How Resilience Scales - OLD VERSION

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- World of Warcraft
87 Tauren Paladin
10570
***THIS GUIDE IS OLD AND OUT OF DATE!!!***

An up-to-date version can be found here: http://us.battle.net/wow/en/forum/topic/6490579264

***THIS GUIDE IS OLD AND OUT OF DATE!!!***

Hi everyone, I have written this guide to explain how resilience currently scales to those who are interested. I wrote it because I have seen and met a LOT of people over the last few months who are under the mistaken impression that resilience operates with diminishing returns and it is only half true. This guide is fairly long and in-depth, it is broken down into sections for easy reading, those interested in the really mathy details will find them at the very bottom.

TLDR: Resilience rating has diminishing returns, but the net effect of resilience has increasing returns. See pretty graphs below.

Table of Contents:
Section 1 - Facts About how Resilience Scales
Section 2 - Understanding Effective Health and Interpreting the Graphs
Section 3 - Graphs
Section 4 - Closing Thoughts and Remarks
Section 5 - The Data and Math

Update: The graphs and formulas have been updated based on a more exact resilience rating to damage reduction conversion formula. The formula was derived by Whitetooth of Elitist Jerks.

Section 1 - Facts About how Resilience Scales
Everyone reading this should already have at least a general understanding of how resilience works, it provides a percentage based damage reduction against all damage done by players, the more you have the less damage you take. That's all well and good, but what many people don't seem to understand is how it scales. There are two main factors that go into how resilience scales, one is the exponential returns of percentage based damage reduction, the other is the diminishing returns of resilience rating.

The effects of percentage based damage reduction scale exponentially*, the more you have the more valuable additional damage reduction becomes. For example, lets say someone is hitting you for 100 damage, if you have 0% damage reduction and you add 1% that 100 damage is reduced to 99 damage, a 1% effective reduction. However if you already have 90% damage reduction and you add another 1% that 100 base damage which was already reduced to 10 is now further reduced to 9. That change in incoming damage from 10 to 9 is a 10% reduction in actual damage taken by adding just 1% of damage reduction. Here is a graph that shows how the value of damage reduction increases as you gain more: http://i109.photobucket.com/albums/n71/cyberstatic/DmgReducValueGraph.jpg

As you can see at 50% damage reduction additional reduction is worth twice as much as normal, at 90% its worth ten times as much as normal. This kind of scaling isn't unique to resilience, armor and any other percentage based damage reduction (even in other games) function the same way, games control the overall scaling of these mechanics by manipulating how fast you are awarded the damage reduction.

(*I am using exponential as a general easy to understand descriptor for quickly increasing returns, not its technical mathematical definition.)

For resilience the controlling factor to those exponential returns on damage reduction is the diminishing returns on resilience rating. The more resilience rating you have, the less damage reduction is awarded by each additional point of rating. This is how Blizzard controls the overall scaling of resilience as a whole, and its what they change when they want to alter the way resilience scales. Currently in 4.3 the rate at which the returns from resilience rating diminish is slower than the rate at which the relative value of damage reduction increases, as a result the net effect of resilience has increasing returns. Simply put the DR on resil rating is not currently intense enough to cancel out the exponential returns of damage reduction.

One final note on this, in World of Warcraft different damage reduction mechanics have multiplicative relationships NOT additive, what this means is that the value scaling for any one of these mechanics is only accurate within that one mechanic. At 50% dmg reduction from resilience an extra 1% from resilience is effectively worth 2%, however none of this has any bearing on the value of additional damage reduction from say armor, that scales separately but similarly. Calculating your total damage reduction from all effects is a rather complicated matter that is beyond the scope of this guide, but I may tackle in it another guide in the future.
Edited by Eldacar on 4/27/2013 11:07 AM PDT
- World of Warcraft
87 Tauren Paladin
10570
Section 2 - Understanding Effective Health and Interpreting the Graphs
Before you can understand the graphs you need to understand what effective health is. Effective health is essentially how much pre-mitigated damage it takes to kill you. If you have 100k health and 0% damage reduction your effective health is just that same 100k. However if you have 100k health and 50% damage reduction your effective health is 200k, because someone would need to do the equivalent of 200k pre-mitigaged damage to kill you. It is also important to note that more than just increasing the size of your effective health pool, that damage reduction also increases the relative effectiveness of heals on you. With 50% damage reduction a 1k heal actually restores 2k of effective health, this is why having a larger effective health through damage reduction is better than having a larger displayed health through stamina.

Because effective health is such a great indicator of survivability it is also a great metric to use for evaluating the overall effectiveness of resilience, which is why I used it in these graphs. It is really the stat that best displays the value you are getting from resilience and the stat you need to be paying attention to in the graphs. Effective health is displayed on the graphs as a percentage relative to displayed health, an EH value of 150% for a player with a 100k displayed health pool would mean that player has an effective health from just resilience of 150k. (When you factor in other effects like armor and dmg reduc from talents your EH is higher but we are just looking at resil by itself here)

Now that you understand all the critical facts its time to get into the graphs. The graphs display the scaling of damage reduction and effective health based on resilience rating in the current version of WoW Patch 4.3 Build 15050. The first graph shows the full resilience rating range from 0 to 6000 with markers in 500 rating increments. The second graph focuses on the range most fully geared PVP'ers play in from 4000 to 5700 with markers in 100 rating increments. These two graphs are based on two formulas; the formula used to convert resilience rating into damage reduction percentage is % = 100 - 100 * 0.99^(resilience rating / 79.12785) and the formula used for determining effective health as a percentage of total displayed health is 100/(1-[dmg reduc %/100]). So without further ado here are the graphs.

Graphs in next post!
Edited by Eldacar on 1/21/2012 6:16 AM PST
- World of Warcraft
87 Tauren Paladin
10570
Section 3 - Graphs

Graph 1: http://i109.photobucket.com/albums/n71/cyberstatic/ResilScalingFS43.jpg

As you can see in this graph, although you get less and less damage reduction per resilience rating as you gain more, your effective health continues to increase faster and faster anyways.

Graph 2: http://i109.photobucket.com/albums/n71/cyberstatic/ResilScalingPZ43.jpg

This graph is just a closer look at the range most fully geared PVP'ers play in.

Section 4 - Closing Thoughts and Remarks
I hope this guide has helped to inform those of you that took the time to read it, and I really hope it will help to dispel the common misconception that resilience as a whole operates with diminishing returns. The net total effect of resilience has increasing returns, the more you get the better it is plain and simple. I cant tell you what the right amount of resil for you or your class/spec is, that's a question to be debated and theory-crafted by the players of your class. However if you are looking to gain more survivability you can stack resil forever and its only going to get better. If you have any suggestions for how I can improve this guide, please feel free to post them. Likewise if you see any errors please let me know so I can correct them, I did my best to be as accurate and factual as possible but im not perfect, not yet anyways....maybe with a bit more resil! =D
Edited by Eldacar on 1/21/2012 6:17 AM PST
- World of Warcraft
87 Tauren Paladin
10570
Section 5 - The Data and Math
This final section is just for those interested in the hard math and where all of this data and these numbers came from.

My original graphs for this guide were based on a resil rating to damage reduction conversion formula approximated by matching a trend line equation to 33 data points in excel. Since then I have updated the guide using a more accurate equation derived by Whitetooth from Elitist Jerks. The formula is as follows: % = 100 - 100 * 0.99^(resilience rating / 79.12785). I have tested this formula in game and found it to be extremely accurate. You can see his post on the subject and how he derived the formula here: http://elitistjerks.com/f15/t29453-combat_ratings_level_85_cataclysm/p24/#post1916319 (I would also like to say thank you to Ptarr for bringing Whitetooth's work to my attention).

I calculated effective health percentages using this formula: 100/(1-[dmg reduc %/100]). For example for the resilience of 5000 the damage reduction is 47.01% so the equation looks like this: 100/(1-0.4701) = 188.72%. You can also calculate your total effective health by plugging in your current displayed health instead of 100, (Displayed Health)/(1-[dmg reduc %/100]) = Effective Health. Keep in mind that resilience is not the only damage mitigation your character has (armor, talents, etc all factor in), so your actual total effective health will be higher than what you calculate with just resilience factored in.

If anyone has any questions about the data or the math feel free to ask me.


Thanks for reading!

________________________________________________
PVP Forum MVP
Edited by Eldacar on 1/21/2012 6:35 AM PST
85 Blood Elf Paladin
4315
Great information, the math seems to match up, and I think this is something that most players have a murky understanding on at best. I didn't know that the effects of resilience had increasing returns, I was under the impression that diminishing returns for resilience kicked in at a level that couldn't be reached in current gear.

Requested sticky for great justice.
85 Night Elf Druid
5650
For healers and DPS especially, I would love to see additional graphs displaying the trade off of damage/healing throughput comparative to increasing resilience rating, corresponding to the graphs you have used here.


Otherwise, great work.
09/25/2011 10:15 AMPosted by Eldacar
Simply put the DR on resil rating is not currently intense enough to cancel out the exponential returns of damage reduction.


are you suggesting resil needs another nerf?
- World of Warcraft
87 Tauren Paladin
10570
For healers and DPS especially, I would love to see additional graphs displaying the trade off of damage/healing throughput comparative to increasing resilience rating, corresponding to the graphs you have used here.


Otherwise, great work.


Those kind of trade off graphs are something I would love to do, but it would be difficult and time consuming. Every class itemizes differently for max healing/dps, and for some classes there isnt even a clear consensus of the best way to go. Mages for example, some prefer stacking mastery, others prefer haste, and some think crit is the way to go. I would need to test and show graphs for all 3. Also would I compare burst DPS/healing, or consistent throughput? I would likely need to show both. In order to have viable data I would need large sample sizes for each test, they would need to be performed at least 10X each. Given the 30 different specs in the game and the different itemization routes for each, testing burst and consistent damage/healing for everyone would require testing around 80 different things with each test set taking around an hour (I need to find perfectly geared people to perform every test too).

Anyways im saying I will never do it, but its a fairly monumental undertaking and would require around 20X the time investment of this original guide. Also the entire thing would need to be re-done and updated after patches, which is really the nail in the coffin for me, I just dont have that kind of time =(

Im sure there are some passionate players out there who could do these kinds of charts for their individual class/spec better and in more depth than I could anyways, hopefully they will step up and contribute =)
- World of Warcraft
87 Tauren Paladin
10570
are you suggesting resil needs another nerf?
Not at all, I was simply stating the reality of the way resilience currently functions. I tried to avoid presenting any opinions in this guide and did my best to stick to the facts that are mathematically backed up by the data. In my personal opinion though resilience could actually use a slight buff. I dont have any hard data to back up that opinion, but based on my own empirical testing I feel that damage has been scaling up faster than effective health this expansion, and that in a fight between fully geared players people are dieing faster than they were at the start of the expansion. As I said though this is just based on my subjective experience, I dont have hard data to back it up.
76 Worgen Hunter
1030
A graphic about resil was just what i was looking for.
sticky requested
09/25/2011 02:24 PMPosted by Eldacar
are you suggesting resil needs another nerf?
Not at all, I was simply stating the reality of the way resilience currently functions. I tried to avoid presenting any opinions in this guide and did my best to stick to the facts that are mathematically backed up by the data. In my personal opinion though resilience could actually use a slight buff. I dont have any hard data to back up that opinion, but based on my own empirical testing I feel that damage has been scaling up faster than effective health this expansion, and that in a fight between fully geared players people are dieing faster than they were at the start of the expansion. As I said though this is just based on my subjective experience, I dont have hard data to back it up.


Ah okay. Requesting for sticky. The hard data is already on live, in pvp as we know it.
90 Blood Elf Paladin
7065
Thank you so much for this. I keep trying to tell my friends that they can't get too much resil but they won't listen to me. Hopefully your graphs can convince them where I had failed.

Its so frustrating when people tell me they want to stop stacking resil at xx point because of diminishing returns!

/hug

edit: also requested sticky.
Edited by Celias on 9/25/2011 4:55 PM PDT
- World of Warcraft
87 Tauren Paladin
10570

Thank you so much for this. I keep trying to tell my friends that they can't get too much resil but they won't listen to me. Hopefully your graphs can convince them where I had failed.

Its so frustrating when people tell me they want to stop stacking resil at xx point because of diminishing returns!

/hug


My pleasure, I actually felt just like you, I had to explain how resilience works to my friends and guild mates like 20 times over the last few months because they always ask me "Dude Eldacar why are you stacking so much resil? What about the DR??" And I finally just got tired of repeating the explanation so many times lol so I made this guide, now when they ask im just responding with a link haha =D
85 Night Elf Druid
5650
For healers and DPS especially, I would love to see additional graphs displaying the trade off of damage/healing throughput comparative to increasing resilience rating, corresponding to the graphs you have used here.


Otherwise, great work.


Those kind of trade off graphs are something I would love to do, but it would be difficult and time consuming. Every class itemizes differently for max healing/dps, and for some classes there isnt even a clear consensus of the best way to go. Mages for example, some prefer stacking mastery, others prefer haste, and some think crit is the way to go. I would need to test and show graphs for all 3. Also would I compare burst DPS/healing, or consistent throughput? I would likely need to show both. In order to have viable data I would need large sample sizes for each test, they would need to be performed at least 10X each. Given the 30 different specs in the game and the different itemization routes for each, testing burst and consistent damage/healing for everyone would require testing around 80 different things with each test set taking around an hour (I need to find perfectly geared people to perform every test too).

Anyways im saying I will never do it, but its a fairly monumental undertaking and would require around 20X the time investment of this original guide. Also the entire thing would need to be re-done and updated after patches, which is really the nail in the coffin for me, I just dont have that kind of time =(

Im sure there are some passionate players out there who could do these kinds of charts for their individual class/spec better and in more depth than I could anyways, hopefully they will step up and contribute =)


I understand completely. There are just times when I feel like I would be gimping myself if I tried gemming/enchanting resilience as a healer, over other stats such as int/spirit. I used to wear the 40 resil chest enchant, straight resilience gems in my yellows, and resilience/stam gems in my blue sockets. Mind you, this was back in season 9, with full Vicious gear.

I never seemed to have problems healing back then. This season, I am almost too afraid to go that route with full Ruthless, since I am already at 4114 resilience without gemming/chanting for it. I do tend to love more resil for my characters, but because I am playing a class that already has a lot of trouble out healing the burst some classes can dish out, I'd almost rather go for more throughput.

It's just a tough call to make without investing in the gems/enchants to try it both ways. A graph would be amazing.
Edited by Bobbyjoealex on 9/25/2011 6:44 PM PDT
85 Tauren Druid
3735
two minor things technically inaccurate

09/25/2011 10:15 AMPosted by Eldacar
Percentage based damage reduction scales exponentially by its nature,

survival is expressed as;
life / (damage)*(mitigation factors)

Represented through division, with the DR, resilience it is not exponential, it is asymptotic. e.g at 100% mitigation you have infinite survival.

damage after DRres% = .99^(x/c)
graph 1000 / [.99^(x/79.12785)] from x = 1..90,000
http://screencast.com/t/1QX6oD8Jyhk

09/25/2011 10:15 AMPosted by Eldacar
armor and any other percentage based damage reduction

woah slow down there, many games do all sorts of things to dampen or alter returns. Now Blizzards own (15+year old) Diablo II, Dr%, +DR, MDR, resistance%, absorb% and +absorb all function asymptotically without any DR, but many without caps.

However In WoW, armor offers linear survival e.g., x armor creates y seconds for a set value of incoming DPS. Whether at 5000 armor or 20k, the seconds added in relation to the dps is the same at either end of those armor values

I could use some enlightenment on that, I suppose this is due to armors "DR" is through division, not exponentiation, thus cancelling out?
Armor / (Armor + (467.5 * AttackerLevel - 22167.5))
wiki graph here
http://images4.wikia.nocookie.net/__cb20070429111816/wowwiki/images/thumb/4/46/Armor.JPG/830px-Armor.JPG
taken from http://www.wowwiki.com/Armor

as for avoidance, the fact that agility, class, and caps exist still doesn't change the fact that +dodge rating does not suffer from DR, at least +dodge rating moves survival asymptotically.. as for agility, i can't find enough info on the avoidance formula per class, so i'm lost on that point

edit[spelling]
Edited by Korba on 9/25/2011 8:01 PM PDT
- World of Warcraft
87 Tauren Paladin
10570
Represented through division, with the DR, resilience it is not exponential, it is asymptotic. e.g at 100% mitigation you have infinite survival.


You are absolutely right, but a good number of people reading the guide are going to have no idea what asymptotic scaling is or even what an asymptote is, so I used the term exponential as a general descriptor for returns that increase faster and faster even though it is not technically accurate to the mathematical definition =). I will add an note of it to the guide though.

woah slow down there, many games do all sorts of things to dampen or alter returns.

Right again, however percentage based damage reduction on its own scales the same way regardless of the game, the games control the scaling by manipulating the speed at which you acquire it, not by changing the way damage reduction itself works, that is mathematically constant. Armor for instance has DR on it's "rating" like resilience, the more you have the slower it awards additional damage reduction. Armor has linear scaling as a whole because blizzard slows the rate at which you gain it through diminishing returns on its rating (I realize armor rating is just called armor, im just need a way to refer to it separately from the net effect).

Edit: I revised that section a bit to make it clearer, I also added a graph showing the relative value scaling of damage reduction which you can view here: http://i109.photobucket.com/albums/n71/cyberstatic/DmgReducValueGraph.jpg

This is what I was talking about I said it functions the same way from game to game, this scaling is mathematically constant and is application agnostic. Games just control the rate at which you gain that damage reduction to control the scaling of the overall mechanic.
Edited by Eldacar on 9/25/2011 10:14 PM PDT
- World of Warcraft
87 Tauren Paladin
10570
I understand completely. There are just times when I feel like I would be gimping myself if I tried gemming/enchanting resilience as a healer, over other stats such as int/spirit. I used to wear the 40 resil chest enchant, straight resilience gems in my yellows, and resilience/stam gems in my blue sockets. Mind you, this was back in season 9, with full Vicious gear.

I never seemed to have problems healing back then. This season, I am almost too afraid to go that route with full Ruthless, since I am already at 4114 resilience without gemming/chanting for it. I do tend to love more resil for my characters, but because I am playing a class that already has a lot of trouble out healing the burst some classes can dish out, I'd almost rather go for more throughput.

It's just a tough call to make without investing in the gems/enchants to try it both ways. A graph would be amazing.


Ya I totally understand, and like I said its something id like to do im just not sure if I have the time. Maybe its something you can suggest to some of the theory crafters on the druid forums? =)
85 Tauren Druid
3735
09/25/2011 08:31 PMPosted by Eldacar
percentage based damage reduction on its own scales the same way regardless of the game
yes

I wonder if we could make an ascii based graph



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lol ^ ^
Edited by Korba on 9/25/2011 11:02 PM PDT
85 Night Elf Druid
5650
Epic ^_^
85 Human Paladin
1940
tldr
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