Eldacar's Guide to Resilience vs Stamina

We come to it at last....the great battle of our time. I know many of you who have been following my guide series on resilience have been asking for and looking forward to this resilience vs stamina guide for some time now and I am happy to finally be able to deliver it to you. It took a LOT of time and work, FAR more than the other guides I have written, so I hope you all enjoy it =). This guide is fairly long and in-depth, it is broken down into sections for easier reading. Those interested in the math and really technical details can find them at the very bottom. As always if you have feedback, questions, or see an error please post a reply/comment and I will do my best to respond to everyone.

TLDR/Summary:In my opinion it's better to gem resilience for survivability in the majority of cases. Although stamina will in some situations grant a slightly larger effective health pool, the extra damage reduction from resilience will easily make up the disparity if you receive pretty much any heals at all while you are being attacked (damage reduction increases the relative effectiveness of heals on you).

Table of Contents:

Section 1 - Introduction and Effective Health

Section 2 - Analyzing the Question Mathematically

Section 3 - Interpreting the Graphs

Section 4 - Graphs

Section 5 - Conclusions

Section 6 - Math and Technical Details

Section 1 - Introduction and Effective Health

Everyone trying to increase or maximize their survivability in PVP has to make a choice between gemming resilience, gemming stamina, or gemming a mix of the two. There are lots of opinions floating around the game and the web, players trying to convince each other one way or another. Yet there hasn't been much hard data presented in a comprehensive manner yet; this guide is intended to fix that. I do present my own opinion here and I do believe resilience is better in the majority of cases, however I invite everyone to examine the facts and the data and draw their own conclusions. It's your gear and your character, only you can decide how you are going to gem it, I just want to help you make an informed decision. Ultimately the differences between the two are fairly minor, and either way you go is not going to make a huge difference, this is really all just min-maxing.

Before I jump into the details there is a critical concept everyone needs to understand - effective health. 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-mitigated 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. The more damage reduction you have, the greater the relative effectiveness of heals you receive is. Effective health is the best metric for looking at your survivability in PVP and it is the metric primarily examined in this guide. However it is the ability of resilience to increase the effectiveness of heals you receive in addition to increasing your effective health that really puts it over the top in my personal opinion, but more on that later.

Section 2 - Analyzing the Question Mathematically

Analyzing the question of resilience vs stamina from a mathematical perspective may seem at first glance to be a simple endeavor, it's primarily just a question of which will give you the most effective health. However determining which will give you more effective health is actually quite complicated. There are a number of factors in play here that need to be considered when making this evaluation. While stamina does have static displayed health returns of 14 hp per stam, it's effective health returns increase the more resilience you have. Resilience on the other hand has increasing returns the more of it you get, if you don't know what I mean see my previous guide on the subject here: http://www.mmo-champion.com/threads/....2-With-Graphs. Additionally resilience becomes more valuable the more stam you have, because it is applying it's damage reduction to a larger pool of health. So because both stat's scale with each other an interdependent relationship exists that prevents the stats from being considered in isolation. In other words when asking the question of which stat will provide more effective health, the answer changes based on how much of each stat you already have, so you need to know how much of both you have in order to make the determination.

The final factors that need to be taken into consideration are the tauren racial bonus and the stamina modifier that tanking spec's get. The tauren racial bonus grants an additional 5% base health, which effectively makes resilience slightly more valuable across the board. The tank spec stamina modifiers on the other hand make stamina more valuable across the board by a decent amount. The stamina modifiers are multiplicative and different for each class. Paladins and Warriors get a +15% modifier from their prot specs and the +5% modifier from their armor specialization so it works out as (Stam X 1.15) X 1.05 = how much stam you get. DK's get slightly more, a +9% modifier from their blood spec, a +8% modifier from blood presence, and a 5% modifier from their armor specialization so it works out to ((Stam X 1.09) X 1.08) X 1.05 = how much stam you get. Druid's get the most (4.3 numbers here) with a +20% modifier for bear form, a +6% modifier for heart of the wild, and a +5% modifier for their armor specialization so it works out to ((Stam X 1.20) X 1.06) X 1.05 = how much stam you get.

Buffs like Blessing of Kings and Fortitude will affect things as well, with Kings slightly increasing the value of stamina and fort slightly increasing the value of resilience, however because these buffs are not always present and are relatively minor factors I am not including them in this analysis. When fully raid buffed the effect of Kings and Fort together will roughly cancel each other out anyways.

Because other damage reduction effects beyond resilience such as armor, or talents are applied multiplicatively to the end results of all these calculations we don't need to consider them here to make our determinations as what we are looking at can be considered independently and won't change when those factors are added in. But it is worth noting that they increase your effective health further and make the number larger than what you get when you consider just displayed health and resilience.

Section 3 - Interpreting the Graphs

Because you need to evaluate this determination based on the two pre-existing values that are your current stamina and resilience, the graphs are presented as contour maps. In order to make a personal determination of which gem will provide the greatest effective health return for you, you need to find your current stamina number and follow the line up to the line for your current resilience number. If at that point the map is red it means a stamina gem will provide you with the most effective health. If at that point the map is blue it means a resilience gem will provide you with the most effective health.

There are three graphs here, the first is the one applicable to most players, it is for non-taurens with non-tank specs. The second graph is for taurens with non-tank specs. The third graph is for tauren prot paladins and prot warriors. For non-tauren prot paladins and prot warriors, and for all tank spec druid and dk players there is no graph because the graphs for you are solid red, gemming stamina will always give you slightly more effective health than gemming resilience.

As I said before ultimately the differences between the two choices are fairly minor, and either way you go is not going to make a huge difference. But again in my personal opinion even where these graphs show that gemming stam would give you more EH I believe resilience is still the better choice overall because of how it increases the effectiveness of heals you receive. I will get into more detail on my reasoning for that following the graphs, but I felt obligated to provide the hard data here and let each of you draw your own conclusions.

Section 4 - Graphs

A pretty even split in the range that most people play in, resilience is clearly favored for well-geared players.

The tauren racial pushes things further in resilience's favor.

The stamina modifiers that tanks get push things nearly completely into stamina's favor.

Section 5 - Conclusions

As I said before it is up to each of you to draw your own conclusions here, if you strictly want the most effective health possible and are not going to be receiving any heals at all then sticking to what the graphs recommend is probably the best way to go for you. However if you are going to be receiving heals, even small heals from your own abilities, I believe that resilience is pretty much always the best way to gem for survivability.

To illustrate my reasoning I am going to use my own character as an example. My character is a tauren prot paladin and stamina is clearly favored for me in the graph for my character, yet resilience is still better for me. I took my projected stats for full season 11 PVP gear with no gems and calculated out what my stamina, resilience, and effective health would be if I gemmed full stamina, and what it would be if I gemmed full resilience. These numbers are not EXACTLY what they will be in game, but they are very very close.

If I gemmed full stamina I would have 10656 total stamina for a displayed health of 196,594. I would have 4,965 resilience giving me 46.59% damage reduction for a grand total effective health of 368,054.

If I gemmed full resilience I would have 9504 total stamina for a displayed health of 180,531. I would have 5676 resilience giving me 50.82% damage reduction for a grand total effective health of 367,061.

As you can see the difference in total effective health between the two configurations is 993 EH in favor of the full stamina configuration. That is a very minor gain and comes at the expense of 4.23% damage reduction, which when adjusted for relative value (damage reduction gets more valuable the more you have) equates to a relative damage reduction of about 7.85%. That means that with the resilience configuration not only will I be taking roughly 7.85% less damage than the stamina configuration all the time, heals will be roughly 7.85% more effective on me than in the stamina configuration. Meaning that if I get healed just one time for 15,000 effective health (7,500 displayed health at 50% dmg reduc) the 993 EH difference will be made up for. If I get healed for more than that (extremely likely being im a flag carrier) the balance shifts so far into the favor of resilience that it's really not even a competition.

It will take slightly more healing to overcome the EH disparity for non-tauren non-paladin tank specs, but really it's still an easy call in favor of resilience in my opinion. For non-tank spec players resilience will give you more effective health straight up most of the time anyways, making the decision totally and completely clear cut in favor of resilience.

Thanks for Reading!

I hope those of you that took the time to read this guide found it useful, and again if you have any feedback, questions, or notice any errors please post a reply/comment and I will do my best to respond to you =). You can find my previous two guides on resilience in the links below.

How Resilience Scales:http://www.mmo-champion.com/threads/....2-With-Graphs

Anticipated Resilience Gains for 4.3/Season 11: http://www.mmo-champion.com/threads/...11-With-Graphs

Additionally if you enjoy these guides you can always find my latest PVP related guides and informational posts at my PVP blog: Battlemasters.org

Section 6 - Math and Technical Details

This last section is just for those of you interested in the hard math and technical details of how this guide and particularly the graphs were created. Everything for this guide was done in Excel, including the graphs. The way I built the graphs was by building data tables for the ranges show in the graphs based on a monster equation calculating the difference in returns between a stamina gem and a resilience gem at each of the 3600 points where the gridlines intersect.

The equation essentially took base health, added health from stamina to determine displayed health, then divided that displayed health by 1-(damage reduction % from resilience/100) to determine effective health, then performed the same calculation again but with the additional damage reduction that an epic +50 resilience gem would provide factored in. It then subtracted the first EH value from the second to determine how much of an EH gain the +50 resil gem provided.

The equation then took the amount of health an epic +75 stamina gem would provide and divided it by 1-(damage reduction % from resilience/100) to determine how much of an EH gain the +75 stam gem would provide (using the original damage reduction value, not the modified value).

The equation then subtracted the potential EH gain of the resilience gem from the potential EH gain of the stamina gem. Where this equation returned a positive value (indicating the return from the stam gem was greater) the graph displayed it as red, where the equation returned a negative value indicating the resil gem provided a greater return the graph displayed it as blue. This entire process was performed at each of the 3600 points with the values for that specific point.

Here is an example of the excel equation in one of the cells:

=(1050/(1-(((-0.0000006*H$5^2)+(0.0123367*H$5)+0.12137)/100)))-(((45449+$C51)/(1-(((-0.0000006*(H$5+50)^2)+(0.0123367*(H$5+50))+0.12137)/100)))-(45449+$C51)/(1-(((-0.0000006*H$5^2)+(0.0123367*H$5)+0.12137)/100)))

I used my equation from the previous guide on resilience scaling to determine how much damage reduction there would be at each of the resilience values. That equation (in excel friendly format) is y=(-0.0000006*x^2)+(0.0123367*x)+0.12137 with x being the resilience rating you are plugging in and y being the resulting amount of damage reduction. Of course when entered in excel the y at the front is dropped and the x's are replaced with cell addresses.

I hope this covers most of the technical questions some of you may have had but if there is anything else you are curious about please feel free to ask.

Anti-Plagiarism Notice: This guide and all related images, graphs, and equations are my original work and my intellectual property but may be shared and re-used freely for non-profit purposes so long as I am credited as the original author and the MMO-champ forums are credited as the original source. If you wish to use my work on a for-profit website please contact me through private message here on the forums and obtain my prior consent.