap rising is necessary, but then you say the returns do not diminish, EVEN THOUGH YOU JUST SAID FOCUSING ONE STAT GIVES YOU LESS DAMAGE. Half your argument, you focus on the metric values and how they do not diminish (true), and the second half you agree you need to diversify to max DPS (true) but you keep ignoring the correlation, the REASON for the correlation, which is diminishing returns.

I understand what your saying about gold optimization, but I'm disagreeing that it has anything to do with this, because you CAN'T get the same about of DPS by building pure damage per cost then you can by building diversely. Maybe if there was no 6 item limit, but there is. And with a 6 item limit, my bloodthirster analogy still holds, as you CANNOT build unlimited items. Plus, as other people and yourself has demonstrated, when worked mathematically, diverse builds have more DPS. And it has no relation to cost.

Your "no diminishing returns, gold optimization" argument only works outside the constraint of limited items, and no stat correlation. Unfortunately, there are constraints, and all the stats have a diminishing softcap that correlates with each other.

IS1281a2aa64f651d96c2ca

Senior Member

Quote:
Oooh, you just contradicted a red, wuzzah.

I don't know what's more amusing here. The fact that you think I care whether I contradict a red, or the fact that you took shamelessly took his statement out of context.

Quote:
Okay, on to the matter now, this time seriously...

You just defined that the damage resistance percentage has smaller returns with every additional point of resistance. Talking about missing the point, we've discussed for a long time about *survivability* here. For the hundreth time, when you buy resistances, you will gain as much survivability as you got from the last point of resistance. Getting more resistances or penetrating more of the enemy's resistance is equally powerful and valuable for every added/subtracted point of resistance.

-What if I tell you that you can have a consistent system in which the sum of a triangle's angles can be greater than π?

-For the hundredth time, the sum of a triangle's angles is exactly π.

Quote:
There is nothing meaningful gained in taking a number that increases slower and slower every time you add something to another number. Period.

There is meaning and I just showed it to you. Define diminishing returns in terms of % increase. Then, when you choose to assign value to HP and armor, you will be able to immediately conclude that mixing stats is optimal for max survivability, because of diminishing returns. You will say that you gain a particular +%EHP/gold for the first point of armor you add. Your +%EHP/gold from each additional point of armor will decrease due to diminishing returns as defined above. Hence, at some point, your +%EHP/gold for extra armor will be less than your +%EHP/gold for extra HP.

If you just say that there aren't diminishing returns because every point of armor leads to the same increase in EHP (at a constant HP), you cannot make the same conclusion as above. Once you assign gold prices to HP and armor, this definition of diminishing returns will yield no new corollaries. It's only with additional calculation that you come to the conclusion that at some point it's better to switch. You could have just as well started by saying "I don't care whether HP and armor have diminishing returns" or "I don't know whether HP and armor have diminishing returns" and arrived at the same conclusion regardless.

So the obvious conclusion here is that when it comes to the question of optimizing survivability, the way you define diminishing returns is irrelevant, which is what rickless tried explaining before. It's just basic logic. If A&B --> C and ¬A&B --> C then A is irrelevant to C.

tl;dr: "What's in a name? That which we call a rose by any other name would smell as sweet."

Texas Snyper

Senior Member

Quote:
Asgrim:
You just ignored one of the strongest arguments I made entirely. If you are agreeing that it becomes more effective to diversify your items into different items, you are agreeing that there are diminishing returns.

The entire point of a carry is to deal damage. Anything that does that, is their goal. According to you, there are no diminishing returns on ANY stat. Which means, it behooves AD carries to purchase ONLY damage, as it will continually give the largest increase of total DPS to a carry.

Except that's not true. Again, while the metric value increase stays the same, the end result is NOT an increase to DPS in comparison to purchasing attack speed and other such stats along with damage.

That means damage, along with all stats in the game, provide diminishing returns. That's why it's important to diversify, in order to keep the cap on the returns climbing. All the stats have a correlation to each for this to happen, and they all have diminished returns without it.

Look, your mixing up the target of your argument and invalidating it. You agree stats need to be diversified, you agree that mixing stats to keep the return cap rising is necessary, but then you say the returns do not diminish, EVEN THOUGH YOU JUST SAID FOCUSING ONE STAT GIVES YOU LESS DAMAGE. Half your argument, you focus on the metric values and how they do not diminish (true), and the second half you agree you need to diversify to max DPS (true) but you keep ignoring the correlation, the REASON for the correlation, which is diminishing returns.

I understand what your saying about gold optimization, but I'm disagreeing that it has anything to do with this, because you CAN'T get the same about of DPS by building pure damage per cost then you can by building diversely. Maybe if there was no 6 item limit, but there is. And with a 6 item limit, my bloodthirster analogy still holds, as you CANNOT build unlimited items. Plus, as other people and yourself has demonstrated, when worked mathematically, diverse builds have more DPS. And it has no relation to cost.

Your "no diminishing returns, gold optimization" argument only works outside the constraint of limited items, and no stat correlation. Unfortunately, there are constraints, and all the stats have a diminishing softcap that correlates with each other.

You are confusing diminishing returns with min/max-ing and optimizing stat values. By definition diminishing returns is when you are getting LESS bang for the same buck. Buying 1 AD will give you 1 damage, period.
Buying 1crit chanc % gives you just that, period.
Buying 1 HP gives you 1 HP, period.
Buying 1 armor gives you 6HP against physical, period. (ignoring %pen)
Buying 1 MR gives you 6HP against magic, period. (ignoring %pen)

No stat in the game gives you less of what you are buying when you buy more of it. You obviously need a quick run down on what DR really is so I'll use a quick WoW example.

(not actual in game values but they have the concept im using)
Tank gems his armor with a 20 dodge rating gem and gets X dodge% out of it.
Tank then gems his armor with another 20 dodge rating gem and gets Y dodge% out of it.
Y < X by a small amount
Each 20 dodge rating gem will give less dodge% than the last.

That is diminishing returns. You are describing optimal stat ratios and calling it diminishing returns. Two TOTALLY different things.

Texas Snyper

Senior Member

Quote:
FORTRAN 77:
There is meaning and I just showed it to you. Define diminishing returns in terms of % increase. Then, when you choose to assign value to HP and armor, you will be able to immediately conclude that mixing stats is optimal for max survivability, because of diminishing returns. You will say that you gain a particular +%EHP/gold for the first point of armor you add. Your +%EHP/gold from each additional point of armor will decrease due to diminishing returns as defined above. Hence, at some point, your +%EHP/gold for extra armor will be less than your +%EHP/gold for extra HP.

That is not diminishing returns, that is min/maxing stat ratios. You are getting the same absolute value regardless of how much you already have. Diminishing returns is when you are getting reduced absolute values at the same cost. Maximizing your gold spent by min/maxing is NOT diminishing returns.

Quote:

If you just say that there aren't diminishing returns because every point of armor leads to the same increase in EHP (at a constant HP), you cannot make the same conclusion as above. Once you assign gold prices to HP and armor, this definition of diminishing returns will yield no new corollaries. It's only with additional calculation that you come to the conclusion that at some point it's better to switch. You could have just as well started by saying "I don't care whether HP and armor have diminishing returns" or "I don't know whether HP and armor have diminishing returns" and arrived at the same conclusion regardless.

If you assign a gold value to HP and to armor, you will get the same amount of HP and armor for its assigned gold value, regardless of how much HP or armor, respectively, you have. Your 6th Giant's Belt does NOT give you less HP than your first Giant's Belt.

Quote:
So the obvious conclusion here is that when it comes to the question of optimizing survivability, the way you define diminishing returns is irrelevant, which is what rickless tried explaining before. It's just basic logic. If A&B --> C and ¬A&B --> C then A is irrelevant to C.

tl;dr: "What's in a name? That which we call a rose by any other name would smell as sweet."

So if I start calling your chair a dog, you'll know exactly what I'm talking about? We assign names to objects to identify and communicate. It is true the names are arbitrary but they are arbitrarily assigned for effective communication. If we start mislabeling things, communications start to break down and the purpose of the name becomes moot.

Asgrim

Member

Quote:
Texas Snyper:
You are confusing diminishing returns with min/max-ing and optimizing stat values. By definition diminishing returns is when you are getting LESS bang for the same buck. Buying 1 AD will give you 1 damage, period.
Buying 1crit chanc % gives you just that, period.
Buying 1 HP gives you 1 HP, period.
Buying 1 armor gives you 6HP against physical, period. (ignoring %pen)
Buying 1 MR gives you 6HP against magic, period. (ignoring %pen)

No stat in the game gives you less of what you are buying when you buy more of it. You obviously need a quick run down on what DR really is so I'll use a quick WoW example.

(not actual in game values but they have the concept im using)
Tank gems his armor with a 20 dodge rating gem and gets X dodge% out of it.
Tank then gems his armor with another 20 dodge rating gem and gets Y dodge% out of it.
Y < X by a small amount
Each 20 dodge rating gem will give less dodge% than the last.

That is diminishing returns. You are describing optimal stat ratios and calling it diminishing returns. Two TOTALLY different things.

"By definition diminishing returns is when you are getting LESS bang for the same buck"

And this is where your contradictory and clearly incorrect argument shines through.

When you start playing a carry, you get damage first, as it provides the greatest return. By YOUR logic, we would ONLY buy damage for the REST OF THE GAME (hence my bloodthirster analogy) and we would be the MOST powerful carry you can be.

Except that's clearly wrong. At some point, it becomes painfully clear that purchasing other attack related stats leads to a higher overall increase of damage, then just pure AD. And that's the same whether your talking about maxing only attack speed, maxing only pen, or anything else.

So clearly, while the METRIC VALUE of gaining stats remains the same, the RETURN of a SINGLE stat as raised by itself, CLEARLY does not return the optimal damage, while other stats will.

The value of gaining that stat has lessened.

Diminishing returns, by every definition ever posted.

And even if we go by your WoW example, that's exactly how Armor and Magic Resist work. It hits softcaps where each point of it gives less % reduction. You can argue that the METRIC VALUE remains the same, but the percentage of reduction given does not.

And NO, this is NOT mixing optimal ratios. The entire POINT is making optimal ratios to max TOTAL DPS. No stat is alone, the entire array of offensive stats add to it. And if ONE STAT becomes LESS viable for overall DPS output while it WAS viable at some point in time before, that means the RETURN of that stat in regards to our DPS, has DECREASED.

This is not "mixing optimal stat ratios" this is playing ****ing LoL. That's the entire POINT. The ONLY stat we care about, is TOTAL DPS. There are multiple stats that contribute to it, and they have DIMINISHING TOTAL RETURNS in regards to TOTAL DPS when stacked.

I don't understand WHY the larger picture is so hard for you guys to understand, when everyone else can see its there.

Can't see the forest but for the trees.

Texas Snyper

Senior Member

Quote:
Asgrim:
"By definition diminishing returns is when you are getting LESS bang for the same buck"

And this is where your contradictory and clearly incorrect argument shines through.

When you start playing a carry, you get damage first, as it provides the greatest return. By YOUR logic, we would ONLY buy damage for the REST OF THE GAME (hence my bloodthirster analogy) and we would be the MOST powerful carry you can be.

Except that's clearly wrong. At some point, it becomes painfully clear that purchasing other attack related stats leads to a higher overall increase of damage, then just pure AD. And that's the same whether your talking about maxing only attack speed, maxing only pen, or anything else.

So clearly, while the METRIC VALUE of gaining stats remains the same, the RETURN of a SINGLE stat as raised by itself, CLEARLY does not return the optimal damage, while other stats will.

The value of gaining that stat has lessened.

Diminishing returns, by every definition ever posted.

And even if we go by your WoW example, that's exactly how Armor and Magic Resist work. It hits softcaps where each point of it gives less % reduction. You can argue that the METRIC VALUE remains the same, but the percentage of reduction given does not.

And NO, this is NOT mixing optimal ratios. The entire POINT is making optimal ratios to max TOTAL DPS. No stat is alone, the entire array of offensive stats add to it. And if ONE STAT becomes LESS viable for overall DPS output while it WAS viable at some point in time before, that means the RETURN of that stat in regards to our DPS, has DECREASED.

This is not "mixing optimal stat ratios" this is playing ****ing LoL. That's the entire POINT. The ONLY stat we care about, is TOTAL DPS. There are multiple stats that contribute to it, and they have DIMINISHING TOTAL RETURNS in regards to TOTAL DPS when stacked.

I don't understand WHY the larger picture is so hard for you guys to understand, when everyone else can see its there.

Can't see the forest but for the trees.

My statement stands, please illustrate an example for me that when under any situation (excluding external causes) you buy a BF Sword and get less AD than is stated on the item? You buy AS and crit because the stats multiply off each other, not because you are getting less AD as you stack it.

You are arguing weighted values, which is not diminishing returns.
I am arguing absolute values, where there are no diminishing returns.

The gold value of a stat may reduce compared to other stats, but that is optimization. You are not getting any less of those values by buying more of it. My WoW example is a great example of NOT how armor and MR work. 1 armor/MR will give you 6 HP against its respective damage type if you have 10 armor/MR or 500 armor/MR. The gain is linear and does not reduce.

You are arguing the "larger picture" of an entirely different argument. I am arguing that you are mislabeling it incorrectly. You talk about diminshing values and call it diminishing returns. Reduced gold value compared to other stats is one thing, diminishing returns from stacking a stat is a totally different beast.

The law of diminishing returns (also law of diminishing marginal returns or law of increasing relative cost) states that in all productive processes, adding more of one factor of production, while holding all others constant, will at some point yield lower per-unit returns. -Wikipedia

The principle that further inputs into a system produce ever lower increases in outputs. Any extra input will not produce an equal or worthwhile return. Thus, while early applications of fertilizer may increase yields, further applications will not see a corresponding rise in output, and even further applications may actually damage the crop, as excessive fertilizer can burn plant tissue. - Oxford Dictionary of Geography via Answer.com

diminishing returns, law of, in economics, law stating that if one factor of production is increased while the others remain constant, the overall returns will relatively decrease after a certain point. Thus, for example, if more and more laborers are added to harvest a wheat field, at some point each additional laborer will add relatively less output than his predecessor did, simply because he has less and less of the fixed amount of land to work with. The principle, first thought to apply only to agriculture, was later accepted as an economic law underlying all productive enterprise. The point at which the law begins to operate is difficult to ascertain, as it varies with improved production technique and other factors. Anticipated by Anne Robert Jacques Turgot and implied by Thomas Malthus in his Essay on the Principle of Population (1798), the law first came under examination during the discussions in England on free trade and the corn laws. It is also called the law of decreasing returns and the law of variable proportions. -Columbia Encyclopedia via Answer.com

An economic law propounded by David Ricardo, also called the law of diminishing marginal returns. It expresses a relationship between input and output, stating that adding units of any one input (labor, capital, etc.) to fixed amounts of the others will yield successively smaller increments of output. -Dictionary of Cultural Literacy: Economics via Answer.com

I found these with a quick 20 sec google search. All of these support and better define my earlier "by definition" statement, and with better wording. Now I challenge you to find some resources that define diminishing returns under your definition.

Asgrim

Member

Quote:
Texas Snyper:
My statement stands, please illustrate an example for me that when under any situation (excluding external causes) you buy a BF Sword and get less AD than is stated on the item? You buy AS and crit because the stats multiply off each other, not because you are getting less AD as you stack it.

You are arguing weighted values, which is not diminishing returns.
I am arguing absolute values, where there are no diminishing returns.

The gold value of a stat may reduce compared to other stats, but that is optimization. You are not getting any less of those values by buying more of it. My WoW example is a great example of NOT how armor and MR work. 1 armor/MR will give you 6 HP against its respective damage type if you have 10 armor/MR or 500 armor/MR. The gain is linear and does not reduce.

You are arguing the "larger picture" of an entirely different argument. I am arguing that you are mislabeling it incorrectly. You talk about diminshing values and call it diminishing returns. Reduced gold value compared to other stats is one thing, diminishing returns from stacking a stat is a totally different beast.

The law of diminishing returns (also law of diminishing marginal returns or law of increasing relative cost) states that in all productive processes, adding more of one factor of production, while holding all others constant, will at some point yield lower per-unit returns. -Wikipedia

The principle that further inputs into a system produce ever lower increases in outputs. Any extra input will not produce an equal or worthwhile return. Thus, while early applications of fertilizer may increase yields, further applications will not see a corresponding rise in output, and even further applications may actually damage the crop, as excessive fertilizer can burn plant tissue. - Oxford Dictionary of Geography via Answer.com

diminishing returns, law of, in economics, law stating that if one factor of production is increased while the others remain constant, the overall returns will relatively decrease after a certain point. Thus, for example, if more and more laborers are added to harvest a wheat field, at some point each additional laborer will add relatively less output than his predecessor did, simply because he has less and less of the fixed amount of land to work with. The principle, first thought to apply only to agriculture, was later accepted as an economic law underlying all productive enterprise. The point at which the law begins to operate is difficult to ascertain, as it varies with improved production technique and other factors. Anticipated by Anne Robert Jacques Turgot and implied by Thomas Malthus in his Essay on the Principle of Population (1798), the law first came under examination during the discussions in England on free trade and the corn laws. It is also called the law of decreasing returns and the law of variable proportions. -Columbia Encyclopedia via Answer.com

An economic law propounded by David Ricardo, also called the law of diminishing marginal returns. It expresses a relationship between input and output, stating that adding units of any one input (labor, capital, etc.) to fixed amounts of the others will yield successively smaller increments of output. -Dictionary of Cultural Literacy: Economics via Answer.com

I found these with a quick 20 sec google search. All of these support and better define my earlier "by definition" statement, and with better wording. Now I challenge you to find some resources that define diminishing returns under your definition.

Thank you, for winning my argument for me. Your definition is exactly what I've been stating.

Let me put this in the very terms you brought to this:
Our net value is TDPS (TDPS). Were going to call this our net value, which we obviously want to grow.

Then, were going to assign to that net value the subsidiary values of A, B, C. Which stat in LoL we assign these too (AD, AS, Pen) is irrelevant, so I won't bother to define them, just understand that these are what they represent.

Now, our net value TDPS is a multiplicative solution of values A, B, and C. In League of Legends, the net value increases MORE when EACH VALUE has been increased in some manner, over only one value.

Each value (while metrically rising the same amount no matter how much you buy) provides a LESSER return in total net value when the other values are lower, or ignored completely, in comparison with raising them together.

The value of that STATISTIC remains the same, but it has a DIMINISHED RETURN in regards to out total value, and more diminished the more it increases. As has been said before, you end up with this example: you increase from 10 damage to 20. You have doubled your damage, which is a huge increase (100% increase!). You increase from 1 million damage to 1 million and ten damage, which is the tiniest percentage of increase (lots of .0's in this percentage), and does NOT effect overall value in as meaningful a way as it DOUBLING. Even if the METRIC VALUE increases the same amount, there is a CLEARLY lesser RETURN to the overall DPS value.

That example is exactly your definition.