Eldacar's guide to resilience scaling
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 ScalesEveryone 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.photobuc...cValueGraph.jpg (im not displaying it directly so when people view the guide its easier to find the graph most of them are looking for).
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.
Section 2 - Understanding Effective Health and Interpreting the GraphsBefore 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.
Section 3 - Graphs
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.
This graph is just a closer look at the range most fully geared PVP'ers play in.
Section 4 - Closing Thoughts and RemarksI 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
Section 5 - The Data and MathThis 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....24/#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!
Edited by Eldacar, 21 January 2012 - 02:49 PM.