I know pretty much every blogger who has done the quest chain has gushed (or will gush, as the case may be) about the Wrathgate in-game event, but the machinema is just too awesome to not join in. Personally, I don't think I could have completed the event at a better time. The lack of a stable internet coupled with a relatively full out-of-game schedule and the pressure to get to level 77 so I could have a reasonable chance to complete the With a Little Helper from My Friends achievement—and thereby the Merrymaker meta-achievement/title—was really beginning to get to me. For a while, I was afraid that I wouldn't manage to complete the meta-achievement before the event packs its backs at 6:00am on January 2nd.
But yesterday morning I finally completed the Wrathgate event...and the experience earned from its completion got me up to level 77. I must admit, I can think of no more satisfying way to gain a level than with the accompaniment of the completion of a truly epic chain of quests, an achievement to underline it (Veteran of the Wrathgate), and an in-game machinema to top it all off like a watermelon-sized cherry marinated in awesomesauce. After completing that chain, I feel like a brand new player. It's as if all of the wonder and excitement for the game that's been waning as I've become increasingly familiar with its mechanics, tables, and inner workings has come back in full force. I can't wait to see what's next.
Oh, and last night I managed to find a group for the Lake Wintergrasp battle, netting me the 47 kills I still needed to complete the With a Little Helper from My Friends achievement! Huzzah!
Wednesday, December 31, 2008
Friday, December 19, 2008
Internet Troubles
Doing much of anything online these past few days has been extremely frustrating. You see, I'm "home" for the holidays, but my internet connection here has been incredibly unstable. I seem to only be able to stay connected for anywhere between 15 minutes to 2 hours at a time before something eventually goes amiss and the connection inevitably gets lost.
Essentially, this means I have a relatively short window of opportunity to actually get stuff done online, like leveling Gryphonheart past level 74, completing as many Feast of Winter Veil achievements as possible, reading blog posts and webcomics, and reading and moderating the PlusHeal forums (not necessarily in that order of priority). As you might imagine, I am getting extremely frustrated by now—to the point of wanting to play offline or console games rather than continue my World of Warcraft-related activities.
To be honest, I was really hoping to get certain things done (such as completing the Aching Feet story, get Gryphonheart to level 80, etc.) by the end of the year, but the internet's shenanigans are making things downright intolerable. So until I manage to get back to my real home in early January, I probably won't be posting much unless something has me excited enough to deal with the incessant disconnects, and for this I sincerely apologize. :(
Anyway, take care, and may you have a safe and happy holiday season. :)
Essentially, this means I have a relatively short window of opportunity to actually get stuff done online, like leveling Gryphonheart past level 74, completing as many Feast of Winter Veil achievements as possible, reading blog posts and webcomics, and reading and moderating the PlusHeal forums (not necessarily in that order of priority). As you might imagine, I am getting extremely frustrated by now—to the point of wanting to play offline or console games rather than continue my World of Warcraft-related activities.
To be honest, I was really hoping to get certain things done (such as completing the Aching Feet story, get Gryphonheart to level 80, etc.) by the end of the year, but the internet's shenanigans are making things downright intolerable. So until I manage to get back to my real home in early January, I probably won't be posting much unless something has me excited enough to deal with the incessant disconnects, and for this I sincerely apologize. :(
Anyway, take care, and may you have a safe and happy holiday season. :)
Thursday, December 18, 2008
Holy Theorycrafting: Revisiting BoK vs. BoW
So, in the PlusHeal thread where I originally posted my Blessing of Kings vs. Blessing of Wisdom theorycrafting, several questions came up about what was included (or omitted) in my calculations. Those questions were:
Alright, so let's compare Blessing of Kings and Blessing of Wisdom with 1000 Intellect and see what that gets us. I'll also try to factor in the additional mana regeneration from the added crit, although I'd like to point out that I didn't factor it in earlier because not only is it difficult to model without assuming certain playstyles or going crazy with theoretical maximums, but also because I was trying to tilt the scale in favor of Blessing of Kings as much as possible. WhileBlessing of Kings will net you 0.6% crit with 1000 Intellect (since current consensus is that it 100 Intellect grants 0.6% crit, and a fully talented Blessing of Kings with 1000 Intellect will provide exactly 100 additional Intellect), it also has the significant opportunity cost of 3 talent points in Sanctified Seals, which grants 3% crit. In other words, spending the 5 points to max out Blessing of Kings instead of 2 points to max out Blessing of Wisdom essentially results in a net loss of 2.4% crit at 1000 Intellect.
Also before we begin, I'd like to note that I'm not going to factor in the additional 1500 mana at the start of each fight as mp5, because the length of each fight is too variable to simply assume a 5 minute duration. 1500 mana is definitely a bonus, but it amounts to 5 Flash of Light casts or 1 Holy Light and 1 Flash of Light cast or 1 Beacon of Light. Also, the usefulness of 1500 mana really depends on how you view that mana added to your total mana pool. For example, someone who sees that mana added to the top of the mana pool may cast a Beacon of Light prior to the fight and think "Wow, Blessing of Kings gave me a free Beacon!", whereas I see the the mana as added to the bottom of my mana pool, so I don't see it as a real factor unless it becomes the difference of having the mana to cast a spell or not having the mana to cast the spell.
That said, let's make the assumption that maxing out Blessing of Kings doesn't force you to choose between Beacon of Light and Sanctified Seals, and you somehow manage to max out all 3 talents (though this is impossible without being level 83). Since we're pretty much riding the Hypotheticalmobile to Impossibleland anyway, we'll make a few more completely unrealistic assumptions. One such assumption is that each crit would yield the maximum mana return possible—the amount returned from a Holy Light crit. Correct me if I'm wrong, but Holy Light should cost about 1274 mana at level 80, which means each Holy Light crit restores 764.4 mana. Thus, 0.1% crit would give about 0.7644 mana per cast. We continue our voyage into Crazyville and assume we have so much haste that Holy Light is now limited by the minimum global cooldown of 1 second. So, 0.1% crit would yield 0.7644 mps. Multiply this by 6, since the additional 100 Intellect from Blessing of Kings would give 0.6% crit, not 0.1%, and then multiply by 5 because we want mp5 and not mps, resulting in a maximum of 22.932 mp5 for 1000 total pre-Kings Intellect.
As for Divine Illumination, let's also model it in a best-case scenario for Blessing of Kings. Basically, this would be to assume that when Divine Illumination is up, we chain cast our most expensive heal to maximize mana return. Our most expensive heal is Holy Light, and since we've assumed that we've capped haste to the point where you are now limited by the 1 second minimum of the global cooldown above, we'll make the same assumption now, which gives us a maximum of 15 Holy Light casts in a single Divine Illumination duration. Using the Holy Light cost of 1274 mana above, Divine Illumination would reduce this cost to 637 mana, and a Holy Light crit would restore 764.4 mana as mentioned earlier. This gives us a net gain of 127.4 mana in an additional 0.6% (or 6 out of each 1000) of Holy Light casts, averaging to a gain of about 0.7644 mana per cast. Since we assumed we can cast 15 Holy Light per Divine Illumination, we get an average of 11.466 mana each Divine Illumination. As Divine Illumination has a 3 minute (or 180 second) cooldown, this yields 36 5-second periods per cast, resulting in approximately 0.3185 mp5 (or a meager 19.11 mana over the course of the hypothetical 5-minute fight).
The equation you'd get would essentially be as follows:
- Doesn't Blessing of Kings also have the added benefit of increasing one's chance to crit, and shouldn't that be factored in to the mana regeneration comparisons due to the Illumination talent?
- Due to the above, wouldn't the Divine Illumination talent (different from Illumination) further push Blessing of Kings' advantage?
- Blessing of Kings also increases the total mana available, since each point of Intellect also grants 15 mana. Shouldn't this be taken into account as a "variable mp5" stat which varies based on the length of the fight?
Alright, so let's compare Blessing of Kings and Blessing of Wisdom with 1000 Intellect and see what that gets us. I'll also try to factor in the additional mana regeneration from the added crit, although I'd like to point out that I didn't factor it in earlier because not only is it difficult to model without assuming certain playstyles or going crazy with theoretical maximums, but also because I was trying to tilt the scale in favor of Blessing of Kings as much as possible. WhileBlessing of Kings will net you 0.6% crit with 1000 Intellect (since current consensus is that it 100 Intellect grants 0.6% crit, and a fully talented Blessing of Kings with 1000 Intellect will provide exactly 100 additional Intellect), it also has the significant opportunity cost of 3 talent points in Sanctified Seals, which grants 3% crit. In other words, spending the 5 points to max out Blessing of Kings instead of 2 points to max out Blessing of Wisdom essentially results in a net loss of 2.4% crit at 1000 Intellect.
Also before we begin, I'd like to note that I'm not going to factor in the additional 1500 mana at the start of each fight as mp5, because the length of each fight is too variable to simply assume a 5 minute duration. 1500 mana is definitely a bonus, but it amounts to 5 Flash of Light casts or 1 Holy Light and 1 Flash of Light cast or 1 Beacon of Light. Also, the usefulness of 1500 mana really depends on how you view that mana added to your total mana pool. For example, someone who sees that mana added to the top of the mana pool may cast a Beacon of Light prior to the fight and think "Wow, Blessing of Kings gave me a free Beacon!", whereas I see the the mana as added to the bottom of my mana pool, so I don't see it as a real factor unless it becomes the difference of having the mana to cast a spell or not having the mana to cast the spell.
That said, let's make the assumption that maxing out Blessing of Kings doesn't force you to choose between Beacon of Light and Sanctified Seals, and you somehow manage to max out all 3 talents (though this is impossible without being level 83). Since we're pretty much riding the Hypotheticalmobile to Impossibleland anyway, we'll make a few more completely unrealistic assumptions. One such assumption is that each crit would yield the maximum mana return possible—the amount returned from a Holy Light crit. Correct me if I'm wrong, but Holy Light should cost about 1274 mana at level 80, which means each Holy Light crit restores 764.4 mana. Thus, 0.1% crit would give about 0.7644 mana per cast. We continue our voyage into Crazyville and assume we have so much haste that Holy Light is now limited by the minimum global cooldown of 1 second. So, 0.1% crit would yield 0.7644 mps. Multiply this by 6, since the additional 100 Intellect from Blessing of Kings would give 0.6% crit, not 0.1%, and then multiply by 5 because we want mp5 and not mps, resulting in a maximum of 22.932 mp5 for 1000 total pre-Kings Intellect.
As for Divine Illumination, let's also model it in a best-case scenario for Blessing of Kings. Basically, this would be to assume that when Divine Illumination is up, we chain cast our most expensive heal to maximize mana return. Our most expensive heal is Holy Light, and since we've assumed that we've capped haste to the point where you are now limited by the 1 second minimum of the global cooldown above, we'll make the same assumption now, which gives us a maximum of 15 Holy Light casts in a single Divine Illumination duration. Using the Holy Light cost of 1274 mana above, Divine Illumination would reduce this cost to 637 mana, and a Holy Light crit would restore 764.4 mana as mentioned earlier. This gives us a net gain of 127.4 mana in an additional 0.6% (or 6 out of each 1000) of Holy Light casts, averaging to a gain of about 0.7644 mana per cast. Since we assumed we can cast 15 Holy Light per Divine Illumination, we get an average of 11.466 mana each Divine Illumination. As Divine Illumination has a 3 minute (or 180 second) cooldown, this yields 36 5-second periods per cast, resulting in approximately 0.3185 mp5 (or a meager 19.11 mana over the course of the hypothetical 5-minute fight).
The equation you'd get would essentially be as follows:
BoK vs BoWSo, even with numbers that are completely impossible in-game (not to mention at a 1000 Intellect gear level), fully improved Blessing of Wisdom gives you about 28.9495 more mp5 with 1000 Intellect. With 1000 Intellect, Blessing of Kings gives you 1500 more mana and 20 more spell power (and 0.6% crit if you want to make that argument, although it still has an opportunity cost of 3% crit from Sanctified Seals), health equal to your pre-Kings Stamina, attack power equal to 20% of your pre-Kings Strength, a small amount of block value from Strength, a small amount of dodge and armor from Agility, a small amount of Spirit-based mana regeneration, and quite possibly a partridge in a pear tree (but only if you've been a good little boy or girl). :P
= [additional mp5 of DP + MTT + replen from BoK] + [additional mp5 of crit from BoK] + [additional mp5 from Divine Illumination + Holy Light crits] vs 109.2mp5
= [1000 * 0.057] + [22.932] + [0.3185] vs 109.2 mp5
= 80.2505 mp5 vs 109.2mp5
Wednesday, December 17, 2008
Holy Theorycrafting: Mana Regen of Kings vs. Wisdom
Back in the Burning Crusade era, there seemed to be a wide variety of ways one could build a Holy Paladin. Some players went Holy/Prot, others Holy/Ret, and still others Holy/Prot/Ret (I myself used a 47/7/7 build). However, since Wrath of the Lich King launched, it seems that two Holy builds have become dominant: the Holy Kings build (51/5/15) and the Holy Critadin build (51/0/18 + 2 points wherever). The primary difference between these to builds boils down to just 5 points. The Holy Kings build spends these 5 points in Blessing of Kings and Improved Blessing of Kings, and the Holy Critadin build spends 3 points in Sanctified Seals and has 2 points left over. These 2 points can be invested in a variety of different talents, but for the sake of this post, we'll invest them in Improved Blessing of Wisdom. So, ultimately, our trees will look something like this: Holy Kings (51/5/15) and Holy Critadin with Wisdom (53/0/18). (As a side note, choice between Improved Judgements and Improved Blessing of Might in tier 2 of Retribution is irrelevant, and either build can take either talent).
So, with the above 2 builds being the most dominant, the question of which is better will almost invariably arise. As the issue was brought up by a supporter of the Holy Kings build, and I myself favor the Holy Critadin with Wisdom build, I figured I would stack the deck in favor of the Holy Kings build and see when it would surpass the Holy Critadin with Wisdom build. Since Intellect is now one of the most valuable mana regeneration stats for Paladins (thanks to Divine Plea, Replenishment, and other mana restoration abilities that scale based on total mana, such as Mana Tide Totem) and Blessing of Kings added stats scale based on gear, whereas Blessing of Wisdom remains a static bonus, the former will certainly overtake the latter at some point. The question deals with where exactly that point is, and whether or not it is obtainable. Now, on with the post!
Question:
Assumptions:
Abbreviation Key:
Given:
Theorycrafting:
Now, even if you stack full INT and have access to all obtainable gear, items, item enhancements, and buffs, you'd still be hard pressed getting to 1916 INT.
As I see it, Blessing of Wisdom allows me to worry less about mana regeneration stats and instead focus on stats that give me a bit better return, such as haste and spellpower. Blessing of Kings, while nice, still functions best when you stack base stats. Don't get me wrong—it can certainly be a life-saver when the extra health, dodge, armor, crit, etc. etc. it provides means the difference between life and death, but that extra mana regeneration from Blessing of Wisdom can also prove to be the difference between a victory and a wipe.
Ultimately, I think my biggest issue with Blessing of Kings is probably that I still see it as a buff which essentially works to mitigate the effect of bad luck, whereas Blessing of Wisdom does more to allow you to play at your best. I can't speak for anyone else, but personally, I'd rather be good than lucky.
So, with the above 2 builds being the most dominant, the question of which is better will almost invariably arise. As the issue was brought up by a supporter of the Holy Kings build, and I myself favor the Holy Critadin with Wisdom build, I figured I would stack the deck in favor of the Holy Kings build and see when it would surpass the Holy Critadin with Wisdom build. Since Intellect is now one of the most valuable mana regeneration stats for Paladins (thanks to Divine Plea, Replenishment, and other mana restoration abilities that scale based on total mana, such as Mana Tide Totem) and Blessing of Kings added stats scale based on gear, whereas Blessing of Wisdom remains a static bonus, the former will certainly overtake the latter at some point. The question deals with where exactly that point is, and whether or not it is obtainable. Now, on with the post!
Question:
How much Intellect is needed for a fully improved Blessing of Kings to equal the mana regeneration of a fully improved Blessing of Wisdom? For the purposes of this example, I'll be stacking everything possible in favor of Blessing of Kings, with the exception of improving Blessing of Wisdom via talents.
Assumptions:
- Blessing of Kings would replace Blessing of Wisdom on the target.
- Replenishment is up on the target 100% of the time (though this is not a particularly realistic assumption).
- The target is a Paladin who happens to be grouped with a Restoration Shaman, and thus has access to both Divine Plea and Mana Tide Totem, so that mana regeneration due to Intellect is maximized.
- Blessing of Wisdom and Blessing of Kings are both fully improved by their respective talents.
- [Glyph of Mana Tide Totem] is used, but other glyphs are not taken into account.
- Relics are not taken into account.
- The highest rank of each spell is used.
Abbreviation Key:
- BoK: Blessing of Kings
- BoW: Blessing of Wisdom
- DP: Divine Plea
- MTT: Mana Tide Totem
- replen: Replenishment
- INT: Intellect, after other multiplicative modifiers have been taken into account
- mps: mana per second
- mp5: mana per 5 seconds
Given:
- (improved) Blessing of Kings = 1.1 * base stat (after other multiplicative modifiers)
- (improved) Blessing of Wisdom mana regeneration = 91mp5 * 1.2 = 109.2mp5
- mana restored per Divine Plea cast = Intellect * 15 * 0.25
- Divine Plea cooldown = 60 seconds
- mana restored per Mana Tide Totem cast = Intellect * 15 * (0.06 + 0.01) * 4
- Mana Tide Totem cooldown = 300 seconds
- mana per second restored from Replenishment = Intellect * 15 * 0.0025 = Intellect * 0.0375
Theorycrafting:
First, let's convert everything into mp5, so it's easier to compare:
mps of DP = [mana restored per DP cast] / [DP cooldown]
= [INT * 15 * 0.25] / [60]
= INT * 0.0625
mp5 of DP = [mps of DP] * 5
= [INT * 0.0625] * 5
= INT * 0.3125
mps of MTT = [mana restored per MTT cast[ / [MTT cooldown]
= [INT * 15 * (0.06 + 0.01) * 4] / 300
= INT * 0.07 * 0.2
= INT * 0.014
mp5 of MTT = [mps of MTT] * 5
= [INT * 0.014] * 5
= INT * 0.07
mp5 of replen = [mps of replen] * 5
= INT * 0.0375 * 5
= INT * 0.1875
Thus, we can say that the mp5 given by DP + MTT + replen is:
mp5 of DP + MTT + replen = [mp5 or DP] + [mp5 of MTT] + [mp5 of replen]
= [INT * 0.3125] + [INT * 0.07] + [INT * 0.1875]
= INT * 0.57
Since INT will increase by 10% with BoK, we can conclude that the mana regeneration of the above will also increase by 10% with BoK, since they scale with INT. Thus, they would yield an additional mp5 of:
additional mp5 of DP + MTT + replen from BoK = [mp5 of DP + MTT + replen] * 0.1
= INT * 0.57 * 0.1
= INT * 0.057
So, how much INT would be needed for BoK to equal BoW on the mana regeneration front?
additional mp5 of DP + MTT + replen from BoK = BoW
INT * 0.057 = 109.2
INT = 109.2 / 0.057
INT = 1915.79 (rounded up to 1916)
Now, even if you stack full INT and have access to all obtainable gear, items, item enhancements, and buffs, you'd still be hard pressed getting to 1916 INT.
As I see it, Blessing of Wisdom allows me to worry less about mana regeneration stats and instead focus on stats that give me a bit better return, such as haste and spellpower. Blessing of Kings, while nice, still functions best when you stack base stats. Don't get me wrong—it can certainly be a life-saver when the extra health, dodge, armor, crit, etc. etc. it provides means the difference between life and death, but that extra mana regeneration from Blessing of Wisdom can also prove to be the difference between a victory and a wipe.
Ultimately, I think my biggest issue with Blessing of Kings is probably that I still see it as a buff which essentially works to mitigate the effect of bad luck, whereas Blessing of Wisdom does more to allow you to play at your best. I can't speak for anyone else, but personally, I'd rather be good than lucky.
A Quick Update
I was planning on posting some theorycrafting comparing Blessing of Kings to Blessing of Wisdom yesterday, but I got caught up with follow-up theorycrafting addressing some of the issues brought up (or neglected) by the first aforementioned theorycraft. Since it's late and I'm completely exhausted from a day full of traveling, I think reformatting my original theorycraft to work on the blog will have to wait until I wake up.
If you just can't wait to see the results, feel free to check out PlusHeal.com, as I've already posted it there. Night!
If you just can't wait to see the results, feel free to check out PlusHeal.com, as I've already posted it there. Night!
Saturday, December 13, 2008
New Header Image
In case you haven't noticed, I am slowly (but surely) updating the look of this blog as I go along. Creating graphics for this site is, unfortunately, taking much more time than I had hoped, primarily due to the fact that I am away from my normal computer and must make do with programs that are different than what I am used to. However, I'm still chugging along, as those of you who have visited this site recently might have seen. ;)
If you are one of those people who, like me, digest blog content primarily via RSS feeds, I've included the blog's new header image at the top of this post. It's not quite the way I originally envisioned it (different images on either side of the text, a background behind the text, and slightly different font), but I think it came out rather nice, regardless. :P
I may update/redesign it once I've found a program easier to work with, but for now I'm satisfied. In the future, I hope to add a footer image as well, in addition to some graphical content along the side bar. I'm also slowly working on a blogroll and a couple other pages, such as a compendium of useful links. Hopefully, everything will be ready before the New Year, although I sincerely doubt it.
And since it's almost upon us, allow me to be the first to wish you a happy (and filling) Feast of Winter Veil this year!
Wednesday, December 10, 2008
On the Sporadic Posting
Once again, I apologize for the lack of posts recently. What with the holidays coming up and my ISP and router waging war against each other, finding the time (and active internet connection) to post has become a real challenge. I will endeavor to post when I can, but until I get home (likely in early January), I probably won't be able to post very often.
Monday, December 8, 2008
Holy Theorycrafting: SoR vs. SoW+Consecration
I apologize for the lack of posts recently. Real life plus the upcoming holidays has really put a hard limit on the amount of time I have to spare, and sadly online activities tend to be the first thing on my chopping block in such situations. Anyway, to continue with the topic at hand...
In case you don't know, I am one of the moderators at the wonderful healing-oriented forums known as PlusHeal. Well, it just so happened that one of the forum posters there asked a question regarding which strategy dealt damage faster: using Seal of Righteousness for straight-up damage dealing, or using Seal of Wisdom to facilitate the mana regeneration required to be able to cast Consecration as often as possible.
As a Seal of Righteousness user myself, I found this to be a very interesting question. Since I was in the mood to do a bit of theorycrafting at the time, I went ahead and mathed it out. In addition to posting this on the PlusHeal forums, I figured I'd may as well post it here as I've been somewhat lacking in post content recently, and because I spent a good chunk of time on it.
So, let's start with the general idea. As I understand it, the entire point of using Seal of Wisdom instead of Seal of Righteousness is that the former allows you to spam Consecration on cooldown without running into mana issues, whereas the latter would result in downtime if you use Consecration too often. In other words, the whole idea comes down to the notion of Seal of Righteousness vs. Seal of Wisdom + Consecration.
Question:
Assumptions:
So, it seems that using Seal of Wisdomand Consecration yields more DPS than Seal of Righteousness without Consecration. Naturally, using Seal of Righteousness with Consecration would deal more than either of the alternatives, but this is not a sustainable DPS cycle (which was the goal).
In case you don't know, I am one of the moderators at the wonderful healing-oriented forums known as PlusHeal. Well, it just so happened that one of the forum posters there asked a question regarding which strategy dealt damage faster: using Seal of Righteousness for straight-up damage dealing, or using Seal of Wisdom to facilitate the mana regeneration required to be able to cast Consecration as often as possible.
As a Seal of Righteousness user myself, I found this to be a very interesting question. Since I was in the mood to do a bit of theorycrafting at the time, I went ahead and mathed it out. In addition to posting this on the PlusHeal forums, I figured I'd may as well post it here as I've been somewhat lacking in post content recently, and because I spent a good chunk of time on it.
So, let's start with the general idea. As I understand it, the entire point of using Seal of Wisdom instead of Seal of Righteousness is that the former allows you to spam Consecration on cooldown without running into mana issues, whereas the latter would result in downtime if you use Consecration too often. In other words, the whole idea comes down to the notion of Seal of Righteousness vs. Seal of Wisdom + Consecration.
Question:
Which deals more DPS, Seal of Righteousness without Consecration or Seal of Wisdom with Consecration?
Assumptions:
- Judgement of Wisdom and Blessing of Wisdom have 100% uptime.
- Divine Plea is used on cooldown.
- Judgement of Wisdom is used on cooldown to maximize damage output. (This does not necessarily have to be true with the Seal of Wisdom playstyle, but we'll assume it to make the math slightly easier.)
- One can maintain Holy Shock and Consecration spamming indefinitely with Seal of Wisdom active, but not with Seal of Righteousness active.
- Librams are not taken into account.
- There are no differences in playstyle other than which seal is used and whether or not Consecration is used on cooldown.
- Seal of Righteousness's Judgement and Seal of Wisdom's Judgement both have the same chance to deal a critical strike, and both deal a 50% bonus damage when they critically strike.
- Multiple cooldowns completing simultaneously are not taken into account.
- SoR: Seal of Righteousness
- SoW: Seal of Wisdom
- Cons: Consecration
- DPS: damage per second
- MWS: melee weapon speed (calculated after haste effects are taken into account)
- AP: attack power
- SPH: spell power
- CritChance: chance to deal a critical strike in decimal form (i.e. percentage divided by 100) (NOT crit rating)
- Cons#: a damage modifier which depends on which rank of Consecration you cast—rank 6 (level 70) = 72, rank 7 (level 75) = 87, rank 8 (level 80) = 113
- JCD: Judgement cooldown (varies depending on talents)
- Seal of Righteousness damage per swing = MWS * (0.022 * AP + 0.044 * SPH)
- Seal of Righteousness Judgement base damage formula = 1 + 0.2 * AP + 0.32 * SPH
- Consecration total damage = 8 * (Cons# + 0.04 * AP + 0.04 * SPH)
- Seal of Wisdom damage = 0
- Seal of Wisdom Judgement base damage formula = 1 + 0.16 * AP + 0.25 * SPH
First, let's calculate the DPS of SoR and Cons:
SoR DPS
= [SoR damage per swing] * [swings / second]
= [MWS * (0.022 * AP + 0.044 * SPH)] * [1 / MWS]
= 0.022 * AP + 0.044 * SPH
Cons DPS
= [Cons damage] / [Cons cooldown]
= [8 * (Cons# + 0.04 * AP + 0.04 * SPH)] / [8]
= Cons# + 0.04 * AP + 0.04 * SPH
Next, let's figure out how much damage Judgement will contribute. Remember that unlike SoR and Cons, Judgements can deal critical strikes, so we should include that into our calculations:
Judgement bonus damage from critical strikes
= [Judgement base damage] * CritChance * 0.5
average Judgement damage
= [Judgement base damage] + [Judgement bonus damage from critical strikes]
= [Judgement base damage] + [[Judgement base damage] * CritChance * 0.5]
= [Judgement base damage] * (1 + (CritChance * 0.5))
average Judgement DPS
= [average Judgement damage] / [JCD]
= [[Judgement base damage] * (1 + (CritChance * 0.5))] / [JCD]
Now that we have the formula for the average Judgement DPS, let's calculate the numbers for both SoR Judgements and SoW Judgements:
average SoR Judgement damage
= [SoR base damage] * (1 + (CritChance * 0.5))
= [1 + 0.2 * AP + 0.32 * SPH] * (1 + (CritChance * 0.5))
average SoR Judgement DPS
= [average SoR Judgement damage] / [JCD]
= [(1 + 0.2 * AP + 0.32 * SPH) * (1 + (CritChance * 0.5))] / [JCD]
average SoW Judgement damage
= [SoW base damage] * (1 + (CritChance * 0.5))
= [1 + 0.16 * AP + 0.25 * SPH] * (1 + (CritChance * 0.5))
average SoW Judgement DPS
= [average SoW Judgement damage] / [JCD]
= [(1 + 0.16 * AP + 0.25 * SPH) * (1 + (CritChance * 0.5))] / [JCD]
We now have all the numbers we really need for our final calculations, but before we get to the really heavy math, let's go ahead and do something that will make later calculations a bit easier. Since SoR Judgements have greater AP and SPH coefficients than SoW Judgements and they both have the same CritChance and JCD, we know for a fact that SoR Judgements will deal more damage than their SoW counterparts. So, let's just go ahead and figure out exactly how much more DPS we get from SoR Judgements than SoW Judgements on average.
difference between SoR and SoW Judgement DPS
= [average SoR Judgement DPS] - [average SoW Judgement DPS]
= [((1 + 0.2 * AP + 0.32 * SPH) * (1 + (CritChance * 0.5))) / JCD] - [((1 + 0.16 * AP + 0.25 * SPH) * (1 + (CritChance * 0.5))) / JCD]
= ((1 + (CritChance * 0.5)) * ((1 + 0.2 * AP + 0.32 * SPH) - (1 + 0.16 * AP + 0.25 * SPH))) / JCD
= ((1 + (CritChance * 0.5)) * ((1 - 1) + (0.2 - 0.16) * AP + (0.32 - 0.25) * SPH)) / JCD
= ((1 + (CritChance * 0.5)) * (0.04 * AP + 0.07 * SPH)) / JCD
And now it's finally time for the really heavy math. Since we're trying to figure out which playstyle deals greater DPS, I would feel uncomfortable equating the two and then mathing it out. So, we'll just use an arbitrary symbol to separate the two sides while we figure it out. Let's go with ">?<" since we're trying to figure out which is greater than and which is less than the other.
[SoR DPS] + [average SoR Judgement DPS] >?< [Cons DPS] + [average SoW Judgement DPS]
[SoR DPS] + [average SoR Judgement DPS] - [average SoW Judgement DPS] >?< [Cons DPS]
[SoR DPS] + [difference between SoR and SoW Judgement DPS] >?< [Cons DPS]
[0.022 * AP + 0.044 * SPH] + [((1 + (CritChance * 0.5)) * (0.04 * AP + 0.07 * SPH)) / JCD] >?< [Cons# + 0.04 * AP + 0.04 * SPH]
That's pretty much as far as my rusty math skills can get me. Now there's nothing left but to plug in the numbers and see what comes out. I'm going to go ahead and input my numbers as an example.
(0.022 * AP + 0.044 * SPH) + (((1 + (CritChance * 0.5)) * (0.04 * AP + 0.07 * SPH)) / JCD) >?< (Cons# + 0.04 * AP + 0.04 * SPH)
(0.022 * 474 + 0.044 * 1071) + (((1 + (0.2201 * 0.5)) * (0.04 * 474 + 0.07 * 1071)) / 10) >?< (72 + 0.04 * 474 + 0.04 * 1071)
(10.428 + 47.124) + (((1 + 0.11005) * (18.96 + 74.97)) / 10 >?< (72 + 18.96 + 42.84)
57.552 + (1.11005 * 93.93) / 10 >?< 133.8
57.552 + 104.2669965 / 10 >?< 133.8
57.552 + 10.42669965 >?< 133.8
67.97869965 < 133.8
Alternately, you can skip the "calculate the difference between SoR and SoW Judgement DPS" step, which yields the actual DPS potential of both playstyles:
[SoR DPS] + [average SoR Judgement DPS] >?< [Cons DPS] + [average SoW Judgement DPS]
[0.022 * AP + 0.044 * SPH] + [((1 + 0.2 * AP + 0.32 * SPH) * (1 + (CritChance * 0.5))) / JCD] >?< [Cons# + 0.04 * AP + 0.04 * SPH] + [((1 + 0.16 * AP + 0.25 * SPH) * (1 + (CritChance * 0.5))) / JCD]
(0.022 * 474 + 0.044 * 1071) + (((1 + 0.2 * 474 + 0.32 * 1071) * (1 + (0.2201 * 0.5))) / 10) >?< (72 + 0.04 * 474 + 0.04 * 1071) + (((1 + 0.16 * 474 + 0.25 * 1071) * (1 + (0.2201 * 0.5))) / 10)
(10.428 + 47.124) + ((1 + 94.8 + 342.72) * (1 + 0.11005) / 10) >?< (72 + 18.96 + 42.84) + ((1 + 75.84 + 267.75) * (1 + 0.11005) / 10)
57.552 + (438.52 * 1.11005 / 10) >?< 133.8 + (344.59 * 1.11005 / 10)
57.552 + (438.52 * 0.111005) >?< 133.8 + (344.59 * 0.111005)
57.552 + 48.6779126 >?< 133.8 + 38.25121295
106.2299126 < 172.05121295
So, it seems that using Seal of Wisdomand Consecration yields more DPS than Seal of Righteousness without Consecration. Naturally, using Seal of Righteousness with Consecration would deal more than either of the alternatives, but this is not a sustainable DPS cycle (which was the goal).
Wednesday, December 3, 2008
Dalaran!
Last night I managed to finally get Gryphonheart to level 74, the level at which you are presented with a quest that grants you a free teleport to the floating city of Dalaran. Up until now, I've managed to avoid spoiling most of the city by a combination of not paying attention to it in beta (I saw it briefly when I created a pre-made character in the Wrath of the Lich King beta, but portaled out before I managed to get a good feel for the city) and not taking any Dalaran portals in live (Shattrath City remained my [Hearthstone]'s home location until last night).I must say, it was definitely worth the wait. The city looks amazing, and you can really feel all the work that Blizzard put into creating and polishing the place. Of course, it doesn't hurt that this past October I attended BlizzCon '08, which included a World of Warcraft Art panel at which several Blizzard folks showed various aspects about designing the artistic elements of World of Warcraft, including a presentation which showcased each stage of the city's development.
It was mind-blowing seeing how much thought went into even the most minor details (including the various flavor objects you see in the shops. For example, the potions displayed in The Agronomical Apothecary (above) are designed after the various different potion icons found throughout the game, as are the shards, essences, and dust found in Simply Enchanting (below).
Some objects were created specifically to enhance the city's aesthetic character, such as the variety of sweets which can be found on and around Aimee's Pie, Pastry & Cakes cart outside The Bank of Dalaran. Also, if you do visit Aimee's cart, keep an eye out for the different kinds of gingerbread cookies :)
Oh, and yes, they did show panel attendees what Dalaran looked like before it picked itself up and floated off to Northrend. Sadly, I don't think it was a sneak preview of an upcoming Dalaran-centric Caverns of Time instance, as some have speculated.PS: In case you're wondering, the image at the top of this blog post is my favorite part of Dalaran. :P
Tuesday, December 2, 2008
New Casting Animations?
One of my favorite unit animations in WarCraft 3 was the Paladin's Holy Light animation. In case you've never seen it, the Paladin raises his hammer high in the air with one arm, and a brilliant golden ray of light comes down from the heavens to briefly envelop the spell's target in its healing embrace. (In other words, it looked somewhat like a golden healing Moonfire beam. :P ) That one animation captured the purity of the Light in such a graceful way that when World of Warcraft first launched I was genuinely excited to see how awesome the spell would look up close and personal.
Boy, was I disappointed. Instead of raising his hammer high into the air to invoke the Light from the heavens and heal himself or his companions, my Paladin (a human male named Ethos, as this was back in Open Beta, before the game first launched) sheathed his weapon, posed himself as if he were in mid-stride of some extreme powerwalk and wiggled his hands about while wearing what looked like translucent tetherballs made into gloves until a brief flash of yellow light obscured my target. I think I sat there shocked for a few minutes, debating whether I should burst into laughter or tears.
Questions filled my head. Where was the strength and purity that was present in the WarCraft 3 Paladin? Why did my Knight of the Silver Hand look like he was some sort of background dancer for a Chris Farley's Motivational Tetherball Sale-o-Palooza commercial? Why did no beam of Holy Light reach down from the skies and bathe my target in divine purity? Did my target just get his picture taken or something?
When the disappointment finally settled, I found myself hoping that the animations would improve as I leveled. Surely such a pathetic animation couldn't be the representation of such an iconic WarCraft 3 spell, could it? They just didn't want to waste all of the awesomeness of the spell's true animation on its level 1 incarnation, right? I'm sure you can guess the answers. :(
Anyway, when Wrath of the Lich King launched, I noticed something interesting as I began doing quests in Howling Fjord. Rather than seeing the same casting animation I had become accustomed to (though never satisfied with), Gryphonheart did something I'd long since stopped expecting—he raised his [Gavel of Naaru Blessings] high into the air as he invoked the power of the Light. While the dinky little flash still doesn't compare to the old beam of heavenly Light, seeing this was still incredibly gratifying.
Now that the awe and excitement has dulled a bit, I'm beginning to wonder...is this new holding of one's weapons while casting phenomenon intentional? Or is it simply some bug in the animation that will eventually be reverted? I really hope that the change is not only intentional, but the beginnings of new casting animation customization functionality. Of course, knowing my luck, the old animation will be back by the next time I log into the game. :P
Boy, was I disappointed. Instead of raising his hammer high into the air to invoke the Light from the heavens and heal himself or his companions, my Paladin (a human male named Ethos, as this was back in Open Beta, before the game first launched) sheathed his weapon, posed himself as if he were in mid-stride of some extreme powerwalk and wiggled his hands about while wearing what looked like translucent tetherballs made into gloves until a brief flash of yellow light obscured my target. I think I sat there shocked for a few minutes, debating whether I should burst into laughter or tears.
Questions filled my head. Where was the strength and purity that was present in the WarCraft 3 Paladin? Why did my Knight of the Silver Hand look like he was some sort of background dancer for a Chris Farley's Motivational Tetherball Sale-o-Palooza commercial? Why did no beam of Holy Light reach down from the skies and bathe my target in divine purity? Did my target just get his picture taken or something?
When the disappointment finally settled, I found myself hoping that the animations would improve as I leveled. Surely such a pathetic animation couldn't be the representation of such an iconic WarCraft 3 spell, could it? They just didn't want to waste all of the awesomeness of the spell's true animation on its level 1 incarnation, right? I'm sure you can guess the answers. :(
Anyway, when Wrath of the Lich King launched, I noticed something interesting as I began doing quests in Howling Fjord. Rather than seeing the same casting animation I had become accustomed to (though never satisfied with), Gryphonheart did something I'd long since stopped expecting—he raised his [Gavel of Naaru Blessings] high into the air as he invoked the power of the Light. While the dinky little flash still doesn't compare to the old beam of heavenly Light, seeing this was still incredibly gratifying.
Now that the awe and excitement has dulled a bit, I'm beginning to wonder...is this new holding of one's weapons while casting phenomenon intentional? Or is it simply some bug in the animation that will eventually be reverted? I really hope that the change is not only intentional, but the beginnings of new casting animation customization functionality. Of course, knowing my luck, the old animation will be back by the next time I log into the game. :P
Monday, December 1, 2008
Mmm...Delicious New RAM
Yesterday, I managed to snag a good deal on some new RAM for my gaming machine. It has now doubled the memory available from 2GB to 4GB (although my operating system supposedly can only utilize a portion of the latter). Everything seems to be working perfectly after installation, which is a big relief considering how hard it was to figure out whether or not the RAM was actually compatible with my machine or not. :)
Now my biggest problem is finding the actual time necessary to fire up a game and put it through its paces. /sigh :(
Now my biggest problem is finding the actual time necessary to fire up a game and put it through its paces. /sigh :(
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