Healing Theory, Part 6: The Mana Economy

Previous posts in this series can be found here

Much of the focus on this series so far has been on Spirit and mana. Choices surrounding mana are some of the least obvious and most interesting character setup choices in WoW. They allow gear decisions to impact gameplay in a way that is somewhat unique. And, from our current perspective at the end of raiding in Mists, the story of how healing gameplay changed since launch is largely a story about mana. This is particularly interesting because I think, for reasons I discuss below, that the designers tried to avoid allowing healers to reach this point of having such ample mana at the end of Mists, after seeing it happen in Wrath and Catalysm.

This post continues the thoughts of earlier posts in the series, which focused on the difference between cooldown and non-cooldown heals and why that difference is important to an understanding of mana. Here I explore some of the theoretical foundation for that distinction and how it helps us make gear and play decisions.

The Balance Sheet: Mana Assets

One obstacle to understanding mana is that information about your total mana income and expenditures is obscure; in typical play, your only information is how full your bar is at a given moment. But since you spend many bars’ worth of mana in even a short encounter, this look is actually not too informative. For a better understanding of where your mana comes from and where it goes, we want to instead look at an accounting that considers an encounter as a whole.

Let’s work through a example on paper and see how it looks. What we’re looking for here isn’t a set of detailed output numbers, which would be better served by a full-blown spreadsheet like my TreeCalcs, but the overall picture and what it can teach us about the way we think about mana.

The first question is how much total mana I have to spend over the course of an encounter. That depends on many variables, but I’ll illustrate a typical hypothetical example for a 6-minute fight. I might have (values in thousands of mana):

Healer Pie

Since all of these returns are quite consistent, except for the small RNG fluctuations in the trinket and meta, I have a very good estimate of how much mana I might have to spend over the course of an encounter of this length. 1.9 million is just over 6 bars’ worth, which should indicate just how limited a view you get by thinking only about your one visible mana bar and how much of it has been spent. Aside: it might be interesting to think about an addon that shows this total at the start of the fight, and how much I’ve spent from it, as an alternative to the conventional mana display.

I left out for this purpose the Druid 2T16 set bonus and Clearcasting, which can only be applied to specific heals that aren’t often used otherwise (unlike the meta), and are more easily accounted for as free healing done rather than free mana. Similarly, the accounting might be a little more complex for certain refund mechanics like Rapture and Mana Tea, but as long as you treat them consistently as either added mana or as reduced costs, your results should be the same either way. To be specific, (jumping ahead for a moment), the curve of total healing done as a function of mana will ultimately look the same whether you think of some mechanics as taking mana and then giving it back, or as simply giving free casts. For purposes of a simple chart rather than a full class spreadsheet, I went with what I thought wouldn’t be misleading out of context.

In general, the picture would not change much for other classes. In fact, the entries other than Innervate and meta gem would not change at all. In place of Innervate, a Paladin would have 146k mana from 3 Divine Pleas, or a Priest 162k from 2 Shadowfiends at low haste (or 174k if one was aligned with Hymn). Shaman and Monk wouldn’t have any, as they only have mechanics that are easier to think of discounts rather than as mana income since they are based on number of spellcasts rather than time. And it turns out that the value of a meta proc is reasonably balanced across classes, loosely speaking, with many typical uses of a proc costing 20k or 30k mana: 2 Chain Heals, a Chain Heal and a Magma Totem, 2 Jabs with Muscle Memory return, a Holy Radiance, etc.

Variations

One key observation, to revisit a point I touched on in Part 2, is that Spirit is only 26% of this makeup (slightly more now that Innervate size depends on Spirit, which it didn’t before patch 5.4). In fact, the only changes that would be made to the accounting if I had 0 Spirit are that I’d lose the 487k mana from Spirit regen, and two Innervates would return 48k mana instead of 120k. The total would still be 1.33 million mana with 0 Spirit, 70% of what it was with 12,000 Spirit above.

One other number. Let’s say I’m back at ilvl 463 at the starts of Mists. The following things were different:

  • With around 5000 Spirit, I’d get only 203k mana from it over 6 minutes.
  • I had no legendary meta.
  • A standard-issue Int&mana trinket, Price of Progress, gave 30k mana in 6 minutes. (A ilvl 463 version of Horridon’s or Dysmorphic would have given closer to 42k mana at 12.5% haste. RPPM generally caused healer trinkets to get stronger).
  • Two Innervates still gave 120k mana, as it didn’t scale with Spirit then.
  • A Shaman with only 5000 Spirit would give me 36k mana with two Tides.
  • The new total is 1.17 million mana, 62% of what it was in the first example.
Mana Bar

Of the difference of 719k mana in this example, only 284k, 39%, is due to an increase in Spirit from 5000 to 12000. The difference would of course be even less if, like many people, you geared heavily towards Spirit early on and less so now. If you maintained similar gearing patterns, that increase from 5000 of a stat to 12000, a 140% increase, would correspond to a gain of 94 ilvls. The amount added from the meta (285k) is almost identical to the entire value of the added Spirit in this example (evaluated at 3 Rejuv casts proc, the meta is in fact worth 7000 Spirit).

So less than half of the mana difference between then and now is allocable to increased Spirit. In fact, you could wear 0 Spirit now (hypothetically–due to healer itemization you probably can’t wear 0 Spirit even if you want to) and have more mana than you did in the early part of the expansion, before the legendary meta.

The Balance Sheet: Mana Expenditures

What can I do with 1.9 million mana in 6 minutes? I’ll continue the example as a Druid, but it should not be too difficult to apply the reasoning to any class. My most important on-cooldown spell is Wild Growth. Let’s be generous and say I cast it every 8 seconds for the entire fight. In other words, I spend as much mana as possible on Wild Growth. 45 casts at 13740 per cast is 619k mana, just under 1/3 of my supply. Similarly a Swiftmend every 16 seconds would add another 115k spent. Lifebloom is very small; even if you manually refreshed it every 14 seconds (as opposed to using Clearcast Regrowth or 2T16 Healing Touch), it would be 91k mana. In reality it will be much less.

The most a Druid can possibly spend on the core rotational heals in 6 minutes is around 800k mana. The remainder is the discretionary budget for no-cooldown heals. That means that I have over a million mana to spend on Rejuvs (including the free ones from the meta), even with the occasional Bloom or other odd spell. 1.1 million mana is 126 Rejuvs, or about one every 3 seconds over the course of the fight.*

Thinking back to the comparison above about mana resources available at the beginning and end of the expansion, let’s see how that chart would look if it was colored to reflect the mana expenditures (instead of mana income) in this simplified model:

Mana Bar 2

You probably don’t play precisely like this. But if you imagine an encounter with relatively consistent healing needs, such that you rarely got for long stretches without casting Wild Growth, this is quite a serviceable picture of how should strive to play. In particular, of how your spell use should be affected by variations in your mana supply. The point illustrated by this graph is one that’s been a consistent theme of this series: extra mana affects how much you use your class’s best heal that has no cooldown (in this example, Rejuvenation). As Part 3 discussed in depth, when healing in a limited-mana environment, you want to solve problems with your efficient cooldown-bearing, rotational heals as much as possible. In other words, by trying to mimic the left bar in the above graph. The more you lean on the spammable (and lower-HPM) heal before you have the resources to support it, the more you cut into your ability to use your best heals as much as possible throughout the fight.

For your interest, here are some references on mana usage from other major rotational spells. To fit with this post, I’ll continue to express these as theoretical max mana (in thousands) spent on a spell in 6 minutes, rather than mean MP5:

*Druid-specific aside: so you simply can’t spam Rejuv nonstop for the entirety of an encounter. If you feel like you do, it’s because you’ve stopped noticing the intuitive pauses most of the time, that let you spam it fully during intense healing phases. It’s a class that requires casting nothing some percentage of the time (although that percentage is small at the gear levels we’re discussing here). Less experienced Druids often haven’t picked this up, and spam Rejuv too readily, resulting in the feeling that they have mana problems or need more Spirit.

The Mana Curve

The above description, that I called a simplified model of casting, differs from reality in two important ways. First, if the upkeep of your rotational heals is too large compared to your total available mana, it can be impractical or impossible to heal using those alone. Second, variation in healing needs during an encounter mean you sometimes need to stack filler heals onto cooldown heals in high-demand moments, regardless of ideal mana planning (notice how these two issues are related).

I’m going to draw the same picture I drew in the previous section, but in a different way. This one is purely conceptual–not to any scale.

Healer Diagram

There’s a lot going on here. If you had 0 net mana to spend, the only healing you could do is with your free heals (e.g EfflorescenceRecalled Healing Stream Totem, Chi Wave). The first points of mana you spend allow you to cast efficient, cooldown-based heals that all classes have. As you fill up on your capacity to cast those as many times as possible per encounter, you spend each marginal point of Spirit on less efficient heals, until you get to the one with no cooldown, which each added point of Spirit is spent on. This is the story I’ve been telling so far, and is reflected in the blue line.

The red line shows what’s more likely to happen in practice, and reflects the two points I just mentioned. Transitions from one phase to another are smoother, since you’re starting to mix in the less efficient heal as needed before fully capping out on use of the previous heal. In particular, at the cusp between the “cooldown” and the “no-cooldown” phase (around where the “curved in practice” arrow is pointing), your filler heals have to be mixed in to some extent in any healing scenario, and they will cut into core heal usage until you have more of a cushion of mana. This results in Spirit retaining some higher value even past the cusp, as you establish enough of a reserve to use the rotational heals to their full extent in practice. While Druids tended not to be too much affect by this early in Mists, Shaman were more so (see this comment from Vixsin and my reply on an earlier entry, anticipating this post). For reference, before the Healing Rain cost reduction mid-Mists, casting a Healing Rain (25860 mana) every 11.5 seconds for 6 minutes took 810k mana, and the Shaman’s mana supply would have been closer to 1 million rather than 1.1 million since they do not have Innervate.

The other important feature of the red line is that its growth falls off when you have a large amount of mana. The problem with continually adding filler heals by increasing in mana is that they only allow you to add healing in one way: more and more uniformly spread over time. At some point, you are already casting full-time during the demanding parts of an encounter, and more mana simply lets you add in casts at other times, which is not especially useful. This is what’s generally responsible for the class-wide turn away from Spirit among healers. As we got to the end of Mists (bearing in mind the large role the meta gem played here), we had the mana to cast at all the times we wanted to. There’s little reason for anyone to go out of the way for more.

In between these two extremes is a roughly linear range where more Spirit allows more useful casts of filler heals. This is primarily where my previous discussions were aimed, where Spirit gear is the most interesting, and where I believe healers are intended to be. The slope of the line in this region corresponds to the efficiency of your best no-cooldown heal, as described in Part 3.

Inflation in Mists

The story of mana in Mists is once again one of healers having more of it than is ideal by the end of an expansion. It’s not as drastic as it was in Wrath or Cataclysm, due to measures the designers took to prevent this. Base mana no longer increases with Intellect. Spirit regen no longer scales with the square root of Intellect (which used to cause it to scale with the 3/2 power of your stats). There is no longer powerful regen like Replenishment based on your max mana (and therefore scaled with Intellect). And the effects of these changes are clearly visible–our total available mana has increased by less than a factor of 2 from the beginning of the expansion to the end, whereas, for example, DPS has increased by far more than that. For raiders with the highest available gear, ilvl 580, total character stats are 297% of where there were at ilvl 463. So healer mana has been kept much more under control than in the past. If not for the singlehanded effect of the legendary meta, this discussion would probably be quite different.

When I first saw the legendary meta, I didn’t think straight away that it was overpowered. Because from a certain perspective, it’s not. The value of the DPS metas to DPS classes is similarly huge. The goal of these legendary rewards was to feel like they brought a transformative bump in character power. The problem with healers was pouring that sudden increase in character strength all into the mana balance. It counteracts all the work described above to make sure that the difference in mana between the beginning of the expansion and the end was not overwhelming. And even with the meta, the situation is not disastrous–mana is dancing around the boundary of being a nonfactor, but has not fallen completely into it. It’s just far enough that you generally don’t want to gear for more.

For some stats, it’s totally fine if they increase by a completely arbitrary amount between the beginning of the expansion and the end. Most importantly, attack power and spell power. These overall damage/healing multipliers could increase by 1000% if the designers wanted them to and it wouldn’t cause any mechanical problems. Haste is a more complicated since it affects the pace of gameplay, you can’t let it get out of control. Healer mana, more than any of these others, wants to stay in a tight range where you don’t have too much and don’t have too little. The importance, and generally low cost, of rotational heals provides an important foundation–it ensures that there is a well-established playstyle for each class even in low-mana setups. Beyond this, Spirit needs to be tuned so people can use filler heals in a small (but not too small) portion of free time at the beginning of the expansion and a large (but not too large) portion at the end.

Conclusion

I started discussing healing in Mists with arguments that people overvalued Spirit as the expansion started out. This was based primarily on the fact that you had a solid core rotation of cooldown-based spells even at minimum Spirit, and throughput stats leveraged those existing spells for added healing that you really needed as you were getting stated. Midway through Mists were the middle posts in this series, looking at the value of Spirit in the ideal range (for the purpose of interesting choices), where you could choose between more throughput on existing casts, or more casts of a filler heal. And now, while those discussions are little academic to most people due to the current state of healer gameplay, there is still a good opportunity to look at the big picture of how mana works, in anticipation of the next iteration of the game. As you can see, the framework in this post is consistent with all of the discussion so far.

This discussion, I think, will continue in full force in Warlords. While they’ve announced that Spirit will be on fewer pieces (to facilitate hybrid gearing), that won’t make the question go away. It will only eliminate the option of full Spirit stacking, and perhaps make it a little easier to limit the variation in mana between the beginning and end of the expansion. I don’t expect we will see something like the healer meta gem again. I look forward to seeing how the theory applies as soon as we have detailed info on the classes in Warlords.

Raid Awareness is a Learned and Practiced Skill

Italicized quotations throughout are from my old raid leader Sebudai, well-known for his efforts to teach his raiders to be better at playing WoW.

I’ve written many WoW guides over the past years, largely covering the details of min/maxing a particular class, but I always knew I was addressing a narrow slice of what makes a good raider. While there are reasons that players who know the nuances of perfectly optimizing their class’s output and ability use are prized, even they are no substitute for a raider who excels at the most important skill of all: not dying.

Volumes have been written on how to do good DPS, healing, or tanking. If you raid or want to raid at an intermediate or high level, I imagine you have long immersed yourself in that discourse already. There are many reasons why existing WoW guides, forums, and discussions are largely about optimizing those roles. They are the primary way players are measured by themselves and by raid groups. Large parts of them can often be solved with math, leading to simple and easily implemented results. But most important, I suspect, is a widespread impression that I hope to refute in this post: that your awareness and survivability in raids is a part of who you are as player and cannot be changed.

After outlining the basic premise that not making avoidable errors that kill you or other raid members is an area of play you should seek to improve, the bulk of this post is about specific things you can do or practice to accomplish that. Through the survey of techniques discussed—gearing your UI towards awareness, being more cognizant of your encounter routines, and constructive behavior post-wipe—what I most want to convey is a mindset. I couldn’t list out all the factors in the mental game of raiding even in much longer post than this. But if you adopt the ethos that every death is a puzzle to be solved, that somewhere in series of events leading to it is a decision you could have made better, you can train yourself to look for it.

You Are Your DPW: Deaths Per Week

“You guys keep dying in the shadow realm. I don’t die in the shadow realm. You just need to play better. That’s my current assessment of the strategy.”

The MVP of your raid group isn’t the person at the top of the DPS meter; it’s the person who hasn’t died by standing in fire in 3 months. Doing elite DPS is rare, but doing quite good DPS is somewhat common. A player who does quite good DPS and dies regularly to avoidable mechanics is nothing special. A player who does quite good DPS and dies very rarely to avoidable mechanics is the best prize a guild recruiter can find in their applicant pool. Because a raid full of those players, even if none of them are at the top of worldwide log rankings, is going to succeed at what matters. They’re going to win boss encounters.

Raiding at any level, it is a virtual certainty that the limiting factor on the speed at which you learn and defeat bosses is the rate of avoidable mistakes made by individual group members. No matter what other factors are present, multiple avoidable deaths (or sometimes even one) scuttle any attempt at a hard boss. With 10 to 25 people having to play for many consecutive minutes, and a win only being likely if virtually all of them make no death-causing errors on the same attempt, you can’t avoid the math of the situation. Even if you think your problem at a boss was “bad strategy”, realize how much this implicates your raiders’ error rates. Without mistakes, any strategy would take only one attempt to try and reject. Any wipe could be followed by a raid-level strategic improvement. Errors in play during the attempts are the reason a strategy persists for many attempts or even whole raid nights before enough evidence is gathered that something needs to be changed.

I won’t belabor this further except to state it as the premise of the remainder of this article: the most important way you can improve your skill as a raider and your contribution to your group is by reducing your rate of avoidable errors. With that said, the next important point in preparation for the meat of the post is that this error rate is not only important, but that you can improve it as a player.

Your Death Was Not An Accident, And It Was Probably Your Fault

“See how it was targeting me, and I moved, and then it didn’t hit me? It’s like magic.”

Raiding is fundamentally a challenge of mental organization. Your attention is a resource that’s every bit as real as your mana. Spending it on the wrong things causes you to make mistakes and potentially die.

When you stand in fire for 3 seconds and die, the problem is not that your reaction time is inhumanly bad (even if it were somewhat poorer than average, it would be well under half a second). A more correct identification of the problem is that you did not realize you were standing in it for at least (in this example) 2.5 seconds. Some possible causes or contributing factors might be:

  • Your visual scan of the screen has gaps of over 2-3 seconds where it doesn’t stop at the relevant part of your screen (here, your character’s feet).
  • Important features of your UI (for example, raid frames) are positioned such that the threat was not in your peripheral vision.
  • It was a boss ability that comes at a predictable time, and you let some other task take precedence over waiting/checking for it at that moment.
  • Your UI does not produce an alert whose attention-grabbing power is commensurate with the importance of the ability.
  • An irregularity earlier in the attempt resulted in your being in a different position from usual or doing different things from usual.
  • A event you typically use as a warning trigger (for example, a Vent call) didn’t occur.

Every one of these is correctible. If you attribute these deaths to random occurrences, a perceived innate limitation in your skills as a gamer, a fluke (an event with no predictive value), or the like, your progress as a raider faces an insurmountable barrier. The remainder of this post is about how to better address these causes of errors. The two primary methods discussed below are:

  1. Never being unaware of abilities or debuffs that are important enough to kill you, through proper setup of your UI before combat and visual scanning in combat, and
  2. Anticipating your response to boss abilities before they occur, through formation of encounter routines and revision of those routines after wipes.

UI is a Tool to Aim Your Attention

“You should have added ‘Corruption:Sickness’ to your UI. If you haven’t, I can’t prove it but you’re an asshole and we all hate you.”

If somebody pricked you with a needle every time the fire appeared under you, you’d notice it immediately 100% of the time. It would grab your attention over anything that you may have been looking at—it’s something that your brain is hard-wired to respond to instantly. Associating it with an event that needs to supersede all others for priority in your response (move out of it now or you die) is a perfect marriage of a threat with a corresponding alert. This is the principle you want to keep in mind when configuring your actual UI to recreate that result in a more practical, and less painful, manner.

UI is necessarily personal, but a good one is one where you’ve made your addons work for you by showing you what you need when you need it. Good UI is less about which addons you have and more about how you configure them. When looking to improve your UI, you want to look for the config option in the addon you already have that addresses some need you have. Pretty much the only wrong answer to “what’s the best addon for this task?” is “a popular one, with all the settings left at default.” If you haven’t decided or thought about what you need to see and when/where you need to see it, you won’t have a good UI.

One concrete example of UI that should be used by every raider is the presentation of debuffs that kill you rapidly unless you move. The UI implications of this are easy to describe because, as discussed, such an event always belongs at the same place in your mental priority: at the top. So the UI’s purpose is simple to understand. Always put this at the forefront. Unless you have an alert for such debuffs that cannot be missed regardless of where your eyes or your mind are, your UI is failing you in one of its simplest and most important functions.

I took screenshots of the moment I had a certain dangerous debuff (Sha Sear at the Protectors encounter) in both the default UI (for buffs/debuffs), and in my raid UI.

WoWScrnShot_012314_232342
WoWScrnShot_010314_010106

The top screenshot shows the default debuff icon near the bottom-left corner of the minimap. The bottom one is my raiding UI.

Not only do people in my raid never have to call out “Hamlet, you’re in the group with Sha Sear”, but this isn’t even hard to accomplish. Setting up this UI widget is a simple bit of preparation. A raider who fails to handle a debuff that can be solved in this way has chosen not to do it. In my view, they shouldn’t be viewed any better than someone who’s playing with no flasks. Worse, in fact, because their poor UI is probably far more likely to cause wipes than a minor DPS loss would be.

Visual Scanning

“I don’t care if you do 0 healing for the rest of this pull, just don’t die to slicers.”

A corollary to the UI discussion is that there’s a lot going on on your screen at any time. You can’t be looking at all of it at once; the best you can do is a sort of rotation that passes through all the important points of interest. Try to start being conscious of where your eyes are while you raid. You might go from your raid frames to your feet and back nonstop, not due to any alert or trigger, but simply as something you always do (it takes a fraction of a second).

At some encounters, not looking at your feet for 2 seconds at the wrong time can kill you. If follows that if your scan doesn’t cycle past them at 2 second intervals at the most, you’re leaving your survival to chance. Maintaining that tight of a visual scan takes very intense focus, but you can ameliorate the constant need for it with good UI alerts, discussed above, and a good encounter plan, discussed below. In contrast, you don’t need to divert your eyes to check your mana nearly that often (you probably have little need to know your mana status more often than every 30 seconds or so).

Once when my old guild asked what information I’d like to see on healer applicants, I told them I’d want to know the best score they could get at this flash game. I was only half joking. If you try it, it should illustrate the concepts of this section. Raiding is often made up of fundamentally easy tasks: reacting to something dangerous in a generous window like 2 or 3 seconds, using abilities in a familiar practiced rotation, using cooldowns at a planned time. The difficulty is in juggling all of it at once.

Note: I borrowed the term “visual scanning”, and the concept, from aircraft pilots, for whom it is a critical skill. Some studies have explored its relation to video games as well.

Keep Your Bossmods Under Control

“Don’t ever say ‘oh shit’ on Vent again. That helps nobody. Say it IRL and don’t push your Vent key.”

The other specific UI example I’ll go into is with regard to bossmods. It is very easy to have far more bossmod spam than you ever need (I surmise this is due to bossmod authors being inclined to show off the widgets they develop and having a strong bias towards turning things on by default that don’t need to be). Since UI is about drawing your attention to the things you most need to react to immediately, then having timers and alerts for everything a boss does causes an inevitable Boy Who Cried Wolf problem when you process the information on your screen. Without curating the alerts you need to have visible, there’s often a timer of some kind ticking down to 0 every few seconds. Realize the significance of this: you can’t know if it’s a timer you need to react to unless you read the small text on the timer bar, a task that absorbs a lot of attention, pulls your eyes away from everything else, and prevents reflexive responses from developing.

The problem is even worse when audio alerts are involved. Sound is a very powerful UI tool. Not only is human reaction time to an audio cue faster than to a visual cue, but it’s completely agnostic to where your eyes were. The catch is, to have a truly instantaneous reaction to the one thing at the fight that most needs it, you should only have one thing at each encounter that throws an audio alert. This is actually a completely practical way of recreating my hypothetical needle-poking feedback mechanism. If a loud chime means you have to move a few steps, and means only that, then after some time at an encounter you can start to do it without even having to think about it consciously. This is the best result. Multiple audio cues with different sounds can also work, but the reflex effect will be slightly less automatic. When every timer in an encounter comes with a bell or whistle, your bossmod is probably doing nothing more than giving you a headache.

My recommendation: the next time (or the first time) you do each fight, go into your bossmod config and turn all alerts off. All of them. After doing a couple attempts like that, turn on timers or alerts for abilities as it becomes specifically clear that you need each one. In particular, you should be able to articulate what you’re going to do based on that alert (“I want to press Barkskin two seconds before Swelling Pride“). Otherwise, think again about whether you need to turn it on.

Good Raiders Are Creatures Of Habit

“Engulfing Flame in 5 seconds, don’t die to this. . . . I specifically told you not to do that.”

UI alerts notwithstanding, the surest way to handle something that might kill you or wipe the raid is to be waiting for it. When you’re thinking of what’s coming next, and even what’s coming after that, not only are your odds of responding correctly very high, but the response will be executed calmly, leaving your attention free to continue thinking ahead. Your goal is to remain in that state continuously for an entire encounter, and much of the intense focus required in raiding at a very high level goes towards constantly updating that mental list of the upcoming events.

When I think back to the hardest fights I’ve done, I can essentially replay the encounter in my head, my own actions in particular. Heroic Lich King (middle phase): run in from the crumbling platform as transition phase ends, but stay to the left or right of the tank to not get hit by the add’s cone attack. Go to the clump spot for first Val’kyr (only actually clumping once add was dead). When the Valks grab 3 people, start running south and keep moving until Defile finishes casting. Circle around to second clump spot. Wait 10 yards away to see if Lich King casts Val’kyr or Defile first (the second one could go either way). If the yell for Val’kyr appears, move onto the raid marker; if not, move out and keep moving until Defile finishes casting. And so on. That encounter was brutal—if you beat it, you probably wiped 50 or 100 times to Defile alone—but once I had that routine, as long as I maintained it on a given attempt, I couldn’t fail it.

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If you’re not familiar with that fight, that’s okay, the point is what a routine for an encounter or a phase sounds like. It’s not merely that you know the response to each ability. It’s that you know what the order of events is. Most bosses use abilities on quite regular cooldowns, and you want to make the habit of noticing the rhythm. Sometimes it’s easy: Garrosh phase 2 always cycles DesecrationTouch of Y’ShaarjWhirling Corruption (but, notice how the 3rd Whirl is late enough to always come while you’re moving out of the 4th Desecration). Sha of Pride casts Reflection, then Banishment, then Imprison, then Manifestation, then Swelling Pride, repeating (as a bonus, Sha’s cycle is just over 60 seconds long, so you can close a Rift at the same point in the routine every time).

I sometimes fail any of the above mechanics, as does anybody. A common case is when an oddity earlier in the fight (say, tank having to move the boss to an unusual position) meant I had to improvise. That is unavoidable at times, and a good ability to think on your feet will of course be valuable. But the raider with no routine is in that situation every time. They’re doing something else like looking at DPS cooldowns, a bossmod alert goes off, and they think “Whoa, Iron Tomb (or Corrupted Brew, or Hurl Amber), guess I’d better move!” and look for somewhere to run to. If they even do notice it and dodge it, that is. You want to be person who’s thinking “I’m going to cast these next three spells, then it will be time to move for Tomb, and I’ll cast this instant while moving.” Or “After that spell I’m going to stare at the ground for 5 seconds until I spot the Amber targets, then go back to check on my DoTs.” When you put yourself in the latter category of player by having a plan, then most of the time handling a boss ability is not an issue of reaction whatsoever. It’s doing what you knew you would do, when you knew you would do it. And you’ll do better DPS to boot.

Postmortems

“Who just said ‘unavoidable’ on Vent? Who was it? I want to know who said that so I can back up and list the numerous ways that death was not ‘unavoidable’”

In the ideal case, upon a death or wipe you cause, you give not only an explanation of what caused it, but of what change could prevent it from happening. There’s not always a raid-level change to be discussed; sometimes it was truly an individual error (I was thinking about DPS and didn’t alert myself that the ability was coming), but even then the player should be asking internally what change should be made. Can you adjust your debuff or bossmod alerts (if so, ask for a resurrect and do it while people are running back)? Maybe your routine should consistently use that DPS cooldown either before or after that boss ability on every pull?

Admitting to being the cause of a wipe is laudable. People who won’t do so are likely outside the audience of this post, as they’re not primarily interested in improving the success of their group. But addressing people who do discuss when they’ve made a mistake, you have to make sure not to let yourself off the hook with responses that are useless. If I’m your raid leader and you missed an interrupt, don’t simply say it won’t happen again. Tell me why it’s unlikely to happen again. If you can do that, I won’t feel like we’re playing Russian Roulette with the raid every time your turn to interrupt comes up.

You’ve all heard an interrupter say: “I pushed the button, I don’t know what happened!” The statement may in fact be 100% true. But what you should focus on is that it accomplishes nothing at all. Train yourself to never say it. Same for “I think was lag” or “it must have been a glitch.” It’s possible you could get away with “lag” if you did it very rarely and only when it was the correct diagnosis, but people like that are so rare that it’s probably a bad habit to try. Don’t even get me started on “it showed up as interrupted on my screen.” Any raid leader worth his salt translates this in his head to “I almost pressed the button in time.” If you caused a wipe and you don’t have anything better to say than one of these confabulations, then accept that there’s nothing you can do this particular time to avoid being placed in the Russian Roulette category.

But if you’ve taken the principles of this post to heart, a failure will usually mean you have a meaningful productive comment to make while the raid runs back. Most of the time it’s as simple as having to make an individual adjustment to your routine. Even that’s valuable to describe as it shows the raid leader the wipe was worth something, and it helps other people in your class or role benefit. And sometimes there will be a raid-level change you can suggest to positioning or even something as simple as Vent calls. When you have any of these sorts of things to say during the runback, a good raid leader won’t even be angry about the wipe. Your job as a raider isn’t to never cause wipes—it’s impossible to learn a boss without wiping unless you’re doing trivial content. It’s to make every wipe you cause into one where the raid learns something.

Sometimes There is Fire

“When I ask what killed you, I’m not looking for you to say ‘Why, damage killed me, Sebudai! I died because I ran out of hit points.’”

If a raider of any level asked me how they could improve their play, I wouldn’t start by worrying about whether they use haste or crit. In truth, I’d much rather a newcomer to a raid team read this rather than any guide I’ve ever written about what talents to select for your class or what stat to reforge for. Most importantly, because knowing whether to use haste or crit is easy. When you start playing a class, you can learn that on the first day. But being a good raider who stays alive during encounters is hard. I’ve been trying to learn it for nine years. No matter how long you’ve been playing, what class or role you are, or what level you play at, you too can find room improve these skills for the benefit of you and your team.

Blizzcon WoW Announcement Responses

I’m finally getting around to writing down my initial reaction to the various things that were announced in WoW panels on Friday and Saturday at Blizzcon. I haven’t even caught up on everyone’s discussions since then due to travelling (…travelling and XCOM expansion being released), but it seems to good to get these down first anyway. Basically my first impressions of everything in no particular order. The biggest part will be on raid changes since those are most interesting for me (well, and there are no detailed class changes yet).

Raid Changes

Putting aside the name changes (which, aside from surely causing constant terminological confusion for the next many months, aren’t too significant), and putting aside LFR (because it’s not raiding), there are still 3 raid difficulties. But we’re going from [easy (Flex), medium (10 or 25), hard (10 or 25)] to [easy (Flex), medium (Flex), and hard (20)]. Many takeaways from that.

  • There’s no longer _any_ difficulty with two disjoint raid sizes. This is great. No more 10 vs. 25 issues. I don’t even want to rehash all the reasons that was a problem, except to the extent it comes up in the remaining points.
  • There is no more hard-mode content with fewer than 20 people. Some will see this as a dubious accomplishment, but I’ve been arguing to do away with 10H for years. It has a lot to do with the problems I discussed in the above blog post: primarily, a game with 11 classes and 34 character types can’t be balanced cleanly around 10-player teams when you’re considering the razor’s-edge tuning of Heroic raiding. “10H WoW raiding” was simply a less great game than “25H WoW raiding.” Slightly less great, but less great. I know there are some of you out there with exactly 9 friends. What I’d want most for you is a game where the systems were made from the ground up to dovetail with 10-player content, rather than a 25- or 40-player game that was pared down as well as could be managed.
  • Guilds can grow to 20 or 25. I think people will take some time to truly internalize this. We’re so used to saying “We’re a 10-person guild, how could we get to 25?” In Cataclysm and MoP, that was a valid question with no good answer. But now? The answer is that you invite people. You can! You’re so used to thinking that you can’t invite people (because there’s no “room” for them), but now you can. I know it sounds crazy, but you get from 10 to 20 by inviting people. You won’t be a 10-player guild in WoD, because there won’t be any such thing. You’ll be “a guild” and until/unless you’re raiding Mythics, you’re not pegged to any one size.
  • Flexible normal-level mode raid tuning. I’d been skeptical of this–not because I thought it would be bad, but simply because I thought (in fact, I’m still quite confident) it’s very hard to do. But they’re only releasing it if they think they’ve got it working, and I’m looking forward to seeing it. One key piece of the puzzle is a new tech feature they briefly mentioned: boss abilities that target N people will no longer stairstep at certain raid sizes, but will, at intermediate sizes, have a pro rata % chance to target 1 extra person each time. This is a crucial bit of tech that allows boss difficulty scaling to be smooth enough to fit within the expected precision for “normal” tuning rather than “easy” tuning.

One thing I still feel isn’t totally answered: why 20 instead of 25? This post very nicely answers the question “why 20 instead of 15 or some other smaller number.” But, to be frank, I didn’t consider 15-player as the only raid size to be a serious option to begin with. People always touted it as a solution to the 10/25 problem, but I never saw how it was a solution at all. 15 would have been tantamount to giving up on “big” raiding. I mention this only because 20 is still too close to 10 or 15 for complete comfort. Even for important goals like ensuring 1 of every class, 25 is a much more comfortable number. Specifically, it’s more than 2x the number of classes, which feels like an important threshold. When you have only 1 of some classes, attendance fluctuation will often give you 0.

I press on this point because the only rationale I have heard people guess so far is that it’s a sort of compromise. Something like, there was a debate between 10 and 25, and if one side flat-out “won,” people would be upset. Or more subtly, it’s the middle ground fallacy: when two sides are debating strongly, the right answer feels like it should be between them. Anyway, I hope that’s not the reason, since it’s a pretty poor one. I don’t know what it is though. I can think of a few other really minor advantages. 10% of the raid is tanks instead of 8%, slightly better for role composition. Hypothetically two 10p groups could merge (I think this is a rare case). There’s some advantage to having the flex size cap out at something higher than the hardmode size so you can bring the whole guild on farm runs. None of these, to me, outweigh the potentially added robustness of the 25-man raid size.

Overall, I think the changes are huge net positive. I said on 6/6/2013, the day Flex was announced: “[It] will probably take some thinking to lay out a good array of raid modes to cover the various kinds of players efficiently. Just to throw out brainstorms, I think the most lightweight extreme would be to have only 2 modes: flex and 25H.” I thought that was just an idealistic example to make a point, but man, they landed pretty close to it.

Just to address the most common complaint about the changes (“what will my guild do?”). If your guild is made of the right stuff–players who want to play together and have generally similar goals in WoW–it will be fine. I’m not worried at all about 25H groups, who are only affected insofar as their recruitment officers get a break at the turn of this expansion (for once). I do understand the plight of 10H guilds. It’s not fun to be the person to has to make changes for the good of the game as a whole. I think the portion who quit will be vastly outnumbered by the portion who find that 20M is no less fun than what they’re currently doing.

One Free Level 90

I know, you’re thinking, “this is the next most important announcement?” To me it is. We live in a different gaming world that we did in 2004 and people’s expectations have changed. In a lot of ways, as a gamer, I heavily resist that–I am perennially nonplussed by microtransactions in any form, for example (and I will be by the inevitable WoW ones that are already appearing in more microtransaction-oriented regions). But one I’m fine with is that newcomers to a game need a smoother experience getting pulled into fun content at the outset without doing a lot of work (WoW needs better onboarding, as the f2p marketing types might say). Some people, or most people in fact, like leveling more than I do, but you’d be hard-pressed to convince me that it’s the best part of WoW.

The only rationale that people seem to give for the requirement of doing all that leveling is that you learn to play the game and play your class in the process (“enjoyable quest content” is not a reason to require players to do it before doing other kinds of content). But any game that required people to go through 100 levels (or the equivalent number of hours) of tutorialization would be a failure. You shouldn’t look at WoW’s new-player experience any differently. Similarly, no game that’s the 6th in a series makes you play the first 5 before being even allowed to play, especially not a multiplayer game where you want to play the 6th with your friends.

At first I thought it was a little odd that new players will level their first character in only 10 levels, but if you want to play another, you’ll have to do 100 levels and it will feel horribly ponderous. But it actually makes a lot of sense. In this game, you’re supposed to hit max level and then decide what types of content you like (this was a specific focus of MoP). If some of the content you like is “leveling,” that’s the time to do it, and alts are the way for you to experience that content.

Garrisons

Short because we’re still short on details (they listed a lot of things, but it’s really hard to put it all together until beta). I think that cosmetically, these look like WoW’s take on player housing–in fact they may have described it that way at one point. But WoW always said it never had a use for “player housing” as most people think of it, and I’m not sure that’s changed. The biggest role I’m seeing for garrisons is “something that makes you log in the next day (that’s not daily quests!).” That’s not what most people think of as “player housing.” It’s a giant version of the Halfhill farm (which I think they also said at some point). It’s another way that WoW is staying with the times–ever notice how every f2p game (like Hearthstone) has a thing making you want to log in at fixed intervals (often 1 day)? But WoW is really staying ahead of the times in that way, because it’s moving on from “do this quest every day to get your carrot” (which is tremendously boring) to “here’s a minigame where you sent a guy on a mission and as soon as you get home from work tomorrow you’re going to log in to see how it turned out.” It sounds infinitely better.

There are traditional player-housing features as well like trophies to show off to your friends. To be honest though, I don’t see the novelty of going to my friends’ houses lasting very long. Even if the customization is as rich as something like Animal Crossing, where people can do truly creative things with the vast array of options (I kind of doubt that it will be), they’ll just tweet their screenshots or whatever. This is probably why WoW never had player housing. It’s the minigame aspect of the Garrison that makes it worth doing. The biggest watershed in quitting any game, in my experience, is the first time a few days go by where you didn’t play or think of it–that’s when you find you’re mentally quit before you even realized it. Dailies were a way of making sure that didn’t happen, but they were so awful to actually do that it probably cut into their retentive effect. Building an entire minigame to leave you with goals that will take place at certain times in the future is a much better effort and I’m looking forward to seeing how it works.

Hit and Reforging

Plagiarizing myself again (lazier than typing). 4/26/2013:

“–Everyone has to hit 100% in PvE. Every single raider of a given class has their hit stat at exactly the same amount. The most telling part of this is that healing specs get 15% to hit. Literally the only effect of the hit stat on a piece of gear is to cause you to reforge to cancel it out.
–Reforging is not very interesting. You shuffle your worst secondary stat to your best. All it really does, other than manage the hit cap, is mute the difference between items with different secondary stats. That may have necessary when stats were less standardized, but now all it does is make gear choice less relevant. Also the little bit of free-from stat choice that it adds is completely redundant with the whole purpose of gems.

We have multiple systems now (the hit/miss attack roll and the hit stat, and the reforging system) whose sole purpose is ensuring that everyone hits everything 100% of the time. I want to argue that they’re all completely vestigial and should be gone next expansion. There are some obstacles, like the need to come up with a fourth DPS stat to replace it, but one thing at a time.”

So yeah, that happened. Unsurprisingly, I approve.

Tertiary Stats

Really neat, not an idea I’d ever even considered. To summarize:

  1. Primary stats are always present in fixed value on items of a given slot/ilvl. There’s no player choice associated with them, but they mediate scaling. The increase in primary stat as you get better gear drowns out most other terms that would cause scaling imbalances.
  2. Secondary stats affect your core min/maxy character ability, such as DPS or healing output. There’s player choice is figuring out which is best, but they tend to be a little one-dimensional (your spreadsheet tells you which to favor). They contribute to scaling and should be generally balanced. All items of a given slot/ilvl have comparable total secondary stats.
  3. Tertiary stats don’t affect DPS and the like (“cleave” does a bit, consider than an open point for now). They don’t affect scaling or balance–your raid leader won’t view you as behind because you have less lifesteal or runspeed than someone else. It’s okay for comparable items in the same tier to have different amounts of tertiary stats (I believe many or most items will have 0, in fact).

Viewed this way, the third stat category makes a lot of sense. When thinking about how to work in e.g. runspeed as a stat, I kept getting stuck on how to balance it against DPS. An interesting debate by the way–normally players always favor DPS (in fact the whole MoP talent redesign was driven by that notion)–but there’s clearly a tipping point (a player who doesn’t use a runspeed enchant on their boots is bad). Anyway, a new category of “optional” stats is great.

As an aside, gems are being changed to an analogue of Thunderforged. It’s an extra bump to non-tertiary stats that you might roll up occasionally. Basically now there are two ways instead of one that an item can be little better than average, a socket or being Forged. So they really like the Forged idea since they’re doubling it, and even the whole tertiary stat concept is a variant of it.

I’m mildly surprised they’re doing away with (traditional) gems as well as reforging. Much of the thrust of my issues with reforging was being redundant with gems (free stat choice). Getting rid one of one mode of free stat adjustment felt like an obvious change to me, but not both. Still, I can’t say picking gems was very interesting, so I have no reason to complain.

—–

Okay, have to stop typing for now, I hit on the big design issues we know about. I didn’t touch on L100 talents, but it mostly would have been “a bunch of neat ideas, too early to worry about min/maxing them anyway.” I think doing in-depth into the L100 talents so far will be a good avenue for launching into thoughts on class changes (which we otherwise haven’t seen). But right now, reading them doesn’t let me infer anything big about what they’re doing with classes in WoD.

Let me know your thoughts.

From Dust to Dust: The Economy of Hearthstone

One of the most fascinating things about Hearthstone is that despite the usual terminology, it is not actually a “trading card game,” in that you cannot trade. Trading is functionally replaced by a crafting system that allows you to inefficiently transform cards into any other cards whenever you like. There are advantages and disadvantages to this from a player’s perspective. The obvious disadvantage is that you can’t shape your collection without destroying value. The advantage lies primarily in not exposing players to the vagaries of a secondary market as a requirement to managing their collections. This should be a big draw for people who have never played a TCG before, as every acquisition of a new card won’t involve the feeling that as a non-expert you might be getting cheated. Related is the topic of this post: since growing your Hearthstone collection is a solo endeavor, we can compute the rate at which it happens without reference to any market conditions or other exogenous factors.

Left out of the post is a discussion of Arena rewards and the efficiency of playing Arena. I want to add this to a follow-up post as soon as I have data on Arena rewards at each tier, particularly since there are a number of good reasons to spend your gold or money on Arena rather than buying packs.

For today, however, the question we explore is how many packs you must expect to buy or otherwise acquire in order to collect any desired set of cards.

The Facts

The key piece of data needed for this analysis is the average distribution of card rarity when you open a pack. For this I turned to any forum posts I could find where people tried to tabulate such information and made the best approximations I could: 1% Legendary, 4% Epic, 21% Rare, and the remainder common. 2% of commons are golden, and 5% of all other rarities.

  • I definitely would appreciate any further light people could shed on this in the form of card distribution data that was collected in a controlled manner (which means, it was non-selectively determined that a set of packs will be recorded). It would be a simple matter to tweak the numbers and re-run the simulations.
  • It’s not important for this purpose that each pack has a guaranteed rare or better. Since packs are only opened as whole units, only the average rarity across the pack is important. In theory the variance in the outcome may be slightly affected.

The other important information is the distribution of cards across each rarity. For this the database filters at Hearthhead come in handy. Select the “expert” set and leave “uncollectible” unchecked, and you can see the number of cards to be collected at each rarity:

  • 94 Common (40 neutral and 6 of every class)
  • 81 Rare (36 neutral and 5 of every class)
  • 37 Epic (10 neutral and 3 of every class)
  • 33 Legendary (24 neutral and 1 of every class)

Blizzard’s initial post on Arcane Dust is a reference for crafting and disenchanting values.

The Big Picture

From the above we can derive a few different things.

  • The total value of dust that would be required to craft a full playset (2 each of the 212 non-legendaries and 1 each of the 33 legendaries) is 106,120 Dust for a non-golden set and 428,800 Dust for a golden set.
  • The average yield of a fully disenchanted pack is 93.03 Dust.
  • Therefore, if you turned every card to Dust and crafted a full playset from scratch, it would take you 1141 packs for non-golden, and 4609 packs for golden. This provides a useful upper bound for comparison when we simulate how many packs it will take with more reasonable behavior.
  • With duplicates taken into account we would expect to open 135 legendaries before having at least one of each. At one legendary every 20 packs, that’s 2700 packs before you get them all by luck alone.

As always, before simply tossing everything into a simulation, it’s good to see what we can ballpark on our own. For example, we know that the expected number of packs opened to complete a set is going to be something substantially less than 1141. Let’s guesstimate that it will be less by a factor of around 2.5. We might think this because, if you imagine 106,120 Dust as that target value you’re trying to acquire, then the early cards you open will in reality contribute more than their disenchant value. They’ll effectively contribute their crafting value (because each one will be a card you don’t have to craft later). Since for the highest-value cards, the craft value is four times the disenchant value, we can think of the value of each opened pack as starting out around 4x the disenchant value and then decaying down to 1x as our collection fills up. So at an average of around 2.5, you might expect to open 450 packs in reality.

This assumes, incidentally, that you are using the optimal strategy for reaching the final goal, which is to disenchant all extras you open and hoard the Dust until you have enough to craft all missing cards all at once. Crafting earlier to reach other goals will be discussed below.

As one other interesting point of napkin math, with 450 packs you expect to open 22.5 legendaries. Obviously not enough to fill out the required 33, and in fact with overlaps you only expect to have about 16. So half of the legendaries will be obtained from crafting. This means we can conclude that crafting is generally going to go “up” (turning common cards into rare cards) and that around 27,000 Dust, almost 300 packs’ worth, will be put towards crafting legendaries to complete your set.

The Law of Large Numbers

The code used to generate the simulation results can be seen here. You can run it yourself in any Python interpreter, if you want to play with some of the options discussed below or make any changes of your own.

The first thing I simulated is the process described above: opening packs until you can obtain a complete playset. For this first run, the simulator disenchanted any card once it had more 2 non-golden and golden copies combined, and will always favor disenchanting golden copies (but the final collection may still have some golden cards in it). In other words, the most efficient approach to obtaining a complete set without regard for golden, and without doing any premature crafting.

The results were, over 10,000 runs:

  • The average number of packs needed was 512, with a standard deviation of 42.
  • The average amount of Dust used to craft cards at the end was 28,522, or 27% of the total craft value of the set.
  • 100% of commons, 99% of rares, 85% of epics, and 54% of legendaries were found by opening (rather than crafting).

There already a lot of meat for discussion here. To start, we finally have a number of packs we can expect to buy to finish a set. Depending on whether 512 is higher or lower than you expected, you might reevaluate your own goals an expectations based on this. Against a target of 51,200 gold to spend on packs, it’s also clear that the 40 per day from dailies is small potatoes. A full collection is going to involve buying a significant number of packs with cash (a fact that should be obvious if you consider how the game’s business model has to work). The desire for a full collection might be seen as an extreme case, but if we’re going to do this analysis at all, we may as well dispel the notion that you’re going to get there by doing less than a few years’ worth of dailies.

If you bought it all with cash, 512 packs would be $640 at the best bulk rate in the in-game store. Any daily quest for 40 coins will save 50 cents off of this, and any Play mode win will save 4.17 cents. In other words, a full card set can be valued at any proportionate mix of $640, 1280 daily quests, or 15630 Play mode wins.

Arenas will complicate this, and I expect will generally increase the efficiency. Your 150 gold investment in an Arena can be bifurcated into a 100 gold purchase of an ordinary pack (your guaranteed prize pack) and a 50 gold Arena fee. The 50 gold Arena fee will get you some mix of gold, Dust, packs, and golden cards, depending on how many games you win. I’ll avoid speculating on the value until I have data like I said, but observe that it would not take much for the mean prize value to exceed 50. To evaluate a Dust, remember that at the end of the process we turn a huge pile of Dust into all of the cards we don’t yet have. The last few packs of cards are likely to be turned mostly into Dust to meet this goal. Since a fully disenchanted pack is worth 93 Dust, acquiring 93 Dust earlier in the process willy likely save us one pack or 100 gold. So as a rule of thumb, 1 Dust will be worth around 1 gold. Coupled with the fact that an extra prize pack (100 gold) or a golden rare+ card (shaving anywhere from 100 to 3200 Dust off of the process) can, even at small probabilities, increase the expected prize by quite a bit.

Before moving on, don’t ignore the fact that the variance of the result is quite high. At something resembling a normal distribution, where 2.3% of samples exceed two standard devations in either direction, 2.3% of people will finish by 428 packs, and 2.3% won’t be done after 596 packs.

Immediate Gratification

All of the above was premised on the fact that you act so as to most efficiently reach the goal. In reality, you will likely be less efficient in a few ways:

  • You might craft cards before your collection is complete, when you need them for decks. This runs the risk of crafting a card you’d have eventually opened.
  • You might disenchant cards you don’t have 3 of, again for the purpose of immediate deck desires. This may cause you to re-craft the same card later.
  • You might purchase packs at less than the bulk rate of 40 at a time, incurring a higher per-pack cost.

On some level these actions can’t be evaluated in detail, as they depend mostly on your specific preferences regarding having cards sooner rather than later. We can estimate the downside however. For example, since in the simulations, 99.9999% of commons were opened in packs rather than crafted, you can assume than any crafting of a common is a waste of 35 Dust in the long run: the craft cost minus the 5 you’ll recover from disenchanting it later. The same is true even for rares–you have a 99% chance to be out 80 Dust at the end of the process. Whether these costs are worth it in any case is up to you, but it’s worth understanding why that Dust is a long-term cost to your collection.

Crafting legendaries is actually a better proposition, as there’s a 46% chance you wouldn’t have opened it even after 512 packs (note the sanity check here against our napkin math of half the legendaries opened after 450 packs). In that case, you incur no cost at all. If you do have to disenchant that same card later, however, it’s a waste of 1200 Dust.

Remember our earlier logical expectation that crafting should generally go upwards. It stands to reason that, early in the process, disenchanting common cards and crafting very rare cards is the safest thing to do, as it’s the most likely to be something you’d have had to do anyway. Finally, keep in mind that your odds of any crafting being wasteful will decrease as your collection fills out.

All That Glitters is Gold

For people interested in the full all-golden set, this is the same simulation over 10,000 runs:

  • The average number of packs has gone up to 2789, with a standard deviation of 101.
  • The average amount of Dust for crafting is 220,369, or 51.4% of the total value.
  • 77% of commons, 69% of rares, 35% of epics, and 19% of legendaries were opened in packs.

So, don’t aim for a full gold set unless it’s worth more to you than a new computer or two. In general you can interpret all of these numbers similarly as the non-golden numbers, but I want to highlight that the increase in pack requirements may be larger than you expected. The more expensive golden cards only require 4 times the Dust of their non-golden counterparts, but the commons you need are no longer easy to find, making the whole operation take substantially longer.

At any rate, these numbers are interesting just for the purpose of being careful with expectations. Goldens are best thought of as a fun bonus but, perhaps even more more so than in games which allow trading, collecting them is not a welcoming proposition. Specifically, in games which allow trading, the variation in people’s preferences allows the market to move foil cards from people who don’t care about them to people who do. Here, you’re on your own.

You Can’t Always Get What You Want

The most important practical refinement of all this is that most people will have goals smaller than a full set. The simulator is easily modified to work toward a “target” which is any subset of the full card set, if you give it the rarity distribution of the target set (for reference, the distribution in the full set is [94, 81, 37, 33]). In this case, it will open packs until the dust collected is sufficient to craft everything missing from the target set all at once. There is an option to either hold “unwanted” cards as usual, or automatically disenchant them.

I will include a few informative examples here. The value in parentheses is the result if you disenchant all cards outside the target subset.

  • No legendaries [94, 81, 37, 0]: 287 (248) packs. This seems like the first reasonable way of reducing the amount of cards you need.
  • 2 specific legendaries only [94, 81, 37, 2]: 306 (267) packs. If there are a couple general-use legendaries with widespread constructed application.
  • Full neutral set + one complete class [46, 41, 13, 25]: 425 (377) packs. Another reasonable goal, as it gives you full access to all possible decks with your favorite class. However, it’s still a lot of packs due to all the neutral legendaries.
  • Same as prior, with only the class legendary [46, 41, 13, 1]: 216 (145) packs.
  • Let’s say half the cards in the game are constructed playable [47, 41, 19, 17]: 389 (326) packs. Perhaps serious constructed players would get some value from going down the entire Expert card list and deciding the cards at each rarity they think are going to be usable, and running the sim with that breakdown.
  • You really want to go straight to some decklist you saw (here I turned one legendary into an epic since the sim currently collects cards in pairs) [5, 4, 2, 2]: 143 (57) packs. So a competitive netdeck with 2 legendaries can be obtained somewhat quickly if you’re willing to disenchant as needed to get it.
  • Downgrading the legendaries to epics [5, 4, 3, 0]: 104 (35) packs.

I’d be curious about any other examples people think are worth running, or run on their own.

From Dust Were Ye Made

For people who have played TCGs before, it can at first be hard to get our heads around the notion of card collection being a single-player experience. And even once you do, the math governing how long it takes to reach various collection goals is nonobvious and counterintuitive.

In particular, your progress towards completing a full set of cards is not even roughly proportional to the number of cards you have already. This not only because early packs give their value by adding cards you don’t have while late packs give value much less efficiently in the form of Dust, but also because a large portion of the value needed to complete the set lies a small number of rare cards. The legendary cards, even though they comprise 33 of the 457 cards in a complete set, account for 50% of the Dust value. And even this slightly understates their worth, as they are also disproportionately difficult to acquire naturally (i.e. despite the high Dust cost, the ultimately efficient use of Dust is mostly to craft legendaries). This is all to say, the best loose estimate of how far along your collection is is not how many cards you have, but how many legendaries you have and/or could craft with your current Dust.

It will be up to every player to decide how they prefer the single-player collection environment of Hearthstone to the market that defines most similar games. But the unique Hearthstone system was very ripe for a mathematical analysis of how it can be expected to play out. Much has been and will continue to be written on the gameplay of Hearthstone, but I hope I could improve our understanding of the other aspects of the game that will in large part shape our experiences playing it.

Theorycraft 101: 5.4 Trinkets

Blizzard’s pattern of trying to make more interesting raid trinkets in MoP has provided a lot of interesting theorycraft material. As in past Theorycraft 101 posts, the goal is here both to give theorycrafters some useful conclusions and equations to save them the trouble of reinventing them independently, and to give everyone some general information that helps them evaluate these new bonuses when selecting items.

Item Budgets

In general, the amount of any stats budgeted to a certain slot scales like:

V cdot Q^I
  • V is the budget value controlling how many stats that item slot gets compared to other slots.
  • Q is a constant equal to the 15th root of 1.15.
  • I is the item’s ilvl.

Often a more convenient way to think of this, especially when dealing with trinkets, is to use ilvl 463 as a baseline. The reason is that most trinket procs are coded into the spelldata with ilvl 463 values (which is the pre-raid baseline for MoP), and then scaled from there on any individual item based on its ilvl. The Int proc on Nazgrim’s Burnished Insignia, for example, is this this spell. So in general, since looking up the ilvl 463 value for any proc/bonus on Wowhead is easy, you can think of the value at higher ilvls as:

V_{463} cdot Q^{(I-463)}

or

V_{463} cdot 1.15^frac{I-463}{15}

This explains, for example, how the 5084 Int on the proc linked above becomes 11761 Int (i.e. 5084*1.15^6, with a slight deviation due to rounding) when applied to an item that’s ilvl 553 (90 ilvls above 463). Sites like Wowhead will correct for those minor rounding issues so they can exactly match in-game values, but we don’t have to worry about them here.

A lot could be said about item budgets, but I wanted to give the overview here so you have the context on what you should expect from a trinket at various ilvls. A handy factoid is the amount of a passive stat a trinket has at normal budgeting: it’s 847 at ilvl 463, or 1959 at ilvl 553. In other words, the most vanilla possible ilvl 553 raid trinket would have 1959 of a primary stat and 1959 of a secondary stat (or 1959*1.5=2939 in the case of Stamina). Real trinkets will replace one or the other (or both) of those with special bonuses, but that 1959 (or whatever it is at the ilvl you’re looking at) is the basis for comparison.

To work a brief example, see Purified Bindings (553). Note that 11761 Int is just about 1959*6, so the trinket is exactly on-budget if the proc is active 1/6 of the time. Since it has a 20 second duration, you’d expect it to proc every 120 seconds. The 115 second ICD is intended to produce this result and have the trinket match the budget that a passive Int trinket would have.

But you came here to talk about more interesting bonuses than stat procs, so without further ado:

Amplification

Amplifies your Critical Strike damage and healing, Haste, Mastery, and Spirit by X%.” (3.03% at ilvl 463, 7% at ilvl 553, 9% at ilvl 580).

At first blush, this increases the value of all your secondary stats by X%. So if you have 30,000 secondary stats on your character sheet and wore an ilvl 553 Amp trinket, it would be very similar to a trinket with 2100 passive secondary stats (placing it slightly above the par of 1959 in this example). Two quirks:

  • It amplifies Spirit but not hit rating, which is a slight asymmetry across caster classes that I think is an oversight.
  • It increases crit bonus rather than crit chance, which makes things slightly more complicated.

Crit bonus effects have some odd stacking properties. The easiest way to think of it is is that when you crit for 200%, there are two components: the 100% “normal damage” and then 100% “critical damage.” Other than the crit meta, which obeys an idiosyncratic rule* but is irrelevant in T16 due to legendary metas, crit bonus effects all apply multiplicatively to the “critical damage” portion only (including Amp, Skull Banner, and Elemental Fury).

Long story short, the crit bonus provided by Amp causes you to do X% more “critical damage” overall. This does in fact increase the value of your crit rating by X%. But crit chance comes from sources other than rating, and the value of that other crit is also increased by X%. So the easiest way to evaluate this bonus is to:

  1. look at your total raid-buffed crit chance,
  2. imagine that it all came from rating (in most cases, multiply the % by 600), and
  3. take X% of that rating.

Putting it all together, say the total of my haste, mastery, and Spirit were 20,000, and my raid-buffed crit were 35% (16.7% from 10,000 crit rating, and 18.3% from other sources) and I had a 553 Amp trinket (7%). I’d evaluate this part of the trinket as being worth 1,400 stats from haste/mastery/Spirit, and 35*600*7% = 1470 from crit, for a total of 2870, significantly above the expected budget of 1959 secondary stats.

Since the other half of the Amp trinket is, in all cases, a primary stat proc that is right on budget, it is looking like a very strong trinket numerically. It will be even more so for classes with very high effective crit chances due to class mechanics, such as Elemental Shaman. The only important caveat is that is that Prismatic Prison loses a little value for healers because having all of the Int delivered as a high-value high-ICD proc is poor for healing purposes.

*The crit meta increases the “critical damage” in such a way that the total damage will have increased by 3%, before other crit bonuses. Now that every class has a 100% base crit bonus, the crit meta essentially works by increasing it to 106%.

Multistrike

Your heals have a X% chance to trigger Multistrike, which causes instant additional healing to your target equal to 33% of the original healing done.” (6.05% at ilvl 463, 14% at ilvl 553, 18% at ilvl 580)

This is the simplest new bonus. Aside from issues like pets, it’s a straightforward X/3% increase to your damage or healing output. I want to emphasize that this is not an RPPM or ICD effect, simply a plain fixed % chance to occur on any damage/healing event.

The only issue is comparing, for example, 4.67% damage/healing (14%/3) to 1959 secondary stats. I’ll leave that up to individual class modelers, but if you note that 1959 secondaries is, for example, 3.26% crit, you can see that Multistrike is generally looking to be in a good position.

Cleave

Your heals have a X% chance to Cleave, dealing the same healing to up to 5 other nearby targets.“ (1.34% at ilvl 463, 3.11% at ilvl 553, 4% at ilvl 580)

Exactly the same as Multistrike, with the twist that output depends on the number of nearby targets other than your main target. The only important note is that it’s tuned so that, if it hits one added target, it’s 2/3 as strong as Multistrike. For example at ilvl 553, 3.11% is 2/3 the value of the 4.67% output you’d have gotten from Multistrike.

So this trinket is dead even with Multistrike when it hits, on average, 1.5 added targets. In situations where it can regularly hit 5 targets, it is far above budget, and in situations where you are attacking a lone target it is useless. The ramifications of this are obvious, but the rule of thumb that it surpasses a “normal” trinket at around 1.5 splash targets should help you decide when to use it. For 25-man raid healers, I suspect you are very often going to be healing targets who have more than 1.5 other people nearby, except at enforced spread fights.

Cooldown Reduction

Increases the cooldown recovery rate of six of your major abilities by X%.

(17% at ilvl 463, 39% at ilvl 553, 50% at ilvl 580, in each case reduced by half on the tank version)

There’s not too much to say about this in terms of item budgeting, since its benefits are based on the vagaries of each particular class rotation, and I imagine the tuning was done ad hoc. Consult your class’s spreadsheet expert. I just want to correct a common misconception about how the bonus works.

50% CDR does not mean you can use the ability twice as often. It’s exactly analogous to the way haste works, it reduces the cooldown to 1/1.5 = 67% of where it started. So in the end, you can use the ability 1.5 times as often over the course of a fight, not twice as often. Since X% CDR means you can use the effect X% more times in the long run, the benefit is generally linear as the budget increases, as it should be.

This chart lists the affected abilities for each class, in case you need. The trinket doesn’t exist for Int users in this tier.

Other Tanking Effects

I’m not going to say too much about Juggernaut’s Focusing Crystal and Rook’s Unlucky Talisman. They have unique effects that can’t be compared in an apples-to-apples way against 1959 primary or secondary stats. I simply want to note that their inherent % bonuses follow the usual item budget rules just like everything else discussed here. As you upgrade through ilvls, these effects will increase in same way that any stat allocation would (because, as discussed above, all trinket procs/effects are built into the ilvl scaling mechanism now).

This does raise an interesting issue I want to touch on, but a full analysis will be for another post. For a bonus like Juggernaut’s, which is based on a flat % of your overall damage output, there’s a question of whether the overall benefit the trinket gives is actually scaling quadratically with your stat growth. Scaling is inherently confusing and I do want to make a post about it overall, but the basic thrust is that normally as you go up in ilvl, each item has more stat points, and each stat point is worth more because your totals of other stats have increased. It’s left as an exercise to the reader how this logic applies to effects that are based on a % of your other stats such as Juggernaut’s and Amplification.

RPPM

I’ve reviewed the math of RPPM in two prior posts, but this is a good time to note the updates for 5.4.

Every 5.4 RPPM trinket is 0.92 RPPM with a 10-second ICD (except that Ticking Ebon Detonator is 1.00).

Also, for reasons described by Blizzard in this post, haste no longer increases the RPPM of most trinkets, with the only T16 exception being Dysmorphic Samophlange.

A 10-second ICD produces an interesting player-favorable quirk. Since the procs are all 10 seconds long, it prevents overlaps that waste uptime. But since RPPM chance “pools” for 10 seconds (as described in earlier posts), blocking out procs for a 10 second period actually does not impair your overall proc chance in any way. In this case you do get the best of both worlds–the same number of procs you’d have normally, but arranged so that there are no overlaps.

To be on-budget, these trinkets whose procs are all 6 times the value a passive stat trinket would need to have 1/6 uptime. With a 10 second proc duration, you’d think all you need is 1.00 RPPM on all trinkets to be on par. The only quirk to this is that the “bad luck protection” system adds about 13% to proc rates in reality (as discussed in the previous post). Blizzard, slightly generously, has started discounting RPPM rates by around 9% to account for this. This results in a proc rate of 0.92 on all trinkets. Except that for some reason on Ticking Ebon Detonator, the they reduced the proc value by 9% instead (1069 per stack at ilvl 553, instead of 1176).*

Given this information–0.92 RPPM, no haste, 10s duration and no overlaps, uptime for most T16 trinkets is much simpler than it used to be. It will always be simply 1.13*0.92*10/60, or 17.33%. In the case of Samophlange, multiply further by your haste factor to get your final uptime.

Long story short, all RPPM trinkets in 5.4 have an average value that’s very close to equivalent to the passive budget. Essentially always, it’s a proc with 6 times the stats a passive trinket would have and an uptime of around 1/6. The only important exception is Samophlange, which gets a haste multiplier on top of the usual budget.**

*Note that Detonator, Samophlange, and Talisman all have per-stack values that are 1/10 of what a “big” RPPM proc values at the same ilvl would be. However, the actual mean stack height over the course of the proc is 10.5, not 10. The same is true for Black Blood, which has a mean stack of 5.5. This amounts to a free 5% added value to the first three trinkets, and 10% on Black Blood.

**I just want to note since the question is posed so often: just as Samophlange is pegged pretty close to its correct budget + haste, the same was true for Horridon’s Last Gasp. Any nontrivial ilvl jump from Horridon’s to Samophlange is likely to be a clear upgrade.

RPPM on the Pull

Starting in 5.4, for purposes of the “bad luck protection” described in earlier RPPM posts, the moment a raid encounter starts, your RPPM procs all behave as though 120 seconds have passed since the last proc.

Given the formula at the end of this post, any trinket or other RPPM effect with a mean proc time of 45 seconds or less will be guaranteed proc on the pull. This corresponds to RPPM of 1.33 or higher (including haste if it applies). Procs that are close to that value will be very likely to proc within the first few seconds.

A 0.92 RPPM trinket will begin each fight with a significant bonus (just about double it’s usual proc rate). It will have a 31%* chance to proc on your first attack, and if that fails, roughly a 35% chance to proc within the first 10 seconds of combat.

Hearthstone Probabilities and the Monty Hall Effect

The Monty Hall Problem

A certain probability puzzle is well-known in math circles for its unusual ability to cause people to refuse to believe the answer when it is explained to them. It’s usually known as the “Monty Hall problem” (after the host of Let’s Make a Deal):

Monty Hall has given you a choice of three identical doors. Behind one is a car and behind the other two are goats. You choose a door, but before it’s opened to reveal your prize, Monty adds a twist. He opens one of the other doors to reveal a goat (he always does this to add to the suspense). He then offers you the choice of staying with the door you chose, or switching to the remaining unopened door. Should you stay, or should you switch, and what’s your chance of winning in either case?

The answer is surprising to most: switching doubles your odds of winning the car (2/3 chance of winning, as opposed to 1/3 if you stay). The key fact is that Monty’s knowledge of which of the other doors (if any) was a car causes him to always remove a goat from the prize pool. The chance that the initial door you chose contained a car was 1/3 to start, and it’s unchanged by Monty’s ritual. But if the car was behind either of the other two (2/3 probability in total), Monty will remove the losing door and leave the winning one, and switching will win.

(If you don’t buy that the probability is anything other than 50% when everything started out equal and there are now two doors remaining, there are myriad sources on the internet trying to explain in different ways).

The Jaina Proudmoore Problem

Let’s say it’s late in the Hearthstone game and you’re about to try playing your bomb legendary. You’re pretty sure you’ll win if it sticks for a turn, but if it gets answered immediately you might be hopelessly behind. You want to guess whether your opponent Jaina is holding the Polymorph you know she has in her deck (assume for the moment she only has 1 for simplicity; the same concept applies with 2 but the math is more intricate). Her hand has 4 cards, and you mouse over her deck and see she has 16 cards left. After her draw next turn, 5 of 20 unseen cards will be in her hand, so you’d think she had a 25% chance holding the card.

Monty Hall, however, tells you differently. Even though she only has 5 cards in her hand next turn, she’s been selecting out non-Polymorph cards and playing them all game. Just as Monty selected out non-winning doors and removed the pool, making the remaining doors of the ones he could have chosen more likely to be winners, Jaina has been casting non-Polymorph cards from her hand, making the ones she’s left in her hand more likely to be Polymorphs.

For now consider the simplest case, where nothing had been cast so far this game that Jaina would have been likely to Polymorph. Applying the logic from above, there’s a 50% chance that the Poly started the game in the bottom 15 cards in the deck, and that probability has not been changed by any subsequent events. There must, then, be a 50% chance that it’s among the 5 cards in her hand. Quite a significant difference from the 25% that seemed completely intuitive before considering this effect.

Complexities

An important subtlety is that Jaina might not be as selective as Monty. Monty never prematurely revealed a car, but Jaina may have cast a Polymorph before the critical turn, if she had it and the game state called for it. The assumption above that the game state on prior turns never looked like one that would have drawn a Polymorph elides a deep point of probability, namely, the mysterious way that Jaina’s/Monty’s selectivity shifts probability between chosen and unchosen cards/doors. I think getting into the depths of how that happens might be beyond the scope of this post, but for now observe the following.

If you know Jaina is going to save her Poly for your bomb no matter what (and this might not be a bad assumption in a constructed card game where people are familiar with each other’s decks), then the situation is identical to Monty Hall: the probability in the above example would have been 50%. But if you made the opposite assumption, that Jaina is not smart and dispenses cards from her hand at random (ignore the vagaries of the mana curve for the moment), the probability would in fact be the 25% we naively estimated at the start. The best way to see the difference is to really understand why the answer to the Monty Hall problem is what it is. It might also be helpful to look at that bit of logic from the end of the previous section (about the 50% chance that Poly started in the bottom 15 cards of the deck) and try to see why it doesn’t apply in the case of the Jaina that plays randomly.

The other complexity is what I alluded to at the start: the arithmetic is more complicated with two Polymorphs in the deck (but as I said, the logic is unchanged). To work the same example with two Polymorphs:

  • The naive estimate is that out of 20C2 (20 choose 2, referring to combinations) places the Polys could be, 15C2 choices have them in the bottom 15, so the chance of having one in hand is 1-(15C2 / 20C2), which evaluates to 17/38, or around 45%.
  • The Monty-corrected estimate would be that out of 30C2 possible placements at the start of the game, 15C2 have them undrawn in the first 15 cards, so the chance of having one in hand is 1-(15C2 / 30C2), which evaluates to 22/29, or around 76%.

The result is the same as before, a much higher chance in the latter case.

Here is a full table of the probabilities for various deck and hand sizes, for reference:

Dropbox Link

Conclusion

The probability subtleties discussed at the beginning of the last section mean that guessing the probability that your opponent has a certain card is never an exact science. It depends on your judgment of how likely it would have been for them to use it at an earlier point in the game if they’d had it. The Monty Hall effect applies most strongly when it is highly unlikely or impossible (for example due to mana cost) that the card in question would have been played already. Where it applies, it causes the probability of the card being in your opponent’s hand to be substantially higher. So it’s both practical and perhaps fascinating to realize that you can’t rely on what you thought you knew about probability: all unseen cards are not equally likely to be the card you care about.

Healing Theory, Part 5: Haste

Previous posts in this series can be found here. In particular, the Haste section of Part 2 might be useful background.

Haste is the most complex of the healing stats, and often appears to be the least well understood. Its effect is a combination of added throughput, increased mana consumption, and increased HoT healing due to those “haste breakpoints” that are so easy to look up online but so hard to evaluate in importance. Part 2 in this series, linked above, gave some high-level comments on the behavior of haste, and generally concluded that based on its basic function, it’s likely to be unattractive. I said that I would dig into its effects on a class-by-class basis in the future, and that is what I’m doing in this post.

Incidentally, this post is written from a patch 5.4 perspective. Among various other things, haste will have no effect on the RPPM proc rate of the legendary meta (and legendary cloak), greatly simplifying the analysis.

Concepts

First, a slightly different framework for how haste effects the two main categories of spells. We’ll refer to this throughout the post.

1) Non-HoTs. Haste does not increase the healing per cast (HPC), nor therefore, the healing per mana (HPM). It increases the healing per cast time (HPCT) by 1% every 425 rating. It is worth pointing out for comparison that a typical mastery, like Druid, Holy Priest, or Paladin, increases all of these metrics (HPC, HPM and HPCT) by 1% per 480 rating. In general even from a pure HPCT (spam throughput) perspective, haste tends to be only slightly ahead of stats that increase your healing on a per-cast basis.

2) HoTs. Haste now increases the HPC. An important point I want to press on: in the long run, haste still increases the HPC by 1% per 425 rating. The “haste breakpoint” (HBP) phenomenon means that that increase to HPC comes in clumps, but the average gain is unchanged. Especially late in the expansion when the difference between a high-haste and low-haste build may be 20000 rating, it’s this overall scaling pattern that generally determines the relative attractiveness of the two. HBPs tell you what haste points to “snap” to in your reforging, but generally don’t control the overall value of haste. The only general exception is the first non-automatic HBP for any important spell, which requires a smaller investment to reach.

Haste2

What about the HPCT of HoTs? After all, if the HPC of HoTs increases, and the cast time comes down, the HPCT should increase like the square of haste. Here is the second important point: nearly all important HoTs have cooldowns or other mechanisms that prevent this. Wild GrowthHealing RainRenewing MistRiptideHealing Stream Totem, and Sanctuary have cooldowns. Rejuvenation and Renew have fixed 1-second GCDs. Lifebloom and Efflorescence are persistent and only allow one concurrent instance. The only notable cases where haste increases both the tick count of a HoT and the frequency with which it can be applied are Eternal Flame (tricky, see Paladin section below), Glyphed Riptide, and Tree of Life.

Summarizing: Haste increases HPC for HoTs but not for other spells. Non-haste stats increase HPC for all spells. Haste increases HPCT for (generally) all spells, but so do non-haste stats, and haste rarely gives a double benefit, so this factor is close to being a wash. Also, HPC is the more important metric than HPCT since firstly, mana is a relevant factor to healing, and secondly, many (most) important spells have cooldowns and cannot be spammed.

The key factor then in evaluating haste for any class is the portion of its total output that consists of HoTs. If a class gets 20% of its output from HoTs, there is essentially no way to justify spending rating to increase that portion of your healing by 1% per 425 rating, instead of increasing all your healing by 1% per 480 rating (or a similar amount depending on the class and stat in question). If a class gets 90% of its healing from HoTs, then in the long run, increasing that 90% by 1% per 425 rating is likely to be the strongest stat allocation.

Since most of the classes wind up with a little more nuance to the analysis that this, I’m going to move through them one at a time, rather than simply posting some WoL breakdowns and being done.

Disc Priest

I’m going to start with an easy one. Disc has the DoT component of Holy Fire and that’s all (ignoring an occasional Renew, if that). The DoT is about 1/6 of Holy Fire, which is itself a few percent of Disc healing. With only a negligible portion of heals having their per-cast strength improved by haste, the attraction of haste for this spec is nil.

One related issue: haste lets you cast more Prayers of Healing during the 10-second duration of Spirit Shell. But of course, what matters isn’t the number of casts you apply, but the total amount of Shell shielding applied. Mastery is nearly as strong as haste for this, doesn’t cost extra mana every Shell, and actually gives a benefit during the other 50 seconds of every minute. So there’s nothing here strongly favoring high amounts of haste. Under the principle that a first HBP is usually efficient, you might make sure to have enough haste to cast 5 Prayers of Healing during 10 seconds. But with the T16 set bonus and if you start Shell with Borrowed Time up, this is only 2116 haste (with some leeway for latency since this isn’t a true HBP).

Haste does theoretically increase your number of Smite casts in a fight, which saves a half-second of Penance cooldown here and there (frequently amounting to nothing if you’re on GCD when the Penance cooldown finishes). Again, nothing approaching a meaningful reason to use the stat.

Conclusion: gear for minimum possible haste.

Holy Priest

RenewSanctuary, and Lightwell Renew. It’s something, but by no means a predominant majority of healing done. A skim of a few top logs shows less than 20% of healing from these spells typically (it tends to be slightly higher in 10-man where Renew/Cascade/Serenity builds are more likely). Not much to add here. It’s simply not enough to make a stat attractive when it adds HPC to this small a portion of your heals, while other stats add slightly smaller percentages to all your heals.

As usual, you can tweak around low breakpoints a little. Your first Renew tick at 3039 (4721 if glyphed) is essentially a free large bump to Renew since you can’t dip your haste much below it anyway (this is what I said above about first breakpoints of important spells generally being good to pick up). Beyond that, 4717 for a 1/3 increase to Lightwell Renew might be worthwhile if Lightwell reaches around 10% of your healing, but this is dubious.

Conclusion: gear to minimum haste, but not below 3039.

Shaman

Now we’re getting somewhere. Healing RainHealing Stream TotemRiptideEarthliving, and Healing Tide Totem (although you might argue that raid cooldowns are best ignored for this purpose). The exact breakdown varies due to content, but over 80% is very common (or even 90% in some 25p encounters), with more Healing Rain at a stationary fight like Megaera, and more HST at spread mobile fight like Primordius. It’s easier to look at it inversely and see that it improves essentially all significant heals except Chain Heal and Greater Healing Wave, which tend to be a small percentage in 25p and higher (often 20-30%) in 10p. When looking at Shaman breakdowns, remember to exclude Restorative MistsAncestral Guidance, and Ancestral Awakening from the tally.

So we don’t have a clear conclusion yet, and my purpose here is more to discuss the mechanics and see where the value of haste is than to completely solve Shaman gearing. Also, more detailed log studies will be better conducted after 5.4 due to the huge buffs incoming to Chain Heal, Healing Rain, and Healing Stream. The above somewhat suggests that you should favor a high-haste build in 25p, and that 10p will be closer. This is all complicated by Shamans’ strong crit and mastery bonuses as well (not to mention Spirit in 25p due to Mana Tide).

Assuming for the moment you do conclude that haste is strong due to a very high usage of the spells listed above, you then do have to consider HBPs. The goal is to pick a level that picks up big chunks of healing on important spells, to minimize the extent to which haste is wasted by ending between HBPs on other spells This does mean that some of the value of haste is always lost at the top end, since the last few points aren’t benefiting all relevant spells. In this case, the 8 ticks of Healing Rain (HR-8) HBP is at 50%, and Healing Stream-11 is at 46.7%. This makes 50% (15316 rating with Ancestral Swiftness) a good stopping point, without another good one until HR-9 at 70% haste, unlikely to be practical or efficient even in better gear. Aside: Healing Stream HBPs are not precise since they depend on the latency of when the totem disappears, so don’t gear exactly to them.

Conclusion: pending 5.4 log analysis, but in general, if using a significant ratio of Chain Heal and other non-HoTs, minimum haste since other stats are better. If output is dominated by haste-favored spells, consider going up to HR-8 unless Spirit stacking for Mana Tide in 25p.

Druid

The HoT class, although as we’ve seen, that moniker is just as apt for Shaman. Haste adds healing to each cast of RejuvenationWild Growth and to the small HoT components of Regrowth and Tranquility. In addition it smoothly improves the tick rate of the omnipresent Lifebloom and Efflorescence (in 5.4). In the non-haste column is healing done by Swiftmend, heals cast with Nature’s Swiftness and the T16 2-piece, and Wild Mushroom non-bonus healing (Mushrooms will charge faster from stronger Rejuvs, but this is irrelevant unless you usually use them before full charge).

The situation is very similar to Shaman, in that the HoT portion is in the ballpark of 80-90%. And again, it’s hard to pin down right now since spells on both sides of the line (Efflorescence and Wild Mushroom) are getting improvements that, while not as dramatic as the Shaman ones, will cause them to do more healing. I’m going to be revisiting this more on EJ since Druid is my native class, but where I’m leaning right now is that making Efflorescence, Rejuvenation, and Wild Growth stronger is generally more important than making Wild Mushroom non-bonus healing and Tranquility stronger. Rejuvenation is actually just about dead even on haste vs. mastery since the instant tick doesn’t benefit from haste, but both the T15 4-piece and T16 2-piece bonuses make the extra tick a better way to deliver the heal. Small soft factors push towards haste as well–increased Clearcasting procs, shorter GCDs on many instants adding a small amount of convenience, better use of Tree of Life, and a better proc rate on some trinkets.

As to HBPs (emphasizing again that we first look at the overall value of haste, then worry about finding a convenient stopping point): Haste without Rejuvenation is a nonstarter. This is exactly why Resto Druids ignored haste in MoP until just now when the Rejuv-6 HBP at 13163 is coming into reach (those middling HBPs for Wild Growth or SotF were never particularly efficient). Rejuv-7 isn’t until 23262 rating and may not be practical even in this tier.

Conclusion: 13163. However it’s only a small benefit over the familiar 3043 Rejuv/Tranq-5 HBP, and the latter may be more convenient depending on gear. Stay at one of the two to avoid wasting stats.

Monk

Back into simpler territory. The only important HoT in this toolkit is Renewing Mist. And while it’s a lot of healing, it’s not over 40% or so (Monks would start liking haste at a lower HoT threshold than other healers since it’s 50% stronger due to Stance). Moreover, their fixed 1 second GCD means that haste’s benefit to HPCT is much more limited than usual, and haste does nothing for some spells. In particular this includes Soothing Mist: due to a quirk of the way the channeling is implemented, spamming the button every GCD allows you to get exactly 2 ticks per second regardless of haste.

So the conclusion is simply going to be to always sit at the lowest convenient Renewing Mist HBP. The conclusion would be to absolutely get down to the lowest possible HBP, but Monks have the unfortunate situation of not liking Spirit or mastery either, so you may not find it to be worth the trouble to shuffle those stats around after maximing crit however you can. Again, the goal here isn’t to write a guide for each class but to discuss the benefits and limitations of haste.

An added complication of Monk healing makes it especially important to reforge to some HBP: you care not only about healing output of Renewing Mist, but also the duration, since that affects your ability to Uplift more targets. Duration of a HoT is highest just after a HBP, when it is half a tick longer than the listed duration, and steadily declines until the next HBP. Dayani at Healiocentric discussed this at length for Monks here (and she also helped me with research for this post). There are lower-order effects where higher haste HBPs slightly reduce total Renewing Mist duration, but slightly speed up the jumps to new targets, shortening or lengthening Uplift windows by fractions of a second in either case. For our purposes here, the important conclusions are that you do not want to have any extraneous haste beyond an RM HBP, but being at higher ones is not especially helpful.

Conclusion: any low haste breakpoint, after you’ve shifted all possible stats to crit. The lowest few are 3145 (RM-11), 6151 (RM-12), and 9158 (RM-13).

Paladin

Before Sanctity of Battle included Holy Shock, what this would come down to is the amount of healing accomplished by the HoT portion of Eternal Flame (including its effects on Beacon of Light and Illuminated Healing). Suffice to say, it was not high enough to justify haste on its own. But let’s put that aside for a moment, since things are lot more complicated now

Sanctity, in brief, reverses the usual function of haste. Its benefit is that it allows the Paladin to use cheap Holy Power generators more often, thereby displacing some portion of more expensive spammable generators that would otherwise be used. The key fact is that the only benefit to all this is efficiency. The biggest problem haste runs into, then, is that the best alternative to the Sanctity-affected spells is Holy Radiance, not an especially inefficient spell. A stat whose principal function is to displace Holy Radiances from your rotation has a big hill to climb in making itself attractive. To be clear, getting to cast Holy Shock more often is still better (that’s why you use Shock on cooldown). The problem comes up when you talk about paying for that privilege with a heavy investment into a stat.

Without building a full-blown Paladin model in a spreadsheet or describing one here, an efficiency-based comparison is therefore a good approach for a simple evaluation. Let’s start with 5.4 Selfless Healer setups.

With no haste, you can cast 10 Holy Shocks and 10 Judgments per minute, as well as 3.33 free buffed Radiances. What happens if you invest into 10% haste (4250 rating)? Now you get 1 extra of each, plus 1/3 of a buffed Radiance. All in all the haste has given you the opportunity to spend 28% base mana to get 2.33 HP, plus the healing done by one Holy Shock, 0.53 Radiances, and 0.33 Daybreaks. Without the haste, 2.33 HP would have cost you 2.33 Radiances, or 84% mana, and I’d also have gotten the healing done by those 2.33 Radiances and 2.33 Daybreaks. The latter option costs more mana (specifically, 56% of base, or 33600 more) and does more healing. To see which is better, realize that instead of 4250 haste rating, I could have taken 4250 Spirit, which gives me 37370 mana in 1 minute (taking Divine Plea into account). So haste, in the end, has saved me less mana than Spirit would have, and caused me to do substantially less healing (as 1.8 Radiances and 2 Daybreaks is far more healing than one Holy Shock).

Eternal Flame builds make this trickier, as haste now provides both a benefit from Sanctity, and a boost to the Eternal Flame HoT. The Sanctity benefit is much smaller than before, since now it doesn’t even give you the extra HP or special buffed Radiance. All you’d get from that 10% haste is 1 more Holy Shock per minute, saving you 20% mana compared to getting that HP from a Radiance (equivalent of 1000 MP5), but doing less healing.

We now have to finally revisit our usual analysis of seeing how much healing is done by the Eternal Flame HoT. This is hard to estimate in logs due to Illuminated Healing and Beacon, but on paper, a Holy Shock+EF pair does 37% of its healing with the HoT, and a Radiance+EF pair does 23%. 30% overall is a fine estimate for now. This by itself, going by the logic throughout the post, would not be enough to justify haste based on the HoT effect. The proper comparison of heals affected by haste to heals affected by mastery would be 30:70, not 30:100, since mastery doesn’t affect the HoT, but that’s still not enough. Let’s even assume that instead of comparing, say 4250 haste to 4250 mastery (8.8% mastery), we siphon off 1400 points into Spirit to account for the 1000 MP5 mentioned in the prior paragraph. Mastery being 1/3 weaker even still doesn’t make the comparison attractive for haste. It looks something like 30:50 now in terms of weighting, analogous to a class that did 60% of its healing with HoTs. But not only does that still make haste subpar, but there’s the value of the extra Holy Radiances in the Spirit/mastery build that we never took into account.

Conclusion (a surprising one, I think): minimum possible haste. If using Eternal Flame, keep the EF-13 HBP at 3506.

Summary

The following healers should avoid haste rating beyond minimal HBPs, if any: Priests, Paladins using Selfless Healer, and Monks.

The following healers get some reasonable value from haste, but barring more detailed models, it appears to be weaker than other stats: Paladins using Eternal Flame, and Shamans who aren’t fully AoE healing.

The following healers get enough value from haste that it is likely advantageous over other stats, but not drastically and only when set to efficient HBPs: Shamans who are fully AoE healing, and Druids.

Cosmetic Armor: Style Analysis, Target Audience, and Store Suggestions

Transmog has been a hit since it launched in Patch 4.3, and it seemed inevitable that armor would eventually find its way to the Blizzard Store, as it finally did last week.

My opinions have gone back and forth on the store helms over the past week. Initially I thought that adding more transmog flexibility was a great idea, then I balked at the prices announced on Tuesday. However, after seeing so many users enthusiastically upload detailed screenshots to Wowhead, I’m thinking that the items have a targeted niche, and I’m just not one of the people intended to  purchase these items.

I want to look at why these helm designs were possibly chosen, explain why I’m not the target audience, and suggest some potential Blizzard Store armor for the future.

Blizzard Store Helm Designs

Helms occupy an interesting place in transmog. It’s one of two slots players can hide, meaning that not everyone will utilize helm transmog in the first place. In addition, players are split between wanting a fantastically-themed helm that covers their faces, or one that leaves hairstyles and facial markings visible. Other times players get attached to a particular helm, such as how many leather-users are with the Cursed Vision of Sargeras.

For Blizzard to release helms people feel compelled to buy from the Blizzard Store, Blizzard’s designs have to fill a noticeable transmog void. With the option to hide helm graphics, new transmog options have to be pretty compelling.

Looking over Wowhead transmog set comments, these three new helms work very well on popular BoE sets that were missing matching helms. (Many vanilla BoE sets did not have matching helms and shoulders.) They also match popular tier sets for outspoken transmog classes–Death Knights and Paladins are very vocal, leaving many comments about matching accessories and weapons on their set pages.

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The Crown of Eternal Winter is a blue crown that periodically glows and covers the user’s face with a skull. A bit too garish for my tastes, but it’s appealed to many players that are Death Knights or enjoy a frosty theme. Looking at the Blizzard preview images, two are of priest T6 and two images are of plate sets. The Wowhead submissions have overwhelmingly been plate sets–the T11 Magma Plated set has shown up at least five times, but Death Knight Tier 10Tier 8, and Tier 13 has also shown up as well. The Magma Plated set may be especially popular because most of the set has lookalike items any plate user can farm up. There’s also some representation among frost mages, with Tier 3 and Tier 4 transmog, and rogues using old tier sets with blue and black accents.

A common theme in these screenshots is that wearing the Crown of Eternal Winter leaves the player’s face more exposed than the completely hooded helms intended for many of these sets. Creating a helm that both has a cool animation and leaves the user’s face exposed may win over some transmoggers who did not farm up a set’s bulky matching helm.

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The helm also appeals to a subset of users who enjoy the appearance of frost resistance gear, which is an elite transmog look since there’s no way to learn recipes for these sets anymore (save for chests/boots and select duplicate quest rewards). I’ve noted in the past that the Naxxramas Plate set has a large number of comments for a set that’s nearly impossible to get, indicating players really like neon blue gear. This helm certainly fits that description, and the Crown’s page has submissions from users wearing full cloth, leather, and plate frost resistance gear–impressive that people have held onto those sets for years.

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The Jewel of the Firelord, a set of fiery horns with golden glowing eyes, seems to appeal to Paladins, players using expensive BoE sets missing helms like Blood Knight Mail or Glorious Plate, and specs with natural affinities towards fire, like Fire Mages and Destro Warlocks. Paladins are one of the most vocal transmog classes–check out the comments on Judgement or Lightbringer pages. Many of their sets feature gold accents, and for players who dislike bulky plate helms, this works as  a lighter alternative.

Gold is also a very versatile color, as this fiery helm can both match sets that are primarily gold, as well as unrelated sets that simply have gold metallic accents. There’s even a few uploaded screenshots of completely bland gear with this fiery helm serving as the only colorful accent.

The user screenshots for this helm include a large number of mail sets, unlike the other two helms. The sets these match are generally expensive BoEs–RadiantMasterworkMagnificentGlimmering Mail. The store helm seems to be building off of the popularity of Ragnaros’ Crown of Destruction serving as a fiery non-set conversation piece, except the color scheme is geared towards yellow instead of orange sets.

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Similar to how frost mages used the Crown of Eternal Winter, there’s pictures of the Jewel of the Firelord using Warlock sets–Tier 10Tier 6, and Tier 5–as well as Mage Tier 5. These sets also got accessorized with fiery spell effects in screenshots.

Another observation is that players really went out of their way to make creative screenshots for this helm, more so than the other two. Players have posed with fiery mounts, core hound pets, and Ragnaros and lava in the background. The Crown of Eternal Winter does have some Arthas-themed screenshots, but there’s less variation in the screenshot creativity.

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The Hood of Hungering Darkness has noticeably less comments and submissions. Perhaps this is due to its face-hiding model, which doesn’t appeal to all players and too-closely resembles bulky helms already designed to match tier. The Blizzard Store images pair this helm with a Sunwell PvP setcloth fire resistanceWarrior Tier 13, and Wrath questing plate. However, the plate sets already come with bulky helms, so this may look too similar to existing models. The cloth fire resistance set doesn’t really have a matching helm though, so perhaps it was hoped matching fire resistance gear would be as popular as the Crown was for matching frost resistance gear, and users do seem excited by my suggestion to pair this helm with the plate fire resistance set.

This helm overall may have slightly more limited use, but based on user submissions, it’s already been paired with both fire resistance gear and BoE transmog sets, both of which are missing helms.

Transmog: Not Like Other WoW Collections

This next part of the blog I originally wrote before analyzing the Wowhead screenshots above. After reflecting on it, I’ve modified this part slightly to get across that I’m probably not the targeted audience for these helms, not that the helms were poorly calculated–because based on user submissions, people are really enjoying them, both new players who just started transmogging, and older players that had expensive items and TCG tabards saved up.

For long-time collectors like myself, transmog is a new fun collecting game, but it’s different from typical WoW collecting in one important way–there’s no shared endpoint. You don’t collect transmog gear to add to a trackable collection total, like mounts or pets. Finishing a set is satisfying on your own creative terms, instead of comparing your progress to a measurable subset of achievements.

Even participating in the traditional collecting model for mounts, pets, and achievements, it’s easy to get choosier as time goes on. At this point, if someone gave me $100 and said I could only spend it on WoW mounts, I would prefer to spend it on a single TCG mount like the Ghastly Charger, instead of four Blizzard Store mounts at $25 each. My collection is at a point where I rotate between the rare mounts I have and don’t feel compelled to rush and acquire the “low-hanging fruit” mounts simply to increase my quantity. After so many years playing WoW, increasing my collection’s quantity isn’t compelling enough of a reason by itself. This is one reason why I’m not going to rush out and buy the three extra helms simply for additional transmog options.

For players who choose sets to compliment a particular meaningful item or express a RP character concept (beyond fire/frost specs), these helms probably won’t be an essential purchase. The BoA status on the helms is nice, but people who devote effort into transmogging all of their alts usually enjoy variation and get tired of the identical heirloom look.

Transmog gear is also one of the few things in WoW that can parallel real life a bit. While much of WoW is pure escapism, transmog is more realistic. Slaying dragons, riding dragons, summoning cute dragons as battle pets–none of that is happening in real life. Transmog is essentially a glorified shopping experience though, where you can buy as many clothes as you like, without having to worry about economics, body image, annoying magazines, or trends.

With transmog, your character’s persona is literally their costume. It’s both addictive and freeing to know that you’re still being judged on your appearance, but you’re completely in control of it in Azeroth. Paying money for helms throws a bit of a wrench in this–it’s not a huge issue with three helms, but if there were a wider variety of high-quality store helms available, people may feel their creativity tread upon.

While I quickly shelled out $25 for the Celestial Steed since it was a fantastical mount, spending $15 on an in-game hat reminds me, as a fashion enthusiast, that I could spend that money towards an actual real-life accessory I’d get much more use out of. And when I think about $45 for three hats vs some dresses on sale…it’s not a hard choice at all.

Potential Future Store Items

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To potentially get more collectors like me engaged with in-game armor, I think selling tabards would be a good development. While tabards did get some gorgeous artwork in Mists of Pandaria, they’re mostly tied to reputation grinds not every player wants to do, like the August Celestials Tabard. There are fewer tabards than there are helms currently: 108 tabards to over 3700 helms. There’s a far greater likelihood that fashion-conscious players are lacking a perfect tabard than they are a helm.

There are currently some luxury tabards like Tabard of Frost, which was discontinued some years ago when the WoW TCG underwent some changes. These items are very expensive, as no new loot codes are being generated, and they are also BoP, so old-time players can’t transfer this tabard to new characters. Adding artistic BoA tabards could have a potential market, as there are so few tabard options, both in-game and via the TCG.

Players have demonstrated they’ve cared about in-game tabards as well. The Tabard of the Scarlet Crusade has over 300 comments, and many player were sad to see it temporarily vanish when the Scarlet instances were revamped in Mists of Pandaria. Playing back in vanilla, it was always exciting to see it drop, and finally getting enough good gear to solo the instance at 60 for the tabard was a big deal. The tabard had a pretty basic design, but players liked it since dungeon tabards were novel and it had cool lore behind it.

The Tabard of the Lightbringer has always been one of the most sought-after rewards from Shadowmourne, currently averaging 150,000g on the AH. It’s dear to many players, especially Paladins, who love that it looks like the Tabard of the Silver Hand. It also has a special Use effect–it encases the player in glowing light.

Very few tabards have on use affects, and even fewer have on use vanity effects, so if Blizzard Store tabards could be both BoA and include special effects, that would be amazing. Relating the tabards to lore would be a good hook–in addition to the two lore-base tabards mentioned above, the Illidari tabards are also very popular, which are from a lore-filled questline.

I personally might be tempted to buy some demon-hunter themed accessories if the Blizzard Store eventually offered them. This may seem too much of a niche, but the TCG has a good number of Illidan-themed items (Path of IllidanDemon Hunter’s AspectDark Portal Hearthstone, etc) and Blizzard has plans to sell more vanity items in the future like the Seesaw and Iron Hitching Post. In the meantime, it appears the helms have been encouraging users to transmog more, in spite of my early worries.

Soylent Green

A collaborative essay by Hamlet and Perculia.

Tuesday night. Like many others, you queued for LFR because you were Looking For a Raid. The question we want to explore here is, is what you found actually a raid?

We know what you’re after when you queue up. It’s not so much a raid, per se, that’s on the forefront of your mind. It’s that you’ll win an epic. Yes, the odds are low (you’re not even totally sure what they are), but maybe this will be the week. Maybe your item is from the final boss, so your hopes are prolonged further before being dashed by a bag of gold. Yes, that bag of gold you bitterly accept, but you’d almost rather throw it away in protest. Preferably at someone’s head. But since WoW doesn’t let you do that, you dutifully click on it and add the gold to your inventory. Nobody will ever know anyway. You’re never going to see these people again.

If ever, in that moment, you wished you hadn’t come to LFR, you’ve already begun to understand what we’re telling you today.

This is at first blush a piece about LFR. But what it’s really about is raiding, and the things that make raiding a unique gaming experience. LFR demonstrates what remains when you strip the element of human interaction away: a shell that resembles raiding only superficially. Through the case study of LFR, we hope to remind you of what raiding is about, why you got started doing it, and why so many people love it.

There is one exception that runs throughout all of our comments. The people who make a group with friends and run LFR because they can’t raid Normal for whatever reason (group size, cross-realm, skill level, scheduling, or maybe they’re also raiding Normal but still doing LFR for gear). This is the exception that proves the rule. Because they’re using the “LFR” system as a workaround for logistical or other issues, not because they need to Look For a Raid. As will be discussed below, these people are the target audience for Flex raiding, which is better suited to their social raiding needs and will hopefully replace LFR for them. Our primary focus is the player who doggedly runs LFR outside the context of an already-established raid group. It is to these people that we send the message: don’t.

Background: The Better Part of Valor

LFR was introduced in Patch 4.3, but its genesis can be traced back to the Dungeon Finder, which was so very appealing to everyone (ourselves included), when it first appeared. The obvious reason for this was that it cut down on time spent queueing for a 5-player dungeon. But even this is a bit idealistic.

The system came in when 5-mans Heroics began to award Emblems of Frost (Tier 9 equivalent of Valor Points). This was the moment the now-familiar daily Heroic became a new chore for each raider, and the predominant sentiment was that anything which could get it out of the way faster was welcome. At that time, Emblems did not have a weekly cap, and moreover they were required for tier gear. So it’s fair to point out at the outset that for many players, the Dungeon Finder was merely a spoonful of sugar that helped make it tolerable to swallow the newly prescribed medicine of enforced time in 5-mans every day.

Specifically, LFD allowed players to easily run dungeons without having to wait around for guildmates, or be one of the unlucky DPS that didn’t nab a guild tank and healer. But soon a narrative began to emerge. To put it simply, people discovered with shocking regularity that their Blizzard-appointed dungeon compatriots were not providing the sort of PvE group experience they were used to. LFD horror stories became a common source of amusement and commiseration in raiding circles.

The tradeoff presented was subtle and was easy to ignore: click a button to queue and you get into your dungeon faster, only to languish in a slow-moving and impersonal clear. Did the downside seem really important at the time? We’re willing to admit that to us it didn’t. Getting those 2 Emblems without having to entreat, beg, or blackmail a guild tank was a powerful motivator indeed. But we wish we could tell our past selves that this path was treacherous, and once you set out on it, it is very easy to lose your way.

At first they seemed innocent, largely a supplement to guild runs in raid groups. The tide really turned in Cataclysm, where suddenly players found themselves turning to LFD as fresh 85s, too impatient to wait for their friends to level up. New talents seemed miserable, dungeons appeared overtuned, and everyone attributed their bad performance to their weak gear. Adding the Satchel of Exotic Mysteries in 4.1 made queuing up more appealing for tanks and healers in theory, but in reality, it ushered in a new wave of horror stories of clueless players in unacceptable gear simply taking on an in-demand role to “earn” a bag with a mount inside. And we still put up with it, since we believed obtaining rewards from LFD were the best way to improve our characters on a daily basis.

We might have seen the fundamental problem sooner. The increasing prevalence of antisocial behavior should have alerted us: the dungeon grouping experience was no longer about people. We needed LFD because we were committed to doing bland content we didn’t want to be doing in the first place. Out of this environment arose LFR in Patch 4.3.

LFR: Bread and Circuses

Many players believe that weekly LFR is a necessary, if unpleasant, undertaking, because it provides essential upgrades and a hefty chunk of Valor. Your WoW experience will be much more interesting and multifaceted when you free yourself from this idea.

LFR’s intentions may have been to draw people into raiding and whet their appetites for more challenges when it was introduced in Dragon Soul. In its current state, LFR is primarily a place where people hope to get Valor Points and gear upgrades without much thought, often walking away empty-handed and frustrated. At the start of Mists, LFR was unfortunately one of the more attractive ways to gain Valor Points and epics (much easier than gated reputation grinds). Initially they provided even more Valor than Normal raids, which was frankly a sign that something had gone terribly wrong. Later Mists patches have continually added more varied and better ways to accomplish these goals.

LFR’s 90 Valor may look appealing at first glance, but there is more to WoW (and, we daresay, to life) than choosing the activity with the highest number of Valor Points. While acquisition of gear is the most visible carrot, through most of WoW’s life the desire to acquire gear sneakily draw you into activities (like raiding) that would help you progress on many important axes: character stats, player skill, and people to play with. LFR, unfortunately, provides them in the reverse order of importance: it gives you gear easily, but does little to nothing to exercise your WoW skills, and its ability to connect you to a stable play group is virtually nonexistent (seemingly by design).

Even insofar as your goal is improving your WoW performance, you can do better than dutifully capping VP every week for gear upgrades. By choosing to acquire Valor from a Heroic Scenario, a Challenge Mode, or even a Barrens weekly, you’ll be testing your character’s skill and improving their performance in ways LFR never could. You’ll also be playing with people, either friends or potential new friends, who will provide the necessary social foundation for any future non-LFR activities. Obsessing over VP and your epic upgrades is a lazy way to view character improvement. Take an active role in your character’s performance instead of attributing it to their LFR loot luck and ilvl.

And with Challenge Modes, the new Proving Grounds (we expect), and Battlegrounds scaling down all gear, there’s more and more content where you can see what the game is like when your gear crutch is temporarily stripped away. These types of content reverse the priorities from LFR: players can simply focus on playing well and coordinating with others to succeed, and they are rewarded with increased ability to play and coordinate rather than with gear. While we don’t expect (or desire) for most WoW content to neutralize gear in this way, the existence of these few helps balance out the influence of LFR.

At some point each week you return to raiding, the activity that puts everything togetherskill, gear, and social. So when you engage in WoW pursuits that are heavily motivated by a desire to support your raiding, you’re better off choosing modes of preparation that help you on all of those fronts, rather than the one which gives gear and VP but has no other redeeming quality.

Friendship is Magic

LFR makes a promise that’s almost mystical in its ability to redefine a person’s entire relationship with WoW: a lifetime supply of epics. With no strings attached.

You don’t have to log in and send your guild leader a tell at 8PM Eastern (7PM server time). You don’t have to whisper someone in trade chat “need a Rogue?”. You don’t have to link any achievements to anyone or have them complain about your ilvl. You don’t have to bring consumables. You don’t have to know the boss abilities (moving boss information from the internet to the Dungeon Journal was nice but still, who wants to read all that?). No required addons, no officer taking attendance. You don’t have to spend 4 hours on Vent with that guy whose voice annoys you. Your gear doesn’t have to be gemmed or enchanted impeccably. Your gear doesn’t have to be gemmed or enchanted at all. You don’t find out at start time whether you have to sit out. You don’t have less DKP than your class partner. You’re not alt-tabbing after a wipe to try to make sense of someone’s MSPaint diagram. In short: for better or worse, you never have to see any of these people again.

It is the Tyler Durden single-serving friendship, the one-night stand of WoW. Nobody is going to call you the next day.

But maybe at times, after finishing an LFR, you’ve felt a little unsatisfied. You’re thinking mostly about the stupid tank who pulled Lei Shen into the wrong quadrant, and above all, about the 12 bags of 28 gold in your inventory. You feel some sense of accomplishment that you got up to 1000 VP as planned and therefore are a Good Raider.

Or is what you feel actually feel a sense of … relief? If you’re trying to figure out why, after spending your evening playing your favorite game World of Warcraft, a certain part of you wishes you could have the evening back, we suggest the answer lies somewhere other than the wipes or the gold or the VP. We suggest you look back above and wonder whether, in the absence of all those “burdens,” you had no earthly reason to care about what was happening in the raid you were participating in, or the people you were playing with.

And this is the essence of what we want to convey here. Raiding is the experience of sharing both defeat and victory with 24 or 9 other people (or soon, any number in between; we’re not picky here). Raiding should not be a painless experience devoid of emotionkilling a boss you’re proud of takes wipes, reworking strategies, and perhaps arguments. Minor annoyances from past raids, once irritating, now take on a strangely nostalgic quality as we reminisce over the planning and challenges that went into each victory.

The payoff is staying up chatting on Vent because you can’t sleep because of the excitement of the kill. Logging into WoW and finding your friends waiting for you. Keeping up with your old guild members and still seeing them around in chat after real life has pulled them away from their raiding schedule. Finding out that the new recruit watches the same TV show you do. Other people being happy when you got an upgrade. Having people help you go to old raids for vanity items. Being excited months in advance for the guild meetup at Blizzcon. And all the rest. If you’ve ever raided, we don’t have to explain. So why did you endure those annoyances we mentioned? Because you knew what they bought you: the real treasures of raiding. Which, and we cannot stress this enough, are not purple.

So every time you queue for LFR, well, we have no doubt that you were indeed Looking For a Raid. But, to answer the question we posed at the beginning: no, you didn’t find one.

/Flex

Flexible Raiding is a new raiding mode that allows cross-realm groups (pre-made only) of any size from 10 to 25 to do raid content that scales to match the group size. It’s designed largely for pre-existing groups of friends, but will be quite amenable to pickup groups (the difficulty is below that of Normal raiding), so long as the players organize the group themselves. It encourages new players to try out raiding in a friendly setting, and gives seasoned raiders a relaxing group activity to do with friends. Flex is a way to fill gear gaps, without being a real threat to the value of Normal or Heroic drops. It allows players to experience fights first-hand with their friends (versions of the fights that will have all the abilities, we expect) without worrying about rigid roster requirements or splitting up loot.

A telling difference between LFR and Flex raiding is the requirement to join. LFR requires players to have gear above a certain ilvl, as a way to exclude dead weight from the group (a goal which is emphatically not accomplished by the requirement, we might add). Flex raiding in contrast has no such ilvl requirement. You’re in the raid because your friends wanted to take you along and thought you’d meaningfully contribute, or that they could teach or carry you. This encapsulates the reason why LFR and Flex, so superficially similar, are such polar opposites in our minds. Even for those without a ready-made group of friends, the only requirement for Flex is a tiny modicum of human interaction to join the group (a low barwe all know how tradechat pugs are formed).

Social interactions are mandatory for Flex raiding. While LFR may have been intended to recreate the raiding experience, without social interactions it only emphasized winning gear for minimal effort. As Flex Raids require you to be among friends (or at the very least, people who are willing to continue playing with you), it raises the bar for good behavior and taking responsibility for your actions. This in turn makes players put effort into fights since the raid team doesn’t consist of 24 anonymous annoyed players they’ll never meet again. It rekindles a spirit of teamwork, which withers in LFR’s loot-fueled atmosphere. You care if one of your fellow teammates moves out of the fire and will try to help them learn to do so. Largely because, in this mode, the fire might actually kill them.

Even the rewards from Flex are better, and not just because of their ilvl. Flex raiding will award achievements, mounts, and items that can’t be obtained in LFR. But more importantly, while raiding may reward players with powerful gear, it’s meaningful only to the extent that you feel you earned it. LFR epics may be a higher ilvl than epics from the previous tier, but nobody is proud of them. If you fail at a boss, you get comically buffed; when the boss dies, loot is automatically passed out and players often drop group if they need nothing else from the instance. Epics held power in past expansions because of the memories and challenge associated with their acquisitionwearing gear from LFR just shows you have a lot of patience, some luck, and a block of free time.

Flex accomplishes every valid purpose that LFR did have, without undermining the entire concept of raiding in such a fundamental way. Our criticisms of LFR have certainly existed for a long time, but the introduction of Flex makes things much simpler. This is what a casual raid should look like.

Conclusion: You Have to Tell Everybody

“And now you know what you’ve been missing. There was a world once, you punk.
I was there. I can prove it.”

Does the advent of a new mode of raiding sound the death knell of LFR? The smart money is on “no”. There will even be some uses that don’t especially bother us, such as the avid lore/art fan who prefers a single LFR trip over Youtube. We don’t need to be dogmatic about wiping LFR from the face of Azeroth, but we can be concerned about its influence on the raiding culture. We can hope that people reading this think twice about LFR and its unique ability to turn a much-loved gaming experience into one of drudgery.

There are a lot of reasons we play WoW. A lot of things that motivate us. Nobody will deny that the prospect of acquiring new in-game items is an omnipresent driving force that shapes people’s activities throughout the entire game. But the moment it’s simplified down to the bare desire to acquire gear with no particular thought as to what you’re doing to get it, why you want it, or with whom you’ll be using it, you should stop and consider what you are doing.

Our not-so-secret hope is that, if nobody remembers anything anything else from this essay, the “don’t pug” movement will capture people. It’s what this whole post is trying to get at. Yes, LFR the difficulty level is one issue, but LFR the ethosthe ethos of WoW being about valor points and ilvls instead of about playing with other people—is the bigger one. And we urge you to let it go.

This essay was for people who enjoy, or are interested in, raiding in WoW. To remind you why you’ve done it, possibly for years. To help you find the way to keep enjoying it has you have before. If you haven’t, to give you an inkling of why you should. If you’ve only ever done solo LFR, while we mean no disrespect at all, you’ve never raided. But we sincerely hope you try. This is in fact one of our chief objectives.

But to all of the people above, take the message to heart. Your time spent raiding is worth as much as your relationships with the people you spend it with. No less, and no more. And spread the word.

Tell everybody. Listen to me. You’ve gotta tell ’em:

WoW Raiding … is made out of people.

Theorycraft 201: Advanced RPPM

This is a continuation of my Theorycraft 101 post that introduced trinket uptimes and RPPM. I’m going to assume here that you read that post. The main audience for this post is people trying to any theorycraft work, whether making a full-blown spreadsheet or simply doing a standalone calculation about some trinket. You should be able to find the equation you need here without needing to redo a lot of work.

A bit of terminology from last time:

  • PPM is the proc’s built-in PPM constant.
  • H is your haste factor (1 + your average haste %)
  • D (used below) will be the duration of a buff

Our first basic conclusion was that if you ignore the possibility of proc overlaps, the uptime of a proc is:

PPM cdot D cdot H / 60

We called this value lambda  (lambda) for any given trinket. It’s a good approximation of uptime as long as uptime is low (overlaps are unlikely), and it will also come into many later results. Conceptually, lambda  is the ratio of the buff’s duration to its mean proc time.

The next conclusion was that if you account for the possibility of overlaps, the uptime is:

1 - e^{-lambda}
Graph1

Seeing how uptime (y) relates to lambda (x) is helpful. In the low range, they’re mostly the same (the curve approximates the y=x line). As lambda increases, overlaps becomes more important and uptime starts to slow down in its asymptotic approach to 1.

Today we’re going to see how this is modified in a few different scenarios.

The “Bad Luck” Correction

In the prior post I commented that the RPPM system was not a correction to increase your proc chance. But they recently added just such a correction in the case of trinkets (for now I won’t discuss why they might have done so). It kicks in anytime you haven’t had a proc for more that 1.5 times your mean proc time, and begins to rapidly increase proc chance. Specifically, from that point on, every 1% of MPT that passes increases proc chance by 3%. I’m not going to walk through in detail a calculation of how much this increases overall proc rate–it’s somewhat tedious and the focus of this post is on the results more than the derivation (and I don’t feel like LaTeX-ing the whole thing). I’ll include my original calculation in an appendix.

Here’s a graph comparing the two:

Graph2

(Wolfram link for reference)

The x-axis is time, in units of mean proc time. The y-axis is the chance that your next proc will come at a particular time after the previous proc. As you can see, the two are identical until x=1.5, and then the new system (purple line) gives a burst of added proc chance that drastically shortens the tail of the curve.

Estimating the new MPT requires finding an equation for the new probability curve and integrating it (see appendix).  In general, what I computed is that, once the boost kicks in, the expected proc time is roughly half (48%) of what it would have been otherwise. Since you only reach that point 22.3% (e^(-1.5)) of the time all in all the average wait for each proc is reduced to 88.4% of what it was, or 13.1% more procs over a given time.

The Effect on Uptime

In the low-uptime case, where we can approximate uptime with  lambda , then we would now simply take it to be  1.13lambda . Unfortunately, to account for overlaps, we can’t simply multiply lambda  by 1.13 in the above formula. This implicitly assumes two events are independent (overlaps, and activation of the boost) when they’re definitely not. In fact, application of the boost can never cause an overlap unless  lambda > 1.5 “> (which is far beyond the uptime range of any real trinket).</p>



<p>The correct model, fortunately, is even simpler. Multiply the previous uptime (including overlaps and all) by 1.13. After all, those 13% new procs have to happen somewhere, and they can’t contribute to overlaps:</p>



<figure class=1.13cdot (1 - e^{-lambda})

If the equation bothers you because it’s not manifestly limited to 1 as an uptime should be, remember that it’s expressly valid only for  lambda < 1.5  (and in that range it reaches roughly 88%). Essentially, what this is model is saying is that everything is happening as it was before, including overlaps, but total proc events are going to happen 13% more often.

Stacking Trinkets

Trinkets like Talisman of Bloodlust and Horridon’s Last Gasp have an added twist–on a repeat proc, they don’t simply overlap and refresh the prior buff, but also add another stack (up to 5). This makes the math more complex but still manageable.

Recall the logic of the main uptime formula from the prior post. In a Poisson or similar process, at any given moment, the chance of not having had an event in the past unit time is  e^{-lambda} .

But now in the (1-e^{-lambda})  case where our buff us up because we have had a recent proc, we need further information: was the buff already up when this proc started? Well, the answer is the same–it was up (1-e^{-lambda})  of the time. The memory-less nature of Poisson processes is key here–the answer to that question is the same no matter when you ask it (we’ve not accounted for the boost yet, but remember that it cannnot affect stacks or overlaps as long as lambda < 1.5 ).

So at any given moment, the chance that we have at least one stack is 1-e^{-lambda} , same as always. The chance that we’ll have at least two stacks is:

(1-e^{-lambda})^2

From here it’s easy to see the chance of having at least k stacks at a given moment. To find the overall average stack height (which gives our actual buff contribution), we need to sum all those components up to the maximum number of stacks, N:

sum_{k=1}^N (1-e^{-lambda})^k

Recalling the partial sum of a geometric series:

sum_{k=1}^N r^k = frac{r(1-r^N)}{1-r}

In our case:

sum_{k=1}^N (1-e^{-lambda})^k = frac{(1-e^{-lambda})(1-(1-e^{-lambda})^N)}{1-(1-e^{-lambda})}
= (e^{lambda} - 1)(1-(1-e^{-lambda})^N)

This should be a clean formula you can use to find your average weighted uptime on a stacking trinket. As in the non-stacking case, to account for the bad-luck boost, simply multiply the entire thing by 1.13.

1.13(e^{lambda} - 1)(1-(1-e^{-lambda})^N)

A complication not addressed here is that Talisman of Bloodlust itself adds haste, which changes the proc frequency slightly at each iteration. This is better handled in a simulation, but if you wanted to write it down as formula you could break the sum back out into 5 individual terms and independently compute lambda for all of them.

ICD trinkets

A lot of people ask how to correctly model trinkets like Wushoolay’s Final Choice (22 second ICD). This family of trinkets uses RPPM, but has an ICD anyway because their mechanics would be too messy if they allowed overlap procs. In this case, the mean proc time, instead of simply being 60/(PPM*H), should be:

frac{60}{PPMcdot H} + ICD - 10

The -10 is due to the fact that the RPPM system accumulates proc chance for up to 10 seconds. So on your first attack after the ICD runs, you get the benefit of 10 seconds worth of stored-up proc chance.

Since these trinkets do not allow overlaps, the uptime is simply the duration over the MPT:

frac{D}{frac{60}{PPMcdot H} + ICD - 10}

Finally, the boost. Though there’s no firm confirmation on this, I’ll assume here that the time during the ICD does count as a time of no procs for purposes of the boost (this would be consistent with the treatment of the usual 10-second RPPM pool). In that case, you can simply increase overall mean uptime by 1.13 as usual:

frac{1.13D}{frac{60}{PPMcdot H} + ICD - 10}

Unerring Vision

A note on Unerring Vision of Lei Shen. Even though the nominal uptime of this proc is 4 seconds, the actual benefit lies in a set of DoTs with 100% crit rate that lasts long after the proc is over (it has little use unless you make use of this DoT effect). If it reprocs while the previous set of buffeds DoTs is still up, you’re going to clip them with new buffed DoTs. So for overlap purposes, the “duration” and “uptime” of UVLS are really analyzed with reference to the DoTs it produces, not the 4s proc itself. Keep this in mind when theorycrafting the trinket.

Beginning of an Encounter

Finally, one less technical discussion, about the beginning of a fight. When the RPPM system was first introduced, one important ramification of its time-independent nature was that you no longer got the reliable fast proc that ICD-based trinkets produced at the beginning of every encounter. But the “boost” reverts this change for most part, since you’ve necessarily been out of combat and not gotten a proc for a few minutes.

With high-frequency trinkets like the 3.3 RPPM melee trinkets, mean proc time may be 15 seconds or lower with some haste. At that frequency (say it’s exactly 15 seconds), after only 25 seconds out of combat, you’re guaranteed a proc on the first swing of the fight. (You’d normally have a 2/3 chance to proc on that swing, since you’ve pooled 10 seconds out of an MPT of 15, and having “failed” to proc for 1.67 MPT’s gives a further 50% boost.

On the flip side, if you’re a UVLS user with an MPT of 2 minutes, then after a typical 2-minute runback and reset the boost will not have kicked in at all. The 2 minutes still matter because you’ll start getting a boost if you fail to proc by one minute into the fight, but that doesn’t help you get a proc during your initial timer stack. Even if you’ve been out of combat (or not had a proc) for 5 minutes (2.5 MPTs), the 4x increase to proc rate as you start the fight still only means you start the fight with an effect MPT of 30 seconds, which is not a crisp start you can plan on. Only after you’ve been out of combat for roughly 10 minutes (5 MPTs) does the whopping 11.5x increase in proc rate mean that you can expect a proc in the first 10 seconds (which is great benefit, as you can now save timers for it). Now, this is a worst case–most people even with trinkets in the 0.5 RPPM range (say Breath of the Hydra) will have an MPT somewhat under 2 minutes due to haste. But point still remains that people with low-frequency trinkets can get a marginal benefit by avoiding using them for up to many minutes before an important pull.

As a general matter, the amount of time you need to have spent without a proc in order to guarantee a proc on the first hit of a fight is:

frac{MPTcdot (MPT+35)}{30}

Where MPT is your usual mean proc time in seconds (60/PPM*H), so this could be also be written as:

frac{120}{(PPMcdot H)^2} + frac{70}{PPMcdot H}

Remember that H should be your haste with no procs or temp buffs active, as it will be on the first attack of a fight. Note that the result is quadratic in MPT, which explains why some trinkets get it so easily and some have to wait so much longer.

Appendix

This is where I first worked out the effect of the boost. I added a few notes at the bottom to try to make it understandable. Time is measured using the variable tau, which is a dimensionless time variable scaled so that MPT=1. The first task was writing the probability function P(tau) when the boost is present (for now assuming that it starts at tau=0), which was done with the differential equation involving Q(tau) (the cumulative chance of not having a proc by time tau). Then I integrate that new probability function to finds its mean (the 0.48 I mentioned earlier). All that’s left is to account for the fact that the boost doesn’t kick in until tau=1.5 by properly averaging the old and new functions together.

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