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

Fox P McCloud

Senior Member

Quote:
Tryptomine:
Because HP and AR multiply to get the EHP. So the Armor he already has is making that new HP he's buying more valuable.

I know that, but he keeps increasing the EHP value of flat HP, which is what I'm having problems seeing why.

Arance

Senior Member

Quote:
Fox P McCloud:
I know that, but he keeps increasing the EHP value of flat HP, which is what I'm having problems seeing why.

1000 HP x 0 AR = 1000 EHP

1010 HP x 0 AR = 1010 EHP

1000 HP x 100 AR = 2000 EHP

1010 HP x 100 AR = 2020 EHP

By buying that 10 HP he added 20 extra EHP because of his armor. HP is not a flat value when calculating EHP. Savvy?

Reiver

Senior Member

Quote:
Fox P McCloud:
I know that, but he keeps increasing the EHP value of flat HP, which is what I'm having problems seeing why.

Because if you have 100 armor, 10 base HP is worth 20 EHP, at 200 armor it's worth 30 EHP

I still disagree that it becomes less effective, it remains equally effective, but it's making another stat progressively more effective, which confuses the whole thing since the stats are multiplicative against each other

It doesn't become less effective, health becomes more effective

Joru

Senior Member

Quote:
ricklessabandon:
i understand the common argument. the problem with it is that it's like saying that i'm going to convert 'mitigation' into 'kittens' and that there are no diminishing returns for that conversion. the oversight is that it doesn't matter that there aren't diminishing returns in that isolated kitten vacuum because once you start reintroduce 'kittens' to all the other factors that mitigation was involved with, 'kittens' would then have diminishing returns again.

and, you know, i'm still going to buy whichever items are most valuable holistically.

Measuring mitigation gained with each successive point of armor in percentage points isn't much less meaningless than measuring it in kittens, because "percentage points" are not a consistent, linear unit of measurement. You're reading the whole situation completely wrong.

Let's say I have 1000 health and 0% mitigation from armor. I spend X gold increasing my percentage mitigation from 0 to 1. It now takes 1% more damage to kill me than it did before my purchase. Big deal. That's probably not even a whole attack.

Now let's say that, hypothetically, I have 98% mitigation from armor. I spend Y gold increasing my percentage mitigation from 98 to 99%. The amount of damage it takes to kill me has DOUBLED since before I made that purchase. And it already took a ton to bring me down. So that one percent increase represents possibly hundreds of additional attacks needed to bring me down.

Now I spend Z gold increasing my mitigation from 99% to 100%. I am now totally immune to physical damage.

The fact that Y is many hundreds of times larger than X, and Z is infinity, is not indicative of armor having less-than-linear benefits when you stack it. It's representative of the fact that percentages are not a linear unit of measurement. The 99th percentage point takes hundreds or thousands of times more gold to earn than the first because it represents hundreds or thousands of times more durability than the first. This is true at all levels: the 50th percentage point is also worth more than the first. So is the 30th, and the third, and the second. All of this applies cumulatively when you do the calculations, and it makes the "percentage mitigation" number on your character sheet effectively meaningless by itself if you want to really understand the mechanics at work.

If my base damage is 100, and I spend 1650 gold on a B.F. Sword, my damage increases to 145. That's a 45% increase. If I then spend another 1650 gold on a second B.F. Sword, my damage increases from 145 to 190, which is a 31% increase. Attack damage doesn't have diminishing returns; each additional sword provides the same 45 damage: a linear benefit. It's just that you're converting the gain into percentage points, which are not linear units.

In practice, the more armor you have, the better health is by comparison, but that's not because gold spent on armor scales less-than-linearly with gold spent previously on armor. It's because gold spent on health scales more-than-linearly with gold spent on armor. There are no diminishing returns on armor, just increasing returns on health when your armor value is high.

Killzerz

Senior Member

The other thing people need to realize is that tanks need to be a threat, unless you are a very, VERY specific character in-game. You need people to hit you, or if they don't you need to be able to take people down. Even if I can mitigate all damage to 10% of its value and have 5000 health while doing so, it matters little if I can't either A) provide massive utility even though I do little damage (Malphite against AD carries, Rammus against AD carries, Amumu) or B) provide good damage while being tanky so they stay off my carries (Udyr, Nocturne, Wukong). Never build straight resistances, always build either some decent damage (Wit's end says hi as well as Atmogs) or build utility (Shurelia's Reverie and Randuin's Omen say hi in this category).

Salganos

Senior Member

Quote:
H911Reiver:
Because if you have 100 armor, 10 base HP is worth 20 EHP, at 200 armor it's worth 30 EHP

I still disagree that it becomes less effective, it remains equally effective, but it's making another stat progressively more effective, which confuses the whole thing since the stats are multiplicative against each other

It doesn't become less effective, health becomes more effective

And because health becomes more effective, you get diminishing returns on the comparative value, and thus your efficiency.

[In the EHP model] I best understand it as "diminishing" returns when viewing the EHP gained as a percentage of one's current EHP.

Most any flat addition becomes less and less impressive in percentages with every iteration, but does not affect the percent value of adding to a multiplier (and vice versa, of course).

Viro Melchior

Recruiter

Quote:
ricklessabandon:
it's a wording thing. it's silly.

even within an 'ehp' system there are diminishing returns if you do all of the math, which is why health and mitigation take turns being more valuable.

we can even use a common example:
-a champion has 2000 health, and 0 armor.
-for the sake of math, we'll say that 10 health and 1 armor have the exact same gold cost.
-since we're examining the potential of diminishing returns on armor, we'll use the '10 health' purchase as a basis of comparison for effectiveness. we'll call the effectiveness gained from purchasing 10 health '1 cookie'.

in this example, our first purchase option looks like:
10 health = 10 ehp
1 armor = 20 ehp

cool, so given a choice between 1 cookie or 2 cookies for the same price, we want 2 cookies so we'll purchase armor.
since armor isn't supposed to have diminishing returns according to the 'ehp' model, we'll make this decision 99 times more.

let's look at our 101st purchase option with 2000 health and 100 armor:
10 health = 20 ehp
1 armor = 20 ehp

so, um, weird. it looks like purchasing armor would be half as effective as it was before... that doesn't make any sense if we're using 'ehp' but we'll pick armor again since it doesn't have any diminishing returns in that model.

let's look at our 201st purchase option with 2000 health and 200 armor:
10 health = 30 ehp
1 armor = 20 ehp

and look at that--armor is worth even less after stacking more of it! 'ehp' why have you failed us?!

so, it's pretty obvious that whether you're using 'ehp' or the actual numbers being used in league of legends, armor becomes less effective as you stack it.
you never see that in a post defending 'ehp' though because all they're focused on is the '1 armor = 1%' bit which is only one part of what needs to be evaluated.

To get a stronger look at the ACTUAL diminishing returns from "1 point of armor":

Going from 10 armor to 11 armor:
10 armor = 9.0909% reduction (suffer 90.909% damage)
11 armor = 9.9099% reduction (suffer 90.090% damage)
11 armor suffers 99.099% as much damage, or a .911% decrease in damage taken.
Going from 200 armor to 201 armor:
200 armor = 66.666% reduction (suffer 33.333% damage)
201 armor = 66.7774086% reduction (suffer 33.2225914% damage)
201 armor suffers 99.667% as much damage, or a .3321% decrease in damage taken.

So by 200 armor, it has gone down by about 2/3 of it's effectiveness.

At the same time, armor and health are impacting each other. So if going from 150 armor to 200 isn't worth it when you have 2000 health, but you pick up a warmogs, suddenly it is going to be worth it to make the 150->200 armor upgrade instead of getting more health.

HOWEVER, another way to look at it that looks more at the big picture...
If you have a pair of champions with 100 armor and 300 armor, both with 2000 health:
100 armor = 50% reduction = 4000 eHP = 2000 bonus eHP.
300 armor = 75% reduction = 8000 eHP = 6000 bonus eHP
100 armor is giving 20 eHP per point of armor.
300 armor is giving 20 eHP per point of armor.

What's that? NO diminishing returns? That's right Kiddos, I have just proven Rickless RIGHT AND WRONG at the same time.
Careful. Don't open the box, as Schrodinger has shown us that as long as we don't actually look, this CAN occur naturally.

So what's going on?
Well, what's actually happening is that while armor IS providing diminishing decreases in damage taken, it actually continues to provide non-diminishing increases in effective HP.
But at the same time, the more damage reduction you have, the bigger a bonus you get from ACTUAL health items.
So its actually not a case of diminishing returns, but rather a case of simple interdependence.

TL; DR
Armor does give diminishing returns, but at the same time, the actual RESULT of those diminishing returns has non-diminishing returns.
But stacking just armor or just MR is still sub-optimal because you get MORE eHP out of health items as your MR/armor increase.

Edit: Downvoted? Can anyone explain WHY they'd downvote this post? Or just hating that it makes you feel stupid?

hollywoodAnimal

Senior Member

Basically what the guy above me said

Stacking armor does not have flat diminishing returns, but comparative diminishing returns.

The marginal benefit of buying resistance is less than the marginal benefit of buying health at a certain point, as well as vice-versa

Spikywarkitten

Senior Member

Ugh, had to post on this because it really bothers me lol. It is not a wording thing. Diminishing return literally means the value you get from something decreases when you have more of it. If you get more movement speed, the amount you actually get from it goes down because of the softcap.

The value of the armor does not go down. IT IS NOT A DIMINISHING RETURN. The value of health increases as you have more armor. That is much different than the actual value of the armor decreasing.

Fox P McCloud

Senior Member

Quote:
Tryptomine:
1000 HP x 0 AR = 1000 EHP

1010 HP x 0 AR = 1010 EHP

1000 HP x 100 AR = 2000 EHP

1010 HP x 100 AR = 2020 EHP

By buying that 10 HP he added 20 extra EHP because of his armor. HP is not a flat value when calculating EHP. Savvy?

Thanks--I get it now; I appreciate it.