Theorycraft 101: The Statistics of WoW Spells

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I’ve been doing a lot of in-game testing of spells lately, as a part of making spreadsheets and other projects. In particular, with the new beta, I’m more inclined to vet the info for any spell I look at by measuring in-game, rather than simply putting the coefficient from wod.wowhead into a spreadsheet, because:

  • The designers are changing spells a lot, and tooltips are out of date much more often than on live.
  • The passives, talents, and Draenor Perks aren’t all familiar, and you have make sure you know what all needs to be multiplied in between the coefficient in the data and the final damage amount.
  • There are frequent bugs on beta, and actually testing means you can help catch/report them.

There are a lot of various techniques and tricks you get used to for doing this stuff quickly, but I wanted to dash off a quick post on one that both saves work and is mathematically interesting.  It looks like Theck is starting a series on general concepts of theorycrafting, and while I don’t expect to do anything that elaborate, I do want to write down ideas that are familiar to me but might be helpful to people who are just getting into it.

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Healing Theory, Part 9: First In-Depth Look at Warlords Heals

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All posts in this series can be found here.

I’ve been waiting since alpha started to sink my teeth into the numbers of six new healing toolkits. Rather, I’ve been doing so for a while, but trying to get the information to the point where I can write about it in an organized way. I’ve been assembling a large spreadsheet of 6.0 heals since even before alpha started (since we had spell data). It’s mostly for my own purposes, to have a good reference for the properties of all the spells. I’ll post it here for people who want the full detailed background, while using the post to discuss various interesting points. The goal for this, and ensuing posts, is to work both for people who don’t peruse the actual sheet and just read the post (so I copy various numbers and such into the post), and also for people who want to look further into the sheet after I use a post to highlight some interesting points.

This is the sheet (download).

HT sheet image

It’s more utilitarian than user-friendly; as I said, it’s mostly an easy place for me to store/compare numbers (it’s not a character setup tool). The main focus for each heal is to compute an index for their HPM and HPCT (healing per unit cast time). In some cases, for non-spammable heals, HPCD (healing per cooldown time) is used to measure how much healing is added if the spell is used as often as possible. Some notes:

  • All of these are in unusual units, which is fine since they’re only meant to be compared against each other. For people who want details, HPCT and HPCD are in units of (spellpower coefficient)/seconds, and HPM is in units of (spellpower coefficient)/(% base mana cost).
  • All heals use the haste, crit, mastery, and multistrike values from the top of the sheet (Multistrike affects all spells equally so is not that interesting, except that Holy Priest heals get 25% more benefit).
  • Mastery is also in unusual units. “0.2″ means, the amount of mastery stat that’s equivalent to 20% crit, or what was once called “20 points of mastery.”
  • The main computation in each row is to combine a spell’s spellpower coefficient from wod.wowhead.com with haste/crit/mastery/MS, any class passives or other auras, and any Draenor perks or other bonuses, to compute an overall effective spellpower coefficient.
  • I make assumptions as needed about talents, glyphs, and other variables. Usually the guideline is, a spell’s row in the sheet represents whatever case I was most interested in when thinking about how it would be used in practice.
  • Similarly, sometimes a spell has multiple entries if I want to see e.g. both glyphed and unglyphed, or if I want to see a combination of spells in a single row.
  • Blanket disclaimer: the beta build is changing often, changes aren’t always documented, some spells’ behaviors don’t match their tooltip data, and so on. I got some help from Dayani of Healiocentric, and we vetted all of the rows against in-game behavior in beta builds 18505 or 18522 (often with the techniques described here), and are continually updating them.

On to some of the interesting patterns. Continue reading →

Healing Theory, Part 8: Three 6.0 Topics

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Previous posts in this series can be found here. 

This is an interim update covering a few loosely related topics about 6.0. Not exactly a normal post in this series that analyzes some point of theory in detail, but I wanted to catch up on a few issues, and I figured most of the same people who read this series will be interested in this.

6.0 Regen Math

Now that I’ve gotten to play the alpha some, I have some more concrete numbers on regen in 6.0.

As a reminder, regen currently (5.0) consists of base regen and spirit regen.  Base regen is an amount of MP5 equal to 2% of your max mana (6000 MP5 currently). Spirit regen is 0.564 MP5 per Spirit, in combat.

Spirit Regen

Two important things are happening to Spirit in 6.0:

  • Each point of Spirit is worth substantially more MP5 (2.061 MP5 in combat). This increase is even more dramatic when you consider that mana pools will be smaller by factor of around 2. Adjusted for this deflation, the real value of Spirit (proportional to the size of your mana bar) is about 6.85 times stronger in 6.0 than it is in 5.0.
  • You will have much less Spirit, even after controlling for the item squish. This is because you will only have it on a few slots: rings, necks, cloaks, and possibly trinkets.

The end result is that these two effects, roughly speaking, cancel each other out. The amount of regen you get from Spirit, controlling for the changed size of your mana bar, will be in the same ballpark as it is now (i.e. at a comparable gear level, your mana bar will “look” like it refills at around the same rate).

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The 6.0 Moonkin, Second Look

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My first post when the new Moonkin patch notes were revealed was about explaining them and giving the highlights, but not too much in-depth analysis (read that one first if you haven’t, though). But I’ve been thinking about the details of the rotation a good bit. To the extent possible on paper that is, without an actual alpha to play, but I got pretty far on a reasonable WrathCalcs model. So here are some more detailed observations on how this rotation will play. You can think of this as, how the basics of my Moonkin guide would look if this rotation were going live right now.

Updates

A few things have been mentioned by Celestalon on twitter since the last post.

  • The cycle will now be 40s long instead of 30.
  • The DoTs are now 40s and 20s long to correspond to that (instead of 32 and 16).
  • The cycle will pause briefly at the top. Instead of a sine wave oscillating from -100 to 100 energy, it will go from -110 to +110, but with a cap on the bonus at 100. This will result in roughly a 5 second pause at the peak of each Eclipse.
  • Starsurge will be instant cast.

Eclipse

DoTs

Moonkin are preserving one aspect of gameplay that is otherwise being removed from most classes for causing too much complexity: DoT snapshotting (DoTs will snapshot their Eclipse bonus, and presumably their mastery level at cast, but not other stats like spellpower). Unsurprising then, that some of the more finicky bits of timing that are likely to appear in the new rotation are related to snapshotting.

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The New 6.0 Moonkin Rotation

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After a conspicuous lack of Balance changes in the 6.0 notes before now, the newest update shows what they’ve been working on: a complete rework of the class.

Eclipse

There is still an Eclipse bar, but it’s changed in two important ways:

  • Its movement is no longer affected by your casts at all; it cycles on its own between the two endpoints, making one complete loop every 30 seconds.
  • Your Arcane and Nature damage bonuses vary continuously based on the Eclipse marker. At the midpoint, you get half of your mastery bonus to either element, and at an endpoint, the full mastery bonus to one element only.

So, some things stay the same. Your Eclipse cycles back and forth regularly, and you cast Starfire half the time and Wrath half the time. You use Starsurge regularly (see below) in either half of the rotation, since it’s buffed by either bonus. You maintain DoTs, and casting them when you have a high Eclipse bonus is still beneficial (even though DoTs will no longer snapshot most effects, they will still snapshot Eclipse).

The reason cited for the change is that Moonkin was daunting to initially learn, but relatively easy to play well once you understood it (which is the reverse of what you usually want in a class). I think this is generally correct, subject to some details of Eclipse management at the highest levels of play. Eclipse is confusing to explain and understand at first, to new players to the class, and the new version hopefully won’t have this problem.

In addition to the stated problem related to the learning curve, the 5.0 Eclipse had some issues that commonly caused frustration among players. I tended to pinpoint the problem as being related to Nature’s Grace–a major DPS buff that lasted a fixed amount of time and whose uptime was determined by your ability to race between Eclipses as quickly as possible. This made the class somewhat reliant on haste to avoid being stuck outside of NG, and severely penalized the class for any time not spent advanced in the Eclipse bar, in particular, movement and AoE. Even before seeing these changes, I’d suggested to the devs that they remove Nature’s Grace in 6.0. With the new constantly-oscillating Eclipse, they are not only removing Nature’s Grace, but making it so that your choice of what to cast doesn’t even effect the uptime of an Eclipse bonus. This should make the performance of the class much more stable.

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Healing Theory, Part 7: Introduction to Active Mana Regeneration

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Previous posts in this series can be found here. 

This is the first post in this series that’s explicitly about new mechanics in Warlords. As a general disclaimer, at the moment there is not yet a public alpha, so all we have to go on is information in patch notes and spell data. So I while I will be going into some numbers in this post, keep in mind that anything can change. The point will be more about how to understand active mana regen, and not as much, in particular, about comparing the relative strengths of each class’s new mechanic.

The Active Regen Spells

  • Druid: Innervate. The Druid casts Innervate (2 seconds), which lasts 8 seconds or until the Druid spends mana on a healing spell. If it runs for the full duration, it regenerates 5% mana.
  • Shaman: Telluric Currents. Lightning Bolt casts return 1.25% mana.
  • Monk: Crackling Jade Lightning returns 2% mana after a full-duration channel, which takes 4 seconds. Monks also still have Mana Tea.
  • Paladin: Divine Plea costs 3 Holy Power, and returns 7% mana.
  • Disc Priest: Penance, when used offensively, returns 1.1% mana per hit (and no longer Atones).
  • Holy Priest: When in Chastise, Smite and Holy Fire each return 0.75% mana. Notably, Chakra shifts have a 10s cooldown.

The idea behind these is pretty easy to see: give every healer an ability that lets them choose to regain some mana, at the cost of giving some opportunity to heal. This is a response by Blizzard to the problem that current mana-related abilities tend to involve little or no decisionmaking; you generally simply use them on cooldown. They were prime candidates for removal during the ability-culling process, and that is what happened at first. And while there was no huge problem with that (mana is still interesting due to the inherent choice in choosing how to spend it), abilities whose purpose is to regain mana are definitely a place to add something to healer gameplay.

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RoS Gear Basics — Addendum on Enchanting

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My last post discussed the basics of picking gear in the Loot 2.0 system. It emphasized that a max level character can be geared up rapidly with good rares if you know what to look for and make use of the enchanting system. I want to add a few small points that can make a big difference in how effectively you can use enchanter, especially with limited resources.

A rare item has up to 4 primary affixes and 2 secondary, as discussed before. Each slot has a pool of primary affixes from which it can draw its 4. This is a helpful resource I linked before to see what they are. When you enchant a primary stat, the item can draw the new stat from the usual primary pool (you can click the “?” icon at the enchanter to see all the possibilities in advance). However, the full array of possible affixes is not always available, because certain affixes are mutually exclusive.

In particular, an item can’t have two +skill bonuses or two +element bonuses. So when enchanting a particular stat, if one of the other stats being left on the item is a +skill or +element affix, all of those will be removed from the enchanting pool. This can be used to your advantage when enchanting. Conversely, if an item does not have a +skill or +element affix (except possibly for the one being enchanted), and those are available in the slot, there will be a very long list of possible reforges. This works against you, even if it’s not the +skill or +element that you’re going for. In that situation you might reconsider enchanting the item unless you are willing to spend a large amount of gold and materials rolling the stat you want out of a large pool.

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Reaper of Souls Gear Basics

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Edit: added a little bit more to this, in a separate post here. 

The “Loot 2.0″ system that is the centerpiece of Diablo 3 2.0 makes acquiring gear both more fun and more interesting. The addition of a few new stats, and the enchanting system in particular, means that a little bit of understanding of the system goes a long way in helping you gear up quite quickly once you hit max level. I’ll first give an overview of important stats, and then some practical tips on how to go about putting it all together. In particular, the “Damage” and “Toughness” scores, while they have their uses in making evaluations, can limit your gear progress if you rely on them too much without understanding the underlying stats.

Offensive Stats

Your character sheet’s “damage” score takes into account your weapon damage, primary stat (“Main”), crit chance (“CC”), crit damage (“CD”), and attack speed (“IAS”) bonuses. Since all damaging skills also scale with those stats (some exceptions for IAS, see below) it is a good starting proxy for how much damage you can output. However, there are some important reasons not to simply rely on the Damage score when looking for upgrades. Here are the most prominent ones:

  1. The “[Element] skills deal X% more damage” affix. This works exactly as advertised, and if your build does most of its damage with skills of a particular element, adds a lot of damage that’s not reflected on your character sheet. This gives a strong incentive in Reaper of Souls to try to choose builds that focus on one elemental damage type. If you do all your damage with one element, and you mouseover a pair of bracers with +15% to that element, then even if they show a -5% Damage loss in the comparison, you should think of them as a 10% damage upgrade.
  2. The “Increase [Skill] damage by X%” affix. Similarly, you can probably imagine how to use this. It’s sometimes hard to leverage if your damage is spread between a few different skills, but value it highly if you use a certain skill for most of your damage.
  3. IAS is factored directly into your damage score. But depending on your class and build, IAS may be more or less useful to you. If you are primarily resource-capped (if combat often consists of dumping a whole energy bar into an expensive spender such a Frozen Orb), IAS actually does very little for you, as it doesn’t change the number of casts you get before you run out. Similarly if you use a lot of cooldown-based skills. Conversely, if you generally spam a resource generator (Monks, often), IAS could be better than it appears. Don’t rely on the Damage score when evaluating IAS; think about whether attacking faster is useful in your build.
  4. A more subtle version of the IAS issue is weapon speed. A 1.2 speed weapon and a 1.5 speed weapon might do the same DPS, but one hits much harder per swing and the other attacks faster. The same logic from the IAS discussion applies; one or the other may be much better for you even if they have the same Damage score.
  5. Some stats are not reflected at all in Damage; notably, cooldown reduction and resource cost reduction. Many of the types of builds that don’t like IAS like these stats, because they let you use your attacks more often in practice. Don’t worry about the fact that favoring these stats and disfavoring IAS makes your Damage score look lower.
  6. The CC/CD engine. While these are reflected correctly in Damage, that can be deceptive at low gear levels. The value of each of these stats depends on the other one, so when both are low (when you’re just starting out), CC and CD affixes might show up as weak in your Damage score. Trust that once you accumulate enough of both of them, the synergy is very strong, and a key part of doing high damage. Even if CC/CD items look weak at first, consider saving them because the effects will snowball as you get more.

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Behavior of DoTs and Haste in Warlords of Draenor

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Among the various bits of mechanical info that’s been revealed about Warlords is the fact DoTs and HoTs will no longer have “haste breakpoints” and will no longer “snapshot” your stats at cast time. Celestalon has mentioned this a few times on twitter and frequently responded to questions about it. Since a lot of people seem to have questions on how the math of this breakpoint-less system will work, I want to to explain some of the behavior that will result from this. First, a brief history of this whole problem.

Current System: Haste Breakpoints and Rounding

Before Cataclysm, haste generally did not affect the rate of DoT ticks. There were a few exceptions, such as the Glyph of Rapid Rejuvenation that caused the tick rate of Rejuvenation to be affected by haste. But this did so by shortening the total duration of the HoT and keeping the number of ticks constant, so it didn’t have to address the big question of DoTs and haste: what do to with the fractional ticks that appear when you do this?

When Cataclysm introduced a general mechanic whereby DoT ticks would be accelerated by haste, it handled this problem by changing the duration of the DoT, rounding it to the nearest integer number of ticks.

To work an example: say a DoT has a 12-second duration and a tick period of 3 seconds. Unhasted, when you cast the DoT, a 12-second debuff appears on the target, and the 4th tick will occur exactly as the debuff expires. If you add 25% haste, the tick period will decrease to 2.4 seconds (3/1.25). Since 5 ticks at 2.4 seconds is exactly 12, you will still get a 12-second debuff when you cast the DoT, and now it will be the 5th tick that occurs as the debuff expires. But what if you only had 20% haste? Now the tick period is 2.5 seconds (3/1.2). Since there is no system in place for handling partial ticks, the game can either give you:

  • A 4-tick DoT that lasts 10 seconds, or
  • A 5-tick DoT that lasts 12.5 seconds.

In fact, you get the latter. The game rounds to the closest whole number of ticks, and since in this example, the 5-tick option is closer to the default duration of 12, that’s what you get.

Finally, if you had 12.5% haste, the tick rate would be 2.667. So a 4-tick DoT would be 10.67 seconds, and a 5-tick DoT would be 13.33 seconds. These are equidistant from 12, and this is the oft-discussed “breakpoint.” At any higher amount of haste, you get 5 ticks, and at any lower amount, you get 4.

DoThaste1

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