• Bares mostly like the taste of fase!

Mathiness

Introduction

It’s been a while since I’ve done a legitimate theorycrafting post. We’ve had everything in MoP figured out for so long that there hasn’t been much incentive to do anything further. However now that we’ve started getting information about Warlords, there’s new things we can do! But first, a story.

A while ago I wrote a little story about how I got into theorycrafting. Normally this wouldn’t be pertinent, but part of this story was about making sure things are accurate and how to do that. One of those ways is of course, to ask for someone to look at your work. Kind-of like proof-reading.

Something that you may also not know (well some of you will) is that while I’m pretty decent at algebra, I’m really terrible at calculus. So I’ve had people review my stuff before, and did so again today. Thankfully both Theck and Ahanss made sure I wasn’t totally off my rocker. Theck may have also implicitly questioned my intelligence (he’s my friend, he’s allowed). I kid, I kid.

In any case, I’m here to talk to you today about Guardian Rage generation in Warlords of Draenor. At least, what we know about it from the alpha patch notes. Well, the first half of it anyway.
 

Spreadsheets and Simulations

In the current iteration of Guardian development, there are two different distinct possible rotations: With and without Pulverize. Today’s post is going to focus on the latter, more simple version of this rotation. Now, before we get into anything specific it’s important to understand that the most accurate way to investigate this kind of thing is through simulations which replicate gameplay. However it’s very possible – and usually much easier – to get most of the way there using a simple spreadsheet. Enough in any case, to pick up on any potential problems that might occur as gear improves throughout an expansion.

You may have seen me mention on Twitter that I want to get into working on SimC. I originally thought I would simply re-teach myself Java and build my own simulator, but Theck convinced me otherwise. Until I manage to teach myself C++ (or whatever they use) to a degree that I’m able to do anything productive, I will approximate situations using spreadsheets as best I can. That’s what I’ve done here. In order to do that though, I made a few assumptions.
 

Assumptions of Play

The results I will describe shortly are based on a set of assumptions of how a Guardian would play while tanking a boss. These are:

Fortunately I can prove all of these assumptions – with a reasonable degree of accuracy – using math. First, we know that Thrash‘s duration is 16 seconds. We also know that the chance of not getting a Mangle proc on 2 consecutive Lacerates is 75%*75% = 56.25%. Bare nekkid our GCD is 1.42857 seconds (5% Haste raid buff). That gives us 16 / 1.42857 = 11.2 GCDs every 16 seconds, or almost 12. That means the chance of not being able to use a Thrash on the 3rd GCD after a Mangle is only around 3% ((1-0.5625)^4).

Second, we know that the RPS to maintain 100% SD uptime (for 42 seconds) is only 6.6666~ if you bank 100 Rage before swapping. Since Mangle and Lacerate together generate at least 10 RPS without considering Mangle procs (60/6) or Haste, then that is definitely possible. I also assume around 10% base Dodge from Agility, which is about what we had at the start of the expansion after suppression.

My third assumption is pretty obvious, since Mangle does the most damage and generates the most Rage. As is by extension, the fourth. The actual formula for calculating the number of Mangles is something I re-purposed from Helistar by removing the “miss” and changing it to a variable GCD based on Haste. We know this formula is accurate to at least 3 sig-figs because of Tangedyn’s simulations during MoP Beta.

The fifth and final assumption is implied from the wording of Primal Fury although never confirmed.
 

Results

The “TLDR” version of the results is that we’re going to be swimming in Rage, and Crit is worse than Haste in the current build until you reach GCD cap. The longer version has a bit of exposition along with visual aids. For example, this is what the graph looks like when you are completely naked and only have raid buffs.

NekkidS

We start at just over 18 RPS with this rotation. To provide a relative example, this is approximately the same amount of RPS we have now in heroic SoO gear. The obvious difference between the two examples is that Tooth and Claw is now free. This liberates an absolutely huge amount of our Rage for Frenzied Regeneration. But what happens when we add around 500 Crit and 500 Haste, an amount you might attain in Warlords dungeon gear?

500stats

Haste is still better, and our base generation has grown to 19.5 RPS. What about 1000 Crit and 1000 Haste, something you might see in the first raid tier?

1000stats

We’re nearly hitting 21 RPS, and Haste is still clearly the superior stat. But what if we choose to purely stack Haste, since it’s clearly objectively better than Crit?

2000Haste

Over 21.5 RPS, and Haste still generates more Rage than Crit until the GCD cap.
 

Conclusions

There are two very clear conclusions visible.

  1. Crit is objectively worse than Haste until GCD cap. Even if the two generated similar amounts of Rage, Haste would still win because of the mitigation benefit from Tooth and Claw, and the increased uptime of Ursa Major.
  2. We are potentially generating too much Rage simply by executing our rotation.

In order to fix (1) Crit needs to either generate substantially more Rage than Haste, or also contribute to our survival in some other manner. However even if you simply increase Crit’s contribute to the Rage pool, I’m not convinced that the additional benefits of Haste won’t continue to outweigh it. Especially given how much base Rage generation we have.

(2) is something that is impossible to evaluate without knowing what Blizzard’s targets are. The concept makes sense from a high level though. The higher our base Rage generation is, the more incentive we will have to seek out secondary stats that do not contribute to Rage generation. I’m just really worried that our base generation will be too high, especially after Tooth and Claw becomes free.

If you want to play with the SS yourself, the link is available under “The Maths Corner” above.

Getting Into Theorycrafting

January 15, 2014

The idea for this post came from a Twitter discussion between myself, Poneria (author of the Warlock column on WoW Insider), Dayani (author of Healiocentric), and Theck (author of Sacred Duty) about how someone should start theorycrafting. Something that was brought up is that noobie theorycrafters find it far too daunting of a hobby to get into. So I thought I’d share with you how I got started, and maybe you can take some inspiration from it.
 

In an Expansion Far Far Away….

Some (or most) of you may not actually know this, but I only started seriously “theorycrafting” at the tail end of Wrath. As you may or may not remember when the pre-Cataclysm patch hit, Swipe was doing basically no damage. It was actually causing some pretty significant problems for Bear tanks (including myself) that were still dallying around in ICC. I looked around the on the forums, and didn’t see anything that would explain why this had started happening. Since nobody else appeared to be doing anything, I took it upon myself to do some digging. Back then I didn’t do any sort of empirical evidence gathering – or turn out to be right even – I did dig deep enough to get a response from a Blizzard CM. That got me noticed by a couple people you might know. Reesi and Fasc.

I had gotten a taste of what it felt like to be recognized…..and to be honest I liked it. I wanted to pursue it a bit further. So naturally the first step was to learn more about combat mechanics. I had a bit of an understanding based on the years of experience already playing the game. I knew what the various stats did but I didn’t really study them in great detail. So I took the next step.
 

Dissection

I took Fasc’s spreadsheet (at the time) and started playing with it. I learned what each of the stats did, how they interacted, coefficients, ratios, the list goes on. This knowledge helped me find defects in the spreadsheet and help Fasc fix them. Not only that, but once I understood how Armor worked, I moved on to what would be my first serious bit of theorycrafting.

Back in Catactlysm beta Astrylian had started a thread on EJ for basic storage and updating of Guardian information. During Cataclysm beta it quickly became evident that this information was not being kept up-to-date. I found that abilities were not doing the amount of damage they should’ve been doing, at least according to the listed AP coefficients. Since Astrylian was no longer updating his post, I decided that I might as well start doing tests myself. This lead to what is now known as the DPS/TPS Spreadsheet which you can find in the menu above. Not only that, but it would also lead to determining what the ideal DPS rotation was for Bears in both Cataclysm and Mists of Pandaria. Tangedyn and Yawning would go on to use this information in Mew, and most recently Pawkets has been using it to keep SimC updated.

None of that would’ve happened if I didn’t first take the time to learn WoW’s combat system, and how it affected my class. Pretty much all of that information is available somewhere on the internet nowadays for your particular class and spec. A quick Google search is usually all you need to get started.
 

It’s All About Accuracy

One of the things that will make or break a serious attempt at theorycrafting is accuracy. I’ve previously mentioned that my first attempt wasn’t even remotely accurate, primarily because there was no practical way to gather the data to make a diagnosis. For most of you out there, this is not the case. There aren’t any ambiguous mysteries left in this game, and any that are introduced are swiftly clarified by Blizzard themselves. Therefore it comes down to making sure that the data you’re presenting is actually accurate. The two methods that I use the most to ensure accuracy are In-Game Experimentation and Peer Review.

In-game experimentation is actually relatively simple, and usually involves things like target dummies. For example the method of verifying the AP ratio on a physical attack reduced by Armor:

  1. Strip all gear and buffs.
  2. Use the ability on one of the respawning target dummies in a starting area (I used Stormwind). These dummies have 0 armor – verified by testing for a difference in damage between a dummy affected by Weakened Armor and one that wasn’t).
  3. Add various levels of gear and repest (2).
  4. Compile the results and determine the slope. This is your AP modifier.
  5. Check the slope by calculating the damage value from AP at various levels of gear. If all have the same base damage, you have the correct slope and your damage equation.

Of course, when you’re presenting your information it’s a general rule that you will include your data and your methods so that they can be replicated by others. That way they’ll know you’re right.

Peer review is the act of asking someone to look over your work. For the information I compiled on trinkets in ToT, I asked Theck and Hamlet to look over it to make sure I had done it right. Since they were the ones that did the original proofs (one of them even at my request – remember Talisman of Bloodlust?), it made sense to ask them for a little help. It’s worth pointing out that asking someone in private – in game or a DM over Twitter – is much different than doing it publicly. Most theorycrafters are actually quite nice, and are very willing to help out when asked. However when you do ask for peer review, don’t harass the person you’re asking. We’re typically a very busy bunch. Here’s a general overview of the projects I have going on right now:

  • Writing Blog Posts for TiB
  • Hosting, Scheduling, and Recording TWP
  • Moderating and Responding to TiB Forums
  • Checking in on the Official, MMOC, Icy-Veins, and EJ Forums
  • Running a Heroic 10m Raid Team
  • Creating Video Guides
  • Streaming

And that’s just the WoW related stuff. We’re very busy people. Nice, but busy. We’re happy to help, but if you ask us you can’t harass us to get it done for you. If you don’t hear anything in a week or so, it’s fine to just check in and see how things are going. But if you nag us daily or something else equally ridiculous, you will swiftly become ignored.

Remember if you want anyone to take you seriously – be it your audience or someone reviewing your work – you must be professional.

Hello Guardians!

I have a lot of things to cover, so this one may be longer than normal. Most of it is just general tank stuff, but there are a couple of Guarfdian-specific things I’ll cover as well.
 

Buraan Joins TiB!

This is by far the most important piece of news I have to announce. After Wens quit because of R/L and my own guild’s inadequacies, there’s been a distinct lack of heroic-level content on TiB. I’ve always maintained that the best theorycrafting is done by 1 part math and 2 parts practical experience. With that in mind, I needed someone to pick up the slack in terms of heroic content.

Who better to have talk about it than (agruably) the #1 Guardian in the world? Yeah, I don’t have an answer to that either.

In any case, it is with great pleasure that I announce Buraan as the new contributing author for TiB. He’ll be covering heroic progression content through SoO and hopefully beyond.

Obviously you should follow him on Twitter and watch his stream as well.

Welcome!
 

PTR Changes

There are an absolute fuckton of these this time around. I’ll try and make sure I catch them all.

Vengeance now grants Attack Power equal to 1.5% of the damage taken, down from 1.8% (The tooltip said 2% but it was actually 1.8%).
Tanks no longer receive Vengeance from many persistent area damage effects (standing in the fire) or from missed attacks (dodging and parrying an attack will continue to work as it has before).
There are now diminishing returns on Vengeance gains while tanking multiple targets. Each additional target grants progressively less Vengeance.

The first two are pretty obvious. Vengeance was getting out of control compared to tank survival, and standing in fire to increase your Vengeance was a design oversight anyway. It’s the last one that’s rather vague. Thankfully Lore posted some details for us:

The basic, concise explanation is as follows: The Nth strongest (based on pre-mitigation average auto attack DPS) mob that has hit you in the last 5 seconds grants 1/Nth of full vengeance with their attacks. N is recalculated on every hit taken.
So here’s an example. Say you’re tanking 3 mobs – we’ll say it’s a boss and two adds. The boss has pre-mitigation average auto attack DPS of 1500k, one add does 400k, and the other add does 300k. The game will form a list of those mobs from 1-3, like so:
1. Boss: 1500k DPS, 1/1 (100%) of normal vengeance is granted
2. First add: 400k DPS, 1/2 (50%) of normal vengeance is granted
3. Second add: 300k DPS, 1/3 (33.333%, repeating of course) of normal vengeance is granted

This would of course continue as more mobs are being tanked (granting 1/4, 1/5, 1/6, and so on). Also, if the second add were to land a hit at any point when the first add hasn’t attacked you in the last 5sec (such as if it swings first), that attack would grant 1/2 Vengeance instead of 1/3.

So the example Lore gave is totally unrealistic. In order to put it in perspective I came up with something that most Guardians are probably familiar with: Heroic Tortos Bats. Details below (note this for 10m heroic):

A Vampiric Cave Bat on 10m heroic has an autoattack DPS of ~85k (taken from a friend’s log from last week’s kill using approxmiate Mastery values) give or take. Click here for log.

Which means under the current Vengeance scenario we’d cap out at around ~240k (20 * 85000 * 0.018 * 8) after 20 seconds. The bats die long before that happens though.

Under the new scenario we’d end up with: 30 + 15 + 10 + 7.5 + 6 + 5 + 4.28 + 3.75 = 81.53.

Slashlove (one of the Tanking forum regulars) made a quick post positing that using 1/sqrt(n) would be a better idea than simply 1/n while accomplishing the same goal (Source). Let’s look at what happens then:

30 + 21.2 + 17.3 + 15 + 13.4 + 12.2 + 11.3 + 10.6 = 131.

Suddenly much more palatable. Yeah, I like Slash’s better. Another thing to remember is this same logic also applies to Challenge Modes and Proving Grounds, both of which feature a plethora of AoE pulls. So maybe we’ll see a change to this formula, and maybe not. Only time will tell.

So as not to affect Challenge Mode leader boards, the above Vengeance changes will not apply there. For Challenge Modes, Vengeance will continue to work as it did in patch 5.3.

Well apparently time did tell. There you go.

Chance on being hit by a melee attack to gain a 20% reduction to all damage taken for 15 sec. (Approximately 2.57 procs per minute, ICD: 3 sec)

So this is the update to the tanking meta gem that was mentioned last week. The change to all damage reduction by itself is really good, but bumping the RPPM up to 2.57 takes it to almost a 50% uptime (actually ~47%, but hey). That makes it incredibly good, and definitely much, much better than it was before.

Does it compare to the existing DPS LMG? Probably not yet. However I’m definitely expecting that tank RPPM mod to get nerfed with extreme prejudice in an upcoming build. That will definitely put the tank LMG solidly ahead.

Trinket, enchant, set bonus, and legendary meta-gem effects whose triggered effect benefits from haste no longer also have their chance to trigger the benefit from haste. Activation chances for those effects have been adjusted to compensate.

There’s been a whole host of changes to the RPPM trinkets. I took the liberty of updating the RPS spreadsheet with the changes, and here’s the result:

Note, all of these trinkets are the double-upgraded versions. Primarily I’m just trying to show how fucking good Renataki and Bloodlust are now. Everything is basically complete shit by comparison. The new RPS trinkets in SoO don’t even come with passive stats, so they’re fucking awful. Granted almost everyone is going to be using the CDR trinket anyway, but still. It’s good to know what your RPS options are. Special thanks to Theck for helping me sim Bloodlust with the new ICD.

Thick Hide now reduces the cooldown on Barkskin by 30 sec.

I’ll admit, my first reaction to this was WHAT THE FUCK. Then I realized this was probably part of the whole “solution to Nazgrim” thing GC was tweeting about last week. I checked with Buraan, and he agreed with me. So with the CDR trinket we’ll have a 25 second CD on Barkskin (30 / 1.2 = 25). This means that we can have up to 2 minutes and 12 seconds of 100% Savage Defense uptime. That’s actually kind of ridiculous. Close to triple the current value.

That screams broken to me, but what the heck do I know. Everything about this patch screams broken to me. However I wouldn’t be surprised if our 2pc bonus changes as a result.

Dream of Cenarius now increases the Critical Strike Chance of Mangle by 10%. Chance to proc a Dream is reduced to 40%.

I actually just tested this on the PTR. The proc is now 20 seconds in duration, which is pretty incredible. The real question becomes is the Mangle change enough of a DPS gain to offset the GCD loss?

Well the number of procs we get in ~553 gear is: 0.8 * 0.4 * 0.21875 * 60 = 4.2. So that’s 4 GCDs we’d spend per minute (out of 40) on Healing Touch / Rebirth. For the sake of argument let’s assume that all of these GCDs are Lacerates. We then know that Lacerate does 0.616*AP in damage, so missing 4 per minute would be a loss of (2.464 + 1.848) or 4.312*AP in damage.

We also know that Mangle does (0.5*AP) + 7*WeaponDPS in damage. In the course of 1 minute you would have ~13 Mangles (0.21875*60). Without DoC those Mangles would deal 11.05*AP + 154.7*WeaponDPS in damage. With DoC this number increases to 11.7*AP + 163.8*WeaponDPS. A difference of 0.65AP and 9.1 WeaponDPS.

Subtracting like terms we get 9.1 WeaponDPS = 3.662AP. Since we know a 561′s weapon DPS is 8187.5 that means the break even point is (9.1*8187.5)/3.662 or 20345 AP.

So yes, it’s still a DPS loss. How much?

At 200k AP it comes out to around 12k DPS or so. Nothing to sneeze at to be sure, but look at what we gain in return. It’s probably most analagous to the old Battle Healer glyph. Yes we trade a bit of DPS, but we gain a ton of very effective healing in return, plus a little Rage as a bonus. I’ll take that trade any day of the week.

Yeah, changing the way it works. Long term, we want Guardian less focused on dodge more on AM. High armor and health are cool.

At first this caught me by surprise. However after a bit of thinking I realized that this is definitely a 6.0-era change. What could it be? Well a while ago on MMO-Champ (I’ll be damned if I can find the exact post) there was a suggestion to have Savage Defense also increase our Armor. I think that’s the direction GC is talking about here. Cool by me.
 

And one more thing…

Oh yeah. And this happened.

<3

TDR: Haste vs Mastery

April 29, 2013

Introduction

One of the things that has intrigued me for some time is the concept of Haste as a TDR stat. Ever since the introduction of the Indomitable Primal Diamond there’s been some interesting questions surrounding the concept of Haste as a TDR Stat. But it hasn’t really been determined exactly how it compares with simply going for Mastery. Well, I have the answer :)
 

RPPM – A Recap

The legendary meta gems all function on the RPPM – or “Real Procs Per Minute” – system. Hamlet does a much better job describing the math behind RPPM than I ever would. In any case it’s enough to say that anything on the RPPM system is improved by how much Haste Rating you have on your gear. Guardians of course are better off than most because of our passive bonus from Bear Form.

The question then becomes is it more effective to add more Haste to increase the effectiveness of the new meta, or add more Mastery for passive damage reduction? Turns out it’s not quite that simple.
 

A Tale of Two RPPMs

You might recall that something called “Bad Luck Protection” was added to RPPM trinkets recently. Well as of yet we have no confirmation whether or not this was actually added to the legendary metas or not. However that doesn’t mean we can’t compare the two and see what happens!

The graph plots total damage reduction on the Y axis, and the amount of stats gained on the X Axis.

Before I go any further I should note that these numbers were generated using my own stats. Now you could replicate the calculations for yourself, but the relative results will be identical to what you see above, until Armor is capped. Hopefully now you understand why I made the point about “Bad Luck Protection”. Unsurprisingly – at least to me – Mastery still comes out on top in terms of overall damage reduction.

That doesn’t mean this added side benefit of Haste might not make it substantially more valuable to some. It’s worth noting as well that this doesn’t count T&C, since I can’t really come up with an effective way of modelling that. It pretty much requires a sim, something that I don’t have the expertise to build….unfortunately.

As always, it’ll be up to you to weigh the pros and cons of each stat and determine what you want for yourself and your raid.

RPS Stats and You

December 9, 2012

Hello Guardians!

I’ve been wanting to do this sort of research for a while, but haven’t really had the time until this weekend. I was looking at how the various Rage generation stats interact, and determining if any one stat was better than the others. I was inspired by something Theck did for Protadin DPS stats some time ago. Thankfully calculating Rage generation is much easier, but that didn’t stop me from making it complicated :)

I had originally thought I would use a similar approach – have a set of assumptions and use a spreadsheet to produce a pretty graph to explain the results. However I realized that was a terribly huge amount of work and went looking for ways to make it easier on myself. Then I realized it would be massively easier if I could just alter the base stats and buffs via options on the spreadsheet itself. In short, I taught myself a bit about how to code things into Excel to produce what I was looking for. Lets look at the results using me as an example:

It turns out there were a couple bugs in the original version of the spreadsheet. While I guess that isn’t really a surprise, It’s unfortunate that I kinda violated my own mantra of “Make damn sure everything is right.” In any case it’s fixed now, and now the real results are shown above.

So it turns out Haste does not actually generate more RPS than Crit. However what is still true is that the RPS increase required to power the additional T&C procs is about half of the total overall RPS gained by choosing Haste over Crit. That being said since T&C is quite worthless for some encounters (Lei Shi, Stone Guardians) and not as powerful as FR – especially not with the 4pc bonus – whether or not it’s advantageous to choose one strategy over the other is debatable.

What has definitely been confirmed is choosing Haste for fights which high physical EH requirements (Heroic Sha of Fear comes to mind) is a good idea. T&C plays very nicely with Savage Defense on fights with high damage melee swings if you have the extra Rage to power it. You can play around with this yourself and move the Haste value up and down.

So what does this mean for you?

Well for heroic 25m encounters with high melee damage it primarily means you’re going to want Haste instead of Crit. There are far more people to make up the tank DPS difference between the two, and you gain increased mitigation by going Haste – which is the big difference for tanks in 25m. For 10m it’s a bit more of a tough sell. Tank DPS is significantly more important in 10m than 25m, so it’s possible that the DPS you lose by going Haste over Crit could make or break a kill. Furthermore bosses don’t hit as hard in 10m as they do in 25m, thus meaning you can definitely afford to sacrifice that little bit of mitigation to do more DPS.

Once we get into the next tier of content I expect Haste stacking to become significantly more common in both raid sizes.

If you want to play with the spreadsheet, you can find it in the “Maths Corner” menu above. Some quick notes on how to use it:

  • Put in your unbuffed stats/ratings in the green section.
  • On the options page you can set the options that will affect the output.
  • It is assumed you aren’t a baddie and always have MotW up.
  • Bear Form, LotP, and Crit Suppression are automatically calculated.

If you find anything you think is an error, feel free to post a comment below, or contact me on twitter or some other means.

The next thing for me to look at is DPS. But I gotta figure it out first.