How much does Grim Focus mitigation actually provide?

HankTwo · April 2019

kaithuzar wrote: »

HankTwo wrote: »

@muh First of all, lets concentrate on the case were you use this skill purely for the 15% damage mitigation bonus. You can add as much extra mitigations in my example as you want, the outcome will be the same. Equal damage values in both case 2 and 3 but different numbers in case of the 'total mitigation'.

Your math is not wrong per se, but you are taking the wrong conclusions from it. The problem is that you are always comparing it to this 'baseline' you calculate. I'm telling you this baseline shouldn't matter to you. Why should I care how much damage a player would deal to a naked target without any CP and buffs. It doesn't make sense to make comparisons with that case. What's important is how much will I mitigate when I add this skill to my bar compared to how much damage I receive without it. And that's exactly 15%. Heck, the fact that you don't take battlespirit into the equation is pure arbitrariness.

And about the mitigation = extra health and healing received. Please calculate some example scenarios were you add 15% damage mitigation in one case and 17.647% extra health and healing received in another. You can add as many other damage reduction and healing received buffs as you like. Apart from adding oblivion damage, both cases should always end at the same relative amount of health.

General example from me: a player with max health 'm' starts at full health and gets damage by a player with constant dps 'd'. The targeted player already has 2 forms of mitigation (r1 and r2) and 2 boosts to his healing received (b1 and b2). He will heal himself with a constant stream of heals 'h'. How much time 't' will it take until the player dies?
Case 1) added damage mitigation 'r3': [ m / (d * r1 * r2 * r3 - h * b1 * b2) = t ]
Case 2) added health bonus and healing received 'b3': [ m *b3 / (d * r1 * r2 - h * b1 * b2 * b3) = t ]
Question: how large must the health and healing received bonus be to be equal to the added damage mitigation?
--> [ m / (d * r1 * r2 * r3 - h * b1 * b2) = m *b3 / (d * r1 * r2 - h * b1 * b2 * b3) ]
--> [ d * r1 * r2 - h * b1 * b2 * b3 = b3 * (d * r1 * r2 * r3 - h * b1 * b2) ]
--> [ d * r1 * r2 - h * b1 * b2 * b3 = b3 * d * r1 * r2 * r3 - b3 * h * b1 * b2 ]
--> [ d * r1 * r2 = b3 * d * r1 * r2 * r3 ]
--> [ 1 = b3 * r3 ]
--> [ b3 = 1/r3 ]
Conclusion: If you insert a resistance bonus of r3 = 0.85 you will find, that a health and healing received bonus of 1 / 0.85 = 1.17647 is equal to that in practice. The other mitigation and healing received sources are irrelevant to the outcome of this calculation.

I haven’t had the need to do anything other than “basic” math for 2+ decades.
Do you mind providing a source for me too understand the type of math you’re providing & how to properly solve/understand it?

Sure, I can explain to you what I did there. The mathematical equations I provided are to show that in practice a damage mitigation bonus of X (example: X=0.85 or 15%) should behave almost equally to a bonus Y=1/X to your max health and healing received (in our example: Y=1/0.85=1.17647 or 17.647%).

Note, that there are 3 situations I can think of where this isn't true:
1) Oblivion damage, since it ignores resistances, health and healing received would be more useful
2) Skills that scale with your maximum health in one way or another
3) Damage shields, which are not affected by healing received, but get a benefit from additional mitigation

Lets look at the general equation: [ m / (d - h) = t ]
Imagine a player with no mitigation at all and m = 24k health. Another player will attack him with a constant stream of d = 12k damage per second. The targeted player on the other hand will heal himself for a constant h = 4k health per second. This means that the targeted player will lose [ d - h = 12k/s - 4k/s = 8k ] health per second. Since he has 24k health he will die after [ m / (h - d) = 24k / 8k/s = 3s ] three seconds.

Now, lets give our targeted player two mitigation and healing received bonuses as in my example: r1 = 0.7, r2 = 0.8, b1 = 1.1 and b2 = 1.2. He will now die after: [ 24k / (12k/s * 0.7 * 0.8 - 4k/s * 1.1 * 1.2) = 24k / 1.44k/s = 16.67s ] around 17 seconds.

Finally, lets look at the 2 cases I provided. In the first case the targeted player will get an additional 15% damage reduction r3 = 0.85 and in the second case a 17.647% bonus to his max health and healing received b3 = 1.17647.
1) [ 24k / (12k/s * 0.7 * 0.8 * 0.85 - 4k/s * 1.1 * 1.2) = 24k / 0.432k/s = 55.56s ]
2) [ 24k * 1.17647 / (12k/s * 0.7 * 0.8 - 4k/s * 1.1 * 1.2 * 1.17647) = 28.235k / 0.508k/s = 55.56s ]
As you can see, both cases lead to the exact same time needed for the targeted player to die.

Since I kept the equations in my earlier post general, I could show that in this case all other sources of damage mitigation and healing received, as well as the initial health, the dps of the attacking player and the hps of the targeted player could be reduced from the equation, which means that they don't matter to the outcome (and that makes sense if you think about it). This means that in this case added damage mitigation is indeed equal to added health and healing received. Apart from the 3 examples I mentioned earlier, this should always be the case. Keep in mind, that bonuses to health and healing received don't show diminishing returns. If mitigation on the other hand showed diminishing returns, why are they in practice equal to each other?

To put the final nail into the coffin of the 'mitigation gets worse the more you have' argument lets look at damage done buffs. Surely, no one would argue that they show diminishing returns and therefore get worse the more you have. How come then, though, that damage mitigation always beats damage done boosts no matter how many you add to an equation, even though mitigation 'gets worse' the more you add while damage done 'gets better' the more you add?

Example 1: attacking player has a 30%, a 20% and a 15% damage done buff, targeted player has a 30%, a 20% and a 15% mitigation buff:
[ 1 * (1.3 * 1.2 * 1.15) * (0.7 * 0.8 * 0.85) = 0.854 ] --> targeted player only receives 85% of the damage he would receive if no damage done or mitigation buffs where present.

Example 2: attacking player has ten 30%, ten 20% and ten 15% damage done buffs, targeted player has ten 30%, ten 20% and ten 15% mitigation buffs:
[ 1 * (1.3^10 * 1.2^10 * 1.15^10) * (0.7^10 * 0.8^10 * 0.85^10) = 0.206 ] --> targeted player only receives 21% of the damage he would receive if no buffs where present.

Now, first of all this shows you that a 30% damage done buff is not equal to a 30% damage reduction buff. In truth, the damage done buff would need to be as large as 1 / 0.7 = 1.4286 --> 43% to be equal. However, even if you use this mathematically correct equivalent, then mitigation and damage done would just cancel each other perfectly out (which is obvious if you look at the equations).

This would mean, however, that a bonus that gets weaker the more you add perfectly cancels out a bonus that gets stronger the more you add, no matter how many of them you add to the scenario. This is a huge contradiction, and shows that this way of thinking about mitigation is flawed! The reason for this is that approaching zero on the defending side is just as powerful as approaching infinity on the attacking side. I hope this clears up the misconceptions about mitigation.

@muh I would like to hear what you think about this.

Insco851 · April 2019

13.8% sounds great to me

RouDeR · April 2019

Working as intended, stop crying. THis is th way how every freaking mitigation source work in the game so gid gud

TheBonesXXX · April 2019

MATTTTTTTTHHHHH

pieratsos · April 2019

muh wrote: »

pieratsos wrote: »

muh wrote: »

pieratsos wrote: »

muh wrote: »

pieratsos wrote: »

muh wrote: »

Kronuxx wrote: »

The OP's beginning post is a perfect example of how human interpretation can still be biased from unbiased mathematical results.

Alright, I guess I am biased towards PvE. That said, I'm curious in which way I've been so obviously biased. What really rubs you the wrong way about the OP? So I maybe can avoid it in the future and look at it more objectively.

The fact that you are calling it useless when its actually on par or better with other forms of mitigation which are considered great in PVP. Thats his point, while ur math do actually tell the truth, ur conclusion that its useless couldnt actually be further from the truth. PVP and PVE tanking are not the same thing.

But ... I never said it's useless?

You did say that the mitigation it gives its laughable no?

Which as far as I know is not a synonym for useless.

po-tay-to, po-tah-to. Im prety sure when someone says the dmg mitigation it gives is laughable and insignificant then he doesnt think that its actually good or even decent for that matter. I mean, you can keep playing with words but the only thing you are achieving is reinforcing the statement that ur analysis was biased

I really don't know what you want... Your interpretation of my OP is as biased if anything. Most of you attacking my interpretation get hung up on the initial use of "laughable", but ignore everything else.

I've covered the mitigation you can expect from it when you're keeping it at 15%, as DD and tank for that matter.
I've gone ahead and covered the mitigation you can expect when you're using the proc as soon as it's available. Which is the mitigation I primarily meant when I wrote laughable.
I never actually said the change overall is bad, I never said I want something else, but for some reason that's what you read into it.
I also never made a comparison to any other defensive buff, that's once again your (generally speaking) interpretation.

So what the actual fluff do you want from me?

I never said that you want something else although you did say that the change doesnt solve the issue and the mitigation it gives wont make it feel less awkward while at the same time you posed the question "what can Zos do to make it better" . All that can easily be interpreted ed by someone as you thinking the change is bad but whatever thats not even the point.

I also know that you never made a comparison to any other defensive buff, that is exactly the point people made when they called you biased. People brought up other sources of mitigation to show you that what you called laughable and insignificant is actually on par or better than other mitigation buffs which are generally considered to be very good buffs. You are the one that keeps getting hang up on words and fail to understand the point other people make.

There is no bias in my interpretation of what you said. I just called it exactly how you put it and i compared it to other sources of mitigation so you can understand why math doesnt always tell the full story. It seems like its your interpretation of what people tell you that is the issue here. No one wants anything from you. Its just criticism of ur post. Not a personal attack.

muh · April 2019

HankTwo wrote: »

kaithuzar wrote: »

HankTwo wrote: »

@muh First of all, lets concentrate on the case were you use this skill purely for the 15% damage mitigation bonus. You can add as much extra mitigations in my example as you want, the outcome will be the same. Equal damage values in both case 2 and 3 but different numbers in case of the 'total mitigation'.

Your math is not wrong per se, but you are taking the wrong conclusions from it. The problem is that you are always comparing it to this 'baseline' you calculate. I'm telling you this baseline shouldn't matter to you. Why should I care how much damage a player would deal to a naked target without any CP and buffs. It doesn't make sense to make comparisons with that case. What's important is how much will I mitigate when I add this skill to my bar compared to how much damage I receive without it. And that's exactly 15%. Heck, the fact that you don't take battlespirit into the equation is pure arbitrariness.

And about the mitigation = extra health and healing received. Please calculate some example scenarios were you add 15% damage mitigation in one case and 17.647% extra health and healing received in another. You can add as many other damage reduction and healing received buffs as you like. Apart from adding oblivion damage, both cases should always end at the same relative amount of health.

General example from me: a player with max health 'm' starts at full health and gets damage by a player with constant dps 'd'. The targeted player already has 2 forms of mitigation (r1 and r2) and 2 boosts to his healing received (b1 and b2). He will heal himself with a constant stream of heals 'h'. How much time 't' will it take until the player dies?
Case 1) added damage mitigation 'r3': [ m / (d * r1 * r2 * r3 - h * b1 * b2) = t ]
Case 2) added health bonus and healing received 'b3': [ m *b3 / (d * r1 * r2 - h * b1 * b2 * b3) = t ]
Question: how large must the health and healing received bonus be to be equal to the added damage mitigation?
--> [ m / (d * r1 * r2 * r3 - h * b1 * b2) = m *b3 / (d * r1 * r2 - h * b1 * b2 * b3) ]
--> [ d * r1 * r2 - h * b1 * b2 * b3 = b3 * (d * r1 * r2 * r3 - h * b1 * b2) ]
--> [ d * r1 * r2 - h * b1 * b2 * b3 = b3 * d * r1 * r2 * r3 - b3 * h * b1 * b2 ]
--> [ d * r1 * r2 = b3 * d * r1 * r2 * r3 ]
--> [ 1 = b3 * r3 ]
--> [ b3 = 1/r3 ]
Conclusion: If you insert a resistance bonus of r3 = 0.85 you will find, that a health and healing received bonus of 1 / 0.85 = 1.17647 is equal to that in practice. The other mitigation and healing received sources are irrelevant to the outcome of this calculation.

I haven’t had the need to do anything other than “basic” math for 2+ decades.
Do you mind providing a source for me too understand the type of math you’re providing & how to properly solve/understand it?

Sure, I can explain to you what I did there. The mathematical equations I provided are to show that in practice a damage mitigation bonus of X (example: X=0.85 or 15%) should behave almost equally to a bonus Y=1/X to your max health and healing received (in our example: Y=1/0.85=1.17647 or 17.647%).

Note, that there are 3 situations I can think of where this isn't true:
1) Oblivion damage, since it ignores resistances, health and healing received would be more useful
2) Skills that scale with your maximum health in one way or another
3) Damage shields, which are not affected by healing received, but get a benefit from additional mitigation

Lets look at the general equation: [ m / (d - h) = t ]
Imagine a player with no mitigation at all and m = 24k health. Another player will attack him with a constant stream of d = 12k damage per second. The targeted player on the other hand will heal himself for a constant h = 4k health per second. This means that the targeted player will lose [ d - h = 12k/s - 4k/s = 8k ] health per second. Since he has 24k health he will die after [ m / (h - d) = 24k / 8k/s = 3s ] three seconds.

Now, lets give our targeted player two mitigation and healing received bonuses as in my example: r1 = 0.7, r2 = 0.8, b1 = 1.1 and b2 = 1.2. He will now die after: [ 24k / (12k/s * 0.7 * 0.8 - 4k/s * 1.1 * 1.2) = 24k / 1.44k/s = 16.67s ] around 17 seconds.

Finally, lets look at the 2 cases I provided. In the first case the targeted player will get an additional 15% damage reduction r3 = 0.85 and in the second case a 17.647% bonus to his max health and healing received b3 = 1.17647.
1) [ 24k / (12k/s * 0.7 * 0.8 * 0.85 - 4k/s * 1.1 * 1.2) = 24k / 0.432k/s = 55.56s ]
2) [ 24k * 1.17647 / (12k/s * 0.7 * 0.8 - 4k/s * 1.1 * 1.2 * 1.17647) = 28.235k / 0.508k/s = 55.56s ]
As you can see, both cases lead to the exact same time needed for the targeted player to die.

Since I kept the equations in my earlier post general, I could show that in this case all other sources of damage mitigation and healing received, as well as the initial health, the dps of the attacking player and the hps of the targeted player could be reduced from the equation, which means that they don't matter to the outcome (and that makes sense if you think about it). This means that in this case added damage mitigation is indeed equal to added health and healing received. Apart from the 3 examples I mentioned earlier, this should always be the case. Keep in mind, that bonuses to health and healing received don't show diminishing returns. If mitigation on the other hand showed diminishing returns, why are they in practice equal to each other?

To put the final nail into the coffin of the 'mitigation gets worse the more you have' argument lets look at damage done buffs. Surely, no one would argue that they show diminishing returns and therefore get worse the more you have. How come then, though, that damage mitigation always beats damage done boosts no matter how many you add to an equation, even though mitigation 'gets worse' the more you add while damage done 'gets better' the more you add?

Example 1: attacking player has a 30%, a 20% a 15% damage done buffs, targeted player has a 30%, a 20% and a 15% mitigation buffs:
[ 1 * (1.3 * 1.2 * 1.15) * (0.7 * 0.8 * 0.85) = 0.854 ] --> targeted player only receives 85% of the damage he would receive if no damage done or mitigation buffs where present.

Example 2: attacking player has ten 30%, ten 20% and ten 15% damage done buffs, targeted player has ten 30%, ten 20% and ten 15% mitigation buffs:
[ 1 * (1.3^10 * 1.2^10 * 1.15^10) * (0.7^10 * 0.8^10 * 0.85^10) = 0.206 ] --> targeted player only receives 21% of the damage he would receive if no buffs where present.

Now, first of all this shows you that a 30% damage done buff is not equal to a 30% damage reduction buff. In truth, the damage done buff would need to be as large as 1 / 0.7 = 1.4286 --> 43% to be equal. However, even if you use this mathematically correct equivalent, then mitigation and damage done would just cancel each other perfectly out (which is obvious if you look at the equations).

This would mean, however, that a bonus that gets weaker the more you add perfectly cancels out a bonus that gets stronger the more you add, no matter how many of them you add to the scenario. This is a huge contradiction, and shows that this way of thinking about mitigation is flawed! The reason for this is that approaching zero on the defending side is just as powerful as approaching infinity on the attacking side. I hope this clears up the misconceptions about mitigation.

@muh I would like to hear what you think about this.

@HankTwo

Most damage and healing buffs are not multiplicative to each other.

very simplified damage formula ignoring every form of mitigation:
Outgoing Damage = X * (1 + Critical Chance * Critical Damage) * (1 + Damage Done)
Incoming Damage = Outgoing Damange * (1 + Damage Taken)
Where X is the tooltip damage of your skill
Where Critical Damage is the sum of all sources of Critical Damage buffs (Base, CP, Minor/Major Force, Khajiit, Templar/Nb)
Where Damage Done is the sum of all sources of Damage Done buffs (Minor/Major Berserk, Minor/Major Slayer, Exploiter, Swords, Morag Tong)
Where Damage Taken is the sum of all sources of Damage Taken debuffs (Minor/Major Vulnerability, some abilities)

Pretty much the same applies to healing:
Outgoing Healing = X * (1 + Critical Chance * Critical Healing) * (1 + Healing Done)
Incoming Healing = Outgoing Healing * (1 + Healing Received)

It seems to me you have no idea what diminishing returns mean.

It's the concept that when adding multiple bonuses of the same kind, that the absolute or relative value each these bonuses provide become less and less the more of them you add.

Do you actually want to tell me that when I multiply 100 by 0.9 five times, that the last 0.9 is reducing the value by the same amount as the first 0.9?

100    * 0.9 = 90     (100    - 10    )
 90    * 0.9 = 81     ( 90    -  9    )
 81    * 0.9 = 72.9   ( 81    -  8.1  )
 72.9  * 0.9 = 65.61  ( 72.9  -  7.29 )
 65.61 * 0.9 = 59.049 ( 65.61 -  6.561)

Do you really want to tell me that 6.561 is the same as 10?
That's exactly what's happening with mitigation.

When we look at Damage Done we see diminishing returns on additive bonuses. Lets say you have tooltip damage of 100 and we add one bonus after the other.

+[Minor Slayer]  100 * (1 + 5%)                  = 105 damage (relative  5   %, total  5%)
+[Minor Berserk] 100 * (1 + 5% + 8%)             = 113 damage (relative  7.6 %, total 13%)
+[Major Slayer]  100 * (1 + 5% + 8% + 15%)       = 128 damage (relative 13.27%, total 28%)
+[Major Berserk] 100 * (1 + 5% + 8% + 15% + 25%) = 153 damage (relative 19.53%, total 53%)

Compared to them being multiplicative (which they're not)

+[Minor Slayer]  100    * 1.05 = 105    damage (relative  5%, total 5   %)
+[Minor Berserk] 105    * 1.08 = 113.4  damage (relative  8%, total 13.4 %)
+[Major Slayer]  113.4  * 1.15 = 130.41 damage (relative 15%, total 30.41%)
+[Major Berserk] 130.41 * 1.25 = 163    damage (relative 25%, total 63   %)

Increases are usually additive to other increases of their type (Crit Damage to Crit Damage, Damage Done to Damage Done, Damage Taken to Damage Taken), which are multiplicative to each other.
While mitigation is always multiplicative.

So to come back to your example equation... You may have a point. You may not have a point.
If we assume you actually mean two healing received bonuses and you're adding another healing received bonus it would look more like:

1) [ 24k / (12k/s * 0.7 * 0.8 * 0.85 - 4k/s * (1 + 0.1 + 0.2) = 24k / 0.512k = 46.88s ]
2) [ 24k * 1.17647 / (12k/s * 0.7 * 0.8 - 4k/s * (1 + 0.1 + 0.2 + 0.17647) = 28.235k / 0.814k/s = 34.68s ]

46.88s =/= 34.68s

But I'm pretty sure you're creative enough to place your bonuses in such a way that you're able to claim they're multiplicative.

Kruwos · April 2019

muh wrote: »

Kruwos wrote: »

I'd be fine with losing any buffs on Grim Focus if they just made it a slotted passive for the mini-game. That way we aren't wasting a GCD and resources up front for nothing and it would become a much less clunky skill to use and maintain. In essence it would become a burst version of crystal shards proc on Sorc.

It would make it worse actually. You couldn't stack light attacks for procs on your backbar unless you're running it on your backbar as well.

Perhaps I should have made it clear that it should still work on your back bar as it does now on live when the buff is active otherwise yes it would be worse.

muh · April 2019

@pieratsos

pieratsos wrote: »

muh wrote: »

pieratsos wrote: »

muh wrote: »

pieratsos wrote: »

muh wrote: »

pieratsos wrote: »

muh wrote: »

Kronuxx wrote: »

The OP's beginning post is a perfect example of how human interpretation can still be biased from unbiased mathematical results.

Alright, I guess I am biased towards PvE. That said, I'm curious in which way I've been so obviously biased. What really rubs you the wrong way about the OP? So I maybe can avoid it in the future and look at it more objectively.

The fact that you are calling it useless when its actually on par or better with other forms of mitigation which are considered great in PVP. Thats his point, while ur math do actually tell the truth, ur conclusion that its useless couldnt actually be further from the truth. PVP and PVE tanking are not the same thing.

But ... I never said it's useless?

You did say that the mitigation it gives its laughable no?

Which as far as I know is not a synonym for useless.

po-tay-to, po-tah-to. Im prety sure when someone says the dmg mitigation it gives is laughable and insignificant then he doesnt think that its actually good or even decent for that matter. I mean, you can keep playing with words but the only thing you are achieving is reinforcing the statement that ur analysis was biased

I really don't know what you want... Your interpretation of my OP is as biased if anything. Most of you attacking my interpretation get hung up on the initial use of "laughable", but ignore everything else.

I've covered the mitigation you can expect from it when you're keeping it at 15%, as DD and tank for that matter.
I've gone ahead and covered the mitigation you can expect when you're using the proc as soon as it's available. Which is the mitigation I primarily meant when I wrote laughable.
I never actually said the change overall is bad, I never said I want something else, but for some reason that's what you read into it.
I also never made a comparison to any other defensive buff, that's once again your (generally speaking) interpretation.

So what the actual fluff do you want from me?

I never said that you want something else although you did say that the change doesnt solve the issue and the mitigation it gives wont make it feel less awkward while at the same time you posed the question "what can Zos do to make it better" . All that can easily be interpreted ed by someone as you thinking the change is bad but whatever thats not even the point.

I also know that you never made a comparison to any other defensive buff, that is exactly the point people made when they called you biased. People brought up other sources of mitigation to show you that what you called laughable and insignificant is actually on par or better than other mitigation buffs which are generally considered to be very good buffs. You are the one that keeps getting hang up on words and fail to understand the point other people make.

There is no bias in my interpretation of what you said. I just called it exactly how you put it and i compared it to other sources of mitigation so you can understand why math doesnt always tell the full story. It seems like its your interpretation of what people tell you that is the issue here. No one wants anything from you. Its just criticism of ur post. Not a personal attack.

The issue they themselves said they want to solve with it is that you're paying resources + global cooldown to participate in a "minigame". You're still doing exactly that. So did they manage to solve the issue they tried to solve?

About comparisons with other buffs. I honestly didn't see the value in it. To me it's fairly obvious that the same formula applies to every other form of mitigation as well. If the tooltip says 15% it's obviously stronger than something that has a tooltip of 8% or weaker than a tooltip of 30%. But I've added something like this to the TL;DR already earlier.

Unfortunately I seem to have missed your first quite a lot of your posts in this thread, because that would've probably solved a lot of what followed. You've provided a lot of good criticism and I'm sorry for how I responded earlier.
Once again, my intention was not to make it look bad or anything. And apparently I failed in doing that.

muh · April 2019

Kruwos wrote: »

muh wrote: »

Kruwos wrote: »

I'd be fine with losing any buffs on Grim Focus if they just made it a slotted passive for the mini-game. That way we aren't wasting a GCD and resources up front for nothing and it would become a much less clunky skill to use and maintain. In essence it would become a burst version of crystal shards proc on Sorc.

It would make it worse actually. You couldn't stack light attacks for procs on your backbar unless you're running it on your backbar as well.

Perhaps I should have made it clear that it should still work on your back bar as it does now on live when the buff is active otherwise yes it would be worse.

Well the thing is... That's not how "while slotted" bonuses work. You either have it slotted or not.
What you're asking for would require to activate a buff with a "while active" effect, which means spending at least one GCD, which is what we have right now.

Masel · April 2019

Damage Mitigation in this game is very weird in actual application. I never made a guide for it because I was never able to actually replicate accurate numbers of incoming damage.

Using an empty template and just speccing 8% into CP and/or getting minor protection from temporal guard, even simple calculations do not add up. I had 0 resistance on both ends and had no skill points invested whatsoever.

I had a duneripper hit me with his sweep for 4084 without any kinds of resistance.

Slotting temporal guard or speccing 8% into cp (taking into account jump points) reduced it to 3758, which sounds about right, since it is a 7.99% damage reduction.

Then using 8% from the Hardy CP or adding protection reduced it to 3472, which is a total mitigation of 14.99%. From 3758, it is a 7.61% damage reduction. So is it working additively or multiplicatively? Both theoretical scenarios don't yield me that number.

If I deduct 16% additively from 4084, I should land at 3430. So that can't be it. If i do it the multiplicative way, it should net me 4084*0,92*0,92, which is 3456. Both scenarios are off already, with the multiplicative one being closer to the actual value, but still off. I also tried different kinds of flooring to get to the 3472, with none of them being accurate to match the ingame value. The more mitigation sourcs I added, the bigger the deviation from the actual ingame number became, up the the point where even the multiplicative calculation was almost 5% off from the actual ingame value when taking all sources of mitigation into account. The only one i could reliably replicate was the part coming from block, that always halved the number i had pre-blocking.

So we can do all these kinds of calculations, but if they don't translate over into the game with sufficient accuracy, what really is the point?

I'm not the biggest fan of the change myself (i didnt see a necessity for changing the skill in the first place, since it does not solve the class stacking meta in pve at all), but you cannot deny that it will be useful for nightblade tanks that can hold it to gain a bit of mitigation.

What is concerning me is that heavyblades will see a noticable buff through the elsweyr changes: higher mobility choices, more mitigation that on the other hand lets them go more offensively elsewhere.

Iskiab · April 2019

I don’t see an issue with Stamblades getting a survivability buff. I main a magblade and have a stamblade alt, but generally believe Stamblades are weak (contrary to everyone else).

Where they perform well is in CP pvp solo and dueling from what I’ve seen. In BGs they’re considered one of the weakest classes because they lack aoe and survivability. I think all the changes will do is push more Stamblades to heavy and away from a ganking playstyle, or it could help the 7 medium stamblade builds in the survivability department.

HankTwo · April 2019

@muh

First of all, there is an error in your outgoing damage calculation concerning the crit. Average damage should be:
X * ((1 - critchance) + critchance * (1 + sum(critmods))
But lets ignore crits, since they don't matter to this discussion anyway.

I know fully well, what you mean from a mathematical standpoint when you talk about diminishing returns, I'm just telling you that the absolute values are not what matters so much, but the relative reduction, which always stays the same. If you're playing naked with no CP or buffs and get hit by an attack that deals 10k damage to you (not the tooltip of the attacker, I mean the actual damage you receive), then 15% extra mitigation would reduce the very same attack to just 8.5k damage. If you are, in contrast to the first scenario, in heavy armor while blocking with CP and major protection and get hit by an attack that would deal 10k damage to you, then the added 15% mitigation would also reduce it to just 8.5k damage. And again, speaking of first and last part of mitigation doesn't make much sense since its multiplicative and you can just switch the order around as you like.

Now, about healing received and damage done, thats my bad, I thought they were also multiplicative. However, since they are calculated additively instead, it interestingly just strengthens the point. In this case, 15% extra mitigation is at least as good as 15% extra health and healing received, and flat out better when you already have multiple healing received bonuses (it shows in your recalculation of my example). Furthermore, stacking mitigation on the defensive side will then outweigh stacking damage done or damage received on the offensive side even more so.

But again, just imagine for a moment that damage done (or received) would indeed behave multiplicative. I'm sure you wouldn't say that they show diminishing returns then (quite the contrary I believe). How come then, that mitigation (which apparently get worse the more you add) would cancel out damage done (which would get better the more you add), no matter how many sources of these buffs are present, as long as they are equal in numbers? Furthermore, if healing received would behave multiplicative, would say that stacking these buffs would show diminishing returns? I would also guess no, but in this scenario extra mitigation should indeed behave the same way as extra health and healing received (apart from the exceptions I posted earlier).

Edit: This is all from a theoretical standpoint. As Masel pointed out, the actual ingame calculations can be wonky and I experienced this as well.

Lightspeedflashb14_ESO · April 2019

.So we can do all these kinds of calculations, but if they don't translate over into the game with sufficient accuracy, what really is the point?

Because arguing on the internet is fun? But really, you are on point with the comments you made.

muh · April 2019

@HankTwo

HankTwo wrote: »

First of all, there is an error in your outgoing damage calculation concerning the crit. Average damage should be:
X * ((1 - critchance) + critchance * (1 + sum(critmods))
But lets ignore crits, since they don't matter to this discussion anyway.

Lets assume Crit Chance of 50%, let's assume Crit Damage of 50%
Your formula:
1 * ((1-0.5) + 0.5 * (1 + 0.5)) = 1.25
What I wrote:
1 * (1 + 0.5 * 0.5) = 1.25

HankTwo wrote: »

I know fully well, what you mean from a mathematical standpoint when you talk about diminishing returns, I'm just telling you that the absolute values are not what matters so much, but the relative reduction, which always stays the same. If you're playing naked with no CP or buffs and get hit by an attack that deals 10k damage to you (not the tooltip of the attacker, I mean the actual damage you receive), then 15% extra mitigation would reduce the very same attack to just 8.5k damage. If you are, in contrast to the first scenario, in heavy armor while blocking with CP and major protection and get hit by an attack that would deal 10k damage to you, then the added 15% mitigation would also reduce it to just 8.5k damage. And again, speaking of first and last part of mitigation doesn't make much sense since its multiplicative and you can just switch the order around as you like.

Just looking at the relative gain of an ability doesn't give you any idea how much it'll contribute to the mitigation of your build.

Imagine you're running a build that already mitigates 90% of incoming damage...
So a 10,000 damage hit you receive gets already reduced to 1,000 damage. Now you have to decide if you want to run another 15% damage mitigation or a cleanse or an offensive ability or whatever.
So the question is, how much is 15% more damage mitigation actually worth? If all you're doing is looking at relative mitigation... Well that's 15%! Ez pz, no one will ever kill you.
But in reality 15% more damage mitigation is only a 1.5% increase in mitigation over what you already have.

HankTwo wrote: »

But again, just imagine for a moment that damage done (or received) would indeed behave multiplicative. I'm sure you wouldn't say that they show diminishing returns then (quite the contrary I believe).
[...]
Furthermore, if healing received would behave multiplicative, would say that stacking these buffs would show diminishing returns? I would also guess no, but in this scenario extra mitigation should indeed behave the same way as extra health and healing received (apart from the exceptions I posted earlier).

Which once again makes me question if you actually know what diminishing returns mean. It doesn't have anything to do with the mathematical operations you perform. But how the result grows (granted, the operation you perform changes how you look at it). If you're getting less benefit when you're adding more and more of it, the gain is diminished.

Which is pretty obvious if you change something repeatedly by the same amount.

Example A )
100 + 100 = 200, 100% gain
200 + 100 = 300, 50% gain
300 + 100 = 400, 33% gain
400 + 100 = 500, 25% gain
The change relative to the previous value is getting smaller and smaller => gains are diminished.

Example B )
100 * 0.5 = 50 (change of 50, or 50% "gain")
50 * 0.5 = 25 (change of 25, or 25% "gain")
25 * 0.5 = 12.5 (change of 12.5, or 12.5% "gain")
12.5 * 0.5 = 6.25 (change of 6.25, or 6.25% "gain")
The change relative to the absolute value is getting smaller and smaller => gains are diminished.

Example C )
100 * 1.5 = 150 (change of 50)
150 * 1.5 = 225 (change of 75)
225 * 1.5 = 337.5 (change of 112.5)
337.5 * 1.5 = 506.25 (change of 168.75
The change relative to the absolute value is getting bigger and bigger => gains are growing.

HankTwo wrote: »

How come then, that mitigation (which apparently get worse the more you add) would cancel out damage done (which would get better the more you add), no matter how many sources of these buffs are present, as long as they are equal in numbers?

Because it's simple % math, isn't it?

100 * 1.3 = 130; 1% of 100 is 1; 30 * 1 = 30
130 * 0.7 = 91; 1% of 130 is 1.3; 30 * 1.3 = 39

And as I've shown... in reality, not in your little thought experiment, Damage Done is not getting better and better the more you add. It's also subject to diminishing returns. In fact, pretty much everything in ESO (and most games) is subject to diminishing returns. Otherwise you'd just stack one thing and pretty much only that one thing for all eternity.

WrathOfInnos · April 2019

@HankTwo is correct here, the only baseline that makes sense is your damage taken before applying the buff.

I’ll use another example:

An archer A shoots 10 arrows at you with 100% accuracy, all 10 arrows hit you.

Then another archer B shoots 100 arrows at you with 10% accuracy, 90 arrows miss and 10 arrows hit you.

Now you a grab a shield that covers half your body. Archer A shoots 10 more arrows, 5 hit the shield, 5 hit you. The shield mitigated 50% of incoming damage.

You still have the shield, Archer B walks up, and shoots 100 arrows with 10% accuracy. 90 arrows miss, 5 hit your shield, 5 hit you.

The shield is equally good against archer A or B. You cannot argue that the shield is weaker against archer B because it only caught 5 of his 100 arrows (5%) instead of 5 of Archer A’s 10 arrows (50%). Using some hypothetical maximum potential unmitigated damage (like total arrows shot or opponent’s damage tooltips) as a baseline is meaningless. Against either archer the shield caught 5/10 arrows that would have otherwise hit you, and is therefore 50% effective in either case.

muh · April 2019

Lol... It's actually getting tiresome.

Your example isn't very fitting at all, but whatever.

I'll leave it at that, I'll not repeat myself more than I already have. If you don't even try to understand what I'm writing, what's the point of it?

Insco851 · April 2019

muh wrote: »

Lol... It's actually getting tiresome.

Your example isn't very fitting at all, but whatever.

I'll leave it at that, I'll not repeat myself more than I already have. If you don't even try to understand what I'm writing, what's the point of it?

Without copy paste... you think you could try one more time? Examples and math would be nice.... just one more....

Skullstachio · April 2019

On an interesting note: I wonder how the grim focus damage mitigation will affect werewolves.

Because seeing as how the damage mitigation bonus from grim focus doesn’t get removed unless it is consumed or when leaving combat, it is possible for werewolves to retain the bonus until they leave combat.

HankTwo · May 2019

@muh At this point it feels a bit like a philosophical debate. What matters more, the relative or absolute reduction? However, I still think you haven't really gotten my point of view, so lemme try to explain it to you one last time.

So, first of all, you just change the way how you calculate the gain in your example A vs example B. Lemme show you what I mean:

muh wrote: »

Example A )
100 + 100 = 200, 100% gain
200 + 100 = 300, 50% gain
300 + 100 = 400, 33% gain
400 + 100 = 500, 25% gain
The change relative to the previous value is getting smaller and smaller => gains are diminished.

Here, you calculated the 'gain' by comparing the result of an iteration with the start of the same iteration. That's the relative difference to the result of the previous step:
1) 200 / 100 = 1.0 --> 100% difference
2) 300 / 200 = 1.5 --> 50%
3) 400 / 300 = 1.33 --> 33%
4) 500 / 400 = 1.25 --> 25%

muh wrote: »

Example B )
100 * 0.5 = 50 (change of 50, or 50% "gain")
50 * 0.5 = 25 (change of 25, or 25% "gain")
25 * 0.5 = 12.5 (change of 12.5, or 12.5% "gain")
12.5 * 0.5 = 6.25 (change of 6.25, or 6.25% "gain")
The change relative to the absolute value is getting smaller and smaller => gains are diminished.

Here, you are calculating the 'gain' by comparing the result of an iteration with the very start of the operation chain, what you call the 'baseline'. That's the relative difference to the baseline:
1) 50 / 100 = 0.5 --> 50% difference
2) 25 / 100= 0.25 --> 25%
3) 12.5 / 100 = 0.125 --> 12.5%
4) 6.25 / 100 = 0.0625 --> 6.25%

But why did you suddenly switch the way how to calculate the 'gain'? If you would have stuck to the way you calculated the 'gain' in example A, then your calculations would look like this (relative difference to the previous step):
1) 50 / 100 = 0.5 --> 50% difference
2) 25 / 50 = 0.5 --> 50%
3) 12.5 / 25 = 0.5 --> 50%
4) 6.25 / 12.5 = 0.5 --> 50%

Now, as far as I understand your whole argument is based on the absolute difference between the result of an iteration and the result of the previous step, as you did in comment #127. I fully understand why you think this leads to diminishing returns. However let me ask you this, what makes mitigation really useful? Surely it is the effect on your health. The more mitigation you have, the more useful your health the healing you receive becomes (as well as your damage shields). This is what most would call 'effective health'. Now, to calculate the 'effective health', we would need an 'effective health multiplier', which we could then apply to our max health or the healing a skill would provide, to estimate the usefulness of our health. To calculate this multiplier, one would need to divide 1 by the mitigation we have. Lets see how that would look:

First, lets look at the total mitigation. We'll do 5 iterations, and every step 10% extra mitigation will be added. This should provide us with numbers that we are already familiar with:
0) 1
1) 1 * 0.9 = 0.9 --> absolute difference to previous step: 0.1
2) 0.9 * 0.9 = 0.81 --> absolute difference to previous step: 0.09
3) 0.81 * 0.9 = 0.729 --> absolute difference to previous step: 0.081
4) 0.729 * 0.9 = 0.6561 --> absolute difference to previous step: 0.0729
5) 0.6561 * 0.9 = 0.59049 --> absolute difference to previous step: 0.06561

Now, from your point of view the calculations above clearly show a case of diminishing returns. However, lets look at the total 'effective health multiplier' now. I will also provide an example with 20k health for each step:
0) 1 / 1 = 1 --> effective health: 20k * 1 = 20k
1) 1 / 0.9 = 1.11111 --> absolute difference to previous step: 0.11111 effective health: 20k * 1.11111= 22.22k
2) 1/ 0.81 = 1.23457 --> absolute difference to previous step: 0.12346, effective health: 20k * 1.23457 = 24.69k
3) 1 / 0.729 = 1.37174 --> absolute difference to previous step: 0.13717, effective health: 20k * 1.37174 = 27.43k
4) 1 / 0.6561 = 1.52416 --> absolute difference to previous step: 0.15241, effective health: 20k * 1.52416 = 30.48k
5) 1/ 0.59049 = 1.69351 --> absolute difference to previous step: 0.16935, effective health: 20k * 1.69351 = 33.87k

As you can see, the effective health shows a behavior that is opposite to diminishing returns. The same is true if you calculate the time to kill a target. This means, that by your argumentation, the impact of an added 'effective health multiplier' is stronger, the more 'effective health multipliers' you already had. Since mitigation and effective health are directly related with each other, and can be calculated without further variables, this is a contradiction. In a sense, both 'effective health multipliers' and 'damage reduction multipliers' aka mitigations are equivalent to each other. You can view mitigation from both sides, and none is more true than the other from a mathematical standpoint. This leads me to believe that it doesn't make sense to speak of diminishing returns in case of mitigation. How can mitigation show diminishing returns, when effective health multipliers would show the exact opposite behavior? Further question, would you say that stacking simple max health (not effective health) multipliers show diminishing returns (forget about how they work ingame, at this point its a purely theoretical discussion anyway)?

Iskiab · May 2019

HankTwo wrote: »

@muh At this point it feels a bit like a philosophical debate. What matters more, the relative or absolute reduction? However, I still think you haven't really gotten my point of view, so lemme try to explain it to you one last time.

So, first of all, you just change the way how you calculate the gain in your example A vs example B. Lemme show you what I mean:

muh wrote: »

Example A )
100 + 100 = 200, 100% gain
200 + 100 = 300, 50% gain
300 + 100 = 400, 33% gain
400 + 100 = 500, 25% gain
The change relative to the previous value is getting smaller and smaller => gains are diminished.

Here, you calculated the 'gain' by comparing the result of an iteration with the start of the same iteration. That's the relative difference to the result of the previous step:
1) 200 / 100 = 1.0 --> 100% difference
2) 300 / 200 = 1.5 --> 50%
3) 400 / 300 = 1.33 --> 33%
4) 500 / 400 = 1.25 --> 25%

muh wrote: »

Example B )
100 * 0.5 = 50 (change of 50, or 50% "gain")
50 * 0.5 = 25 (change of 25, or 25% "gain")
25 * 0.5 = 12.5 (change of 12.5, or 12.5% "gain")
12.5 * 0.5 = 6.25 (change of 6.25, or 6.25% "gain")
The change relative to the absolute value is getting smaller and smaller => gains are diminished.

Here, you are calculating the 'gain' by comparing the result of an iteration with the very start of the operation chain, what you call the 'baseline'. That's the relative difference to the baseline:
1) 50 / 100 = 0.5 --> 50% difference
2) 25 / 100= 0.25 --> 25%
3) 12.5 / 100 = 0.125 --> 12.5%
4) 6.25 / 100 = 0.0625 --> 6.25%

But why did you suddenly switch the way how to calculate the 'gain'? If you would have stuck to the way you calculated the 'gain' in example A, then your calculations would look like this (relative difference to the previous step):
1) 50 / 100 = 0.5 --> 50% difference
2) 25 / 50 = 0.5 --> 50%
3) 12.5 / 25 = 0.5 --> 50%
4) 6.25 / 12.5 = 0.5 --> 50%

Now, as far as I understand your whole argument is based on the absolute difference between the result of an iteration and the result of the previous step, as you did in comment #127. I fully understand why you think this leads to diminishing returns. However let me ask you this, what makes mitigation really useful? Surely it is the effect on your health. The more mitigation you have, the more useful your health the healing you receive becomes (as well as your damage shields). This is what most would call 'effective health'. Now, to calculate the 'effective health', we would need an 'effective health multiplier', which we could then apply to our max health or the healing a skill would provide, to estimate the usefulness of our health. To calculate this multiplier, one would need to divide 1 by the mitigation we have. Lets see how that would look:

First, lets look at the total mitigation. We'll do 5 iterations, and every step 10% extra mitigation will be added. This should provide us with numbers that we are already familiar with:
0) 1
1) 1 * 0.9 = 0.9 --> absolute difference to previous step: 0.1
2) 0.9 * 0.9 = 0.81 --> absolute difference to previous step: 0.09
3) 0.81 * 0.9 = 0.729 --> absolute difference to previous step: 0.081
4) 0.729 * 0.9 = 0.6561 --> absolute difference to previous step: 0.0729
5) 0.6561 * 0.9 = 0.59049 --> absolute difference to previous step: 0.06561

Now, from your point of view the calculations above clearly show a case of diminishing returns. However, lets look at the total 'effective health multiplier' now. I will also provide an example with 20k health for each step:
0) 1 / 1 = 1 --> effective health: 20k * 1 = 20k
1) 1 / 0.9 = 1.11111 --> absolute difference to previous step: 0.11111 effective health: 20k * 1.11111= 22.22k
2) 1/ 0.81 = 1.23457 --> absolute difference to previous step: 0.12346, effective health: 20k * 1.23457 = 24.69k
3) 1 / 0.729 = 1.37174 --> absolute difference to previous step: 0.13717, effective health: 20k * 1.37174 = 27.43k
4) 1 / 0.6561 = 1.52416 --> absolute difference to previous step: 0.15241, effective health: 20k * 1.52416 = 30.48k
5) 1/ 0.59049 = 1.69351 --> absolute difference to previous step: 0.16935, effective health: 20k * 1.69351 = 33.87k

As you can see, the effective health shows a behavior that is opposite to diminishing returns. The same is true if you calculate the time to kill a target. This means, that by your argumentation, the impact of an added 'effective health multiplier' is stronger, the more 'effective health multipliers' you already had. Since mitigation and effective health are directly related with each other, and can be calculated without further variables, this is a contradiction. In a sense, both 'effective health multipliers' and 'damage reduction multipliers' aka mitigations are equivalent to each other. You can view mitigation from both sides, and none is more true than the other from a mathematical standpoint. This leads me to believe that it doesn't make sense to speak of diminishing returns in case of mitigation. How can mitigation show diminishing returns, when effective health multipliers would show the exact opposite behavior? Further question, would you say that stacking simple max health (not effective health) multipliers show diminishing returns (forget about how they work ingame, at this point its a purely theoretical discussion anyway)?

Nice summary. Basicly this argument has four types of opinions:

Those that understand the game’s mechanics and like the change

Those that don’t understand the game’s mechanics and don’t like the change

PvP gankers who wouldn’t benefit from the mitigation so don’t like the change, and prefer more damage for better ganking

PvE dps who aren’t happy with the change because self mitigation isn’t as important as damage.

By the way the only problem with looking at mitigation as more effective health is when you add healing. Once you add healing mitigation is actually better then more health, to directly compare mitigation and health you have to treat mitigation like a +healing modifier.... if you know what I mean.

HankTwo · May 2019

Iskiab wrote: »

HankTwo wrote: »

@muh At this point it feels a bit like a philosophical debate. What matters more, the relative or absolute reduction? However, I still think you haven't really gotten my point of view, so lemme try to explain it to you one last time.

So, first of all, you just change the way how you calculate the gain in your example A vs example B. Lemme show you what I mean:

muh wrote: »

Example A )
100 + 100 = 200, 100% gain
200 + 100 = 300, 50% gain
300 + 100 = 400, 33% gain
400 + 100 = 500, 25% gain
The change relative to the previous value is getting smaller and smaller => gains are diminished.

Here, you calculated the 'gain' by comparing the result of an iteration with the start of the same iteration. That's the relative difference to the result of the previous step:
1) 200 / 100 = 1.0 --> 100% difference
2) 300 / 200 = 1.5 --> 50%
3) 400 / 300 = 1.33 --> 33%
4) 500 / 400 = 1.25 --> 25%

muh wrote: »

Example B )
100 * 0.5 = 50 (change of 50, or 50% "gain")
50 * 0.5 = 25 (change of 25, or 25% "gain")
25 * 0.5 = 12.5 (change of 12.5, or 12.5% "gain")
12.5 * 0.5 = 6.25 (change of 6.25, or 6.25% "gain")
The change relative to the absolute value is getting smaller and smaller => gains are diminished.

Here, you are calculating the 'gain' by comparing the result of an iteration with the very start of the operation chain, what you call the 'baseline'. That's the relative difference to the baseline:
1) 50 / 100 = 0.5 --> 50% difference
2) 25 / 100= 0.25 --> 25%
3) 12.5 / 100 = 0.125 --> 12.5%
4) 6.25 / 100 = 0.0625 --> 6.25%

But why did you suddenly switch the way how to calculate the 'gain'? If you would have stuck to the way you calculated the 'gain' in example A, then your calculations would look like this (relative difference to the previous step):
1) 50 / 100 = 0.5 --> 50% difference
2) 25 / 50 = 0.5 --> 50%
3) 12.5 / 25 = 0.5 --> 50%
4) 6.25 / 12.5 = 0.5 --> 50%

Now, as far as I understand your whole argument is based on the absolute difference between the result of an iteration and the result of the previous step, as you did in comment #127. I fully understand why you think this leads to diminishing returns. However let me ask you this, what makes mitigation really useful? Surely it is the effect on your health. The more mitigation you have, the more useful your health the healing you receive becomes (as well as your damage shields). This is what most would call 'effective health'. Now, to calculate the 'effective health', we would need an 'effective health multiplier', which we could then apply to our max health or the healing a skill would provide, to estimate the usefulness of our health. To calculate this multiplier, one would need to divide 1 by the mitigation we have. Lets see how that would look:

First, lets look at the total mitigation. We'll do 5 iterations, and every step 10% extra mitigation will be added. This should provide us with numbers that we are already familiar with:
0) 1
1) 1 * 0.9 = 0.9 --> absolute difference to previous step: 0.1
2) 0.9 * 0.9 = 0.81 --> absolute difference to previous step: 0.09
3) 0.81 * 0.9 = 0.729 --> absolute difference to previous step: 0.081
4) 0.729 * 0.9 = 0.6561 --> absolute difference to previous step: 0.0729
5) 0.6561 * 0.9 = 0.59049 --> absolute difference to previous step: 0.06561

Now, from your point of view the calculations above clearly show a case of diminishing returns. However, lets look at the total 'effective health multiplier' now. I will also provide an example with 20k health for each step:
0) 1 / 1 = 1 --> effective health: 20k * 1 = 20k
1) 1 / 0.9 = 1.11111 --> absolute difference to previous step: 0.11111 effective health: 20k * 1.11111= 22.22k
2) 1/ 0.81 = 1.23457 --> absolute difference to previous step: 0.12346, effective health: 20k * 1.23457 = 24.69k
3) 1 / 0.729 = 1.37174 --> absolute difference to previous step: 0.13717, effective health: 20k * 1.37174 = 27.43k
4) 1 / 0.6561 = 1.52416 --> absolute difference to previous step: 0.15241, effective health: 20k * 1.52416 = 30.48k
5) 1/ 0.59049 = 1.69351 --> absolute difference to previous step: 0.16935, effective health: 20k * 1.69351 = 33.87k

As you can see, the effective health shows a behavior that is opposite to diminishing returns. The same is true if you calculate the time to kill a target. This means, that by your argumentation, the impact of an added 'effective health multiplier' is stronger, the more 'effective health multipliers' you already had. Since mitigation and effective health are directly related with each other, and can be calculated without further variables, this is a contradiction. In a sense, both 'effective health multipliers' and 'damage reduction multipliers' aka mitigations are equivalent to each other. You can view mitigation from both sides, and none is more true than the other from a mathematical standpoint. This leads me to believe that it doesn't make sense to speak of diminishing returns in case of mitigation. How can mitigation show diminishing returns, when effective health multipliers would show the exact opposite behavior? Further question, would you say that stacking simple max health (not effective health) multipliers show diminishing returns (forget about how they work ingame, at this point its a purely theoretical discussion anyway)?

Nice summary. Basicly this argument has four types of opinions:

Those that understand the game’s mechanics and like the change

Those that don’t understand the game’s mechanics and don’t like the change

PvP gankers who wouldn’t benefit from the mitigation so don’t like the change, and prefer more damage for better ganking

PvE dps who aren’t happy with the change because self mitigation isn’t as important as damage.

By the way the only problem with looking at mitigation as more effective health is when you add healing. Once you add healing mitigation is actually better then more health, to directly compare mitigation and health you have to treat mitigation like a +healing modifier.... if you know what I mean.

I already made the comparison earlier that mitigation behaves similar to extra max health + healing received. However, you can just apply the 'effective health modifier' to all forms of health, so not only your max health but also healing you get from skills or damage shields.

muh · May 2019

@HankTwo

HankTwo wrote: »

@muh At this point it feels a bit like a philosophical debate. What matters more, the relative or absolute reduction?

Neither matters more or less than the other, different use cases to look at the same thing. That's what I've been writing all this time.

HankTwo wrote: »

So, first of all, you just change the way how you calculate the gain in your example A vs example B. Lemme show you what I mean:

muh wrote: »

Example A )
100 + 100 = 200, 100% gain
200 + 100 = 300, 50% gain
300 + 100 = 400, 33% gain
400 + 100 = 500, 25% gain
The change relative to the previous value is getting smaller and smaller => gains are diminished.

Here, you calculated the 'gain' by comparing the result of an iteration with the start of the same iteration. That's the relative difference to the result of the previous step:
1) 200 / 100 = 1.0 --> 100% difference
2) 300 / 200 = 1.5 --> 50%
3) 400 / 300 = 1.33 --> 33%
4) 500 / 400 = 1.25 --> 25%

muh wrote: »

Example B )
100 * 0.5 = 50 (change of 50, or 50% "gain")
50 * 0.5 = 25 (change of 25, or 25% "gain")
25 * 0.5 = 12.5 (change of 12.5, or 12.5% "gain")
12.5 * 0.5 = 6.25 (change of 6.25, or 6.25% "gain")
The change relative to the absolute value is getting smaller and smaller => gains are diminished.

Here, you are calculating the 'gain' by comparing the result of an iteration with the very start of the operation chain, what you call the 'baseline'. That's the relative difference to the baseline:
1) 50 / 100 = 0.5 --> 50% difference
2) 25 / 100= 0.25 --> 25%
3) 12.5 / 100 = 0.125 --> 12.5%
4) 6.25 / 100 = 0.0625 --> 6.25%

But why did you suddenly switch the way how to calculate the 'gain'? If you would have stuck to the way you calculated the 'gain' in example A, then your calculations would look like this (relative difference to the previous step):
1) 50 / 100 = 0.5 --> 50% difference
2) 25 / 50 = 0.5 --> 50%
3) 12.5 / 25 = 0.5 --> 50%
4) 6.25 / 12.5 = 0.5 --> 50%

Because additive operations have different growth patterns than multiplicative operations. That's why I wrote "the operation you perform changes how you look at it". And I don't know if you noticed, I wrote what I did in bold below each of those chains.
I also never said the original value is the 'baseline'.

That said.... I don't think in any of this you understood that I'm not saying you're wrong (except maybe with some of your effective health calculations), but that your whole premise is that I am wrong. All this time I've tried to explain to you why looking at absolute gains has value as well.

Can't be bothered with this anymore.

Have a nice day.

Ulfgarde · May 2019

muh wrote: »
Ulfgarde wrote: »
"On average you get just 6% tooltip damage mitigation from it as a DD, which in reality gives about 3% actual mitigation."

Let's just look at your calculations, that you supplied us with:
10,000 * 0.77 [Ironclad] * 0.88 [Hardy] * 0.75 [Resistance] = 5082
10,000 * 0.77 [Ironclad] * 0.88 [Hardy] * 0.75 [Resistance] * 0.85 [Grim Focus] = 4322
5082 damage from a 10k hit, 4322 with grim focus, right? Now if we divide the latter calculation by the former one, we find that the latter calculation is close to 85% of the 5082 damage we saw earlier. That's means the latter calculation had 760 less damage than the former. Everything is working just as it should be here; it's still 15% reduction.

You can't realistically base damage received calculations off "tooltip damage mitigation". To reiterate what I just did, by removing Grim Focus's new damage mitigation in a seperate calculation with the same CP and resists, the difference in a 10k base ability's received damage between your first calculation and your second calculation WITH grim focus will be decisively around 15%, with some very small diminishing returns. You are 100% right that, based on the tooltip, the TOTAL mitigation is much less, but you will NEVER realistically base your damage received off TOTAL mitigation.

Your tl;dr would lead people to believe that the damage received is far less than it advertises, which is not true. No damage reduction source is stacking additively off the raw tooltip because that would be fundamentally broken for the game.

Consider the fact this change is intended to mostly benefit nightblades in PVP. In pvp you will often hold assassin's bow for burst of course, so that means this mitigation bonus is going to be a game-changer. For PVE I can agree that the "average" damage received is kinda redundant, but it is obvious that this change was PvP-leaned.

Overall, the damage you receive should not be practically viewed through the perspective of the tooltip damage, but rather through what difference the damage received is before the buff is considered and afterwards. It just causes misinformation otherwise.
Well the initial quote you put up there is specifically looking at the case where you're using the proc as soon as it becomes available. Which is most likely not a PvP usecase already.

I'm well aware that the relative difference between those two equations comes down to be 15%. But at some point you have to ask yourself if the mitigation you gain in the broad picture is worth it to slot additional defense. You can't evaluate this if you're only looking at the relative 15% mitigation it provides. like BlackMadara wrote just a few post before this. If my mitigation already is high, do I really need to slot another 15% if it just reduces the damage I take by 1-2% overall?

You can't evaluate how much a defensive ability is worth in your current situation if all you're looking at is its tooltip. And that's what my OP is looking at.

Rebuttal is from a PvP perspective, as I've said it's a PvP-tilted change but can also apply to PvE.

You asked why is there any point to slotting grim focus as a defensive. The problem is that you aren't. You are slotting grim focus to do burst damage to a target, but for some reason, by slotting an offensive ability, you are gaining a defensive bonus. That is why it makes more sense as a PvP change, and that's why it's a bad one at that. Nightblades should be a glass cannon class but instead they're gaining damage reduction that they never needed, despite losing Major Fracture, defile, and Minor Berserk (assuming you aren't going to use soul harvest).

"If my mitigation already is high, do I really need to slot another 15% if it just reduces the damage I take by 1-2% overall?"

This is never the case EVER. Nobody thinks like this and nobody is taking that percentage and applying it to the overall TOOLTIP. I already told you why mitigation off a tooltip is an unrealistic perspective and that it makes no sense to base damage reduction off tooltip damage. You can never know really know the total damage in PvP nor in PvE, so you always going off the prior damage you took before you got buffed by damage reduction. Perspectively, you keep trying to view things far smaller than they actually are. 9-15% damage reduction is seriously no small matter, just consider shadowrend or old wizard's riposte, which made sorcs crazy tanky pre-nerf because you had such a massive reduction in damage (To be fair it as also back when shields had 0 resists, but still, minor maim is quite ridiculous). Many builds are running temporal guard backbar primarily for minor protection, so I wonder how impactful Grim Focus will be on live. :thinking:

The more damage you can mitigate, the more offensive you can be, since you are taking less damage and you don't have to worry about health dipping to the point where you have to play defensive. And in PvP, damage reduction in essence means you can manage your health far better and go for riskier plays. Note that damage reduction like this mitigates damage like bleeds, corrosive, penetration, those that only go through resists and not flat mitigation. Thus, NBs are just more imbalanced and more tanky unnecessarily.