This change seems so weird without giving us a 11 heal 5 spi gem. I've been eagerly awaiting it every time the PTR was updated but aparantly that's more fun than we are allowed to have.
That, and a green int/spi gem. It's worth pointing out that the heroic versions of both ([Imperial Tanzanite] and [Seer's Chrysoprase]) are worse compared to the single-stat epic for each; I assume it's some rounding thing with the heroic gems due to their lower ilvl (since not all gems have this problem; [Royal Tanzanite] is exactly the same as [Royal Shadowsong Amethyst]).
On a side note, when comparing spirit to intellect as a stat goes, i have run some numbers using this formula. I forget where i wrote them down, but it came out to be that you needed roughly twice as much intellect compared to spirit to get the same amount of regen out of this new formula.
so, With 460 Intellect, 500 Spirit we get 500 OOC mp5
We will now increase the spirit by 100, which gives us 600 OOC mp5
When we solve the above equation for intellect we get
Running this math gives us a needed 662.5 Intellect, an increase of 202.5 to reach the given increase in regen.
For the basics of it, if you aren't getting at least 2x the intellect versus spirit on an item, the intellect will not give you more regen than the spirit.
Oh, one more thing, with this formula, the higher above 460 intellect you go, the less each additional intellect point increases your regen since it is the √(Intellect). And i am guessing that many people are above 500 at least.
Conclusion:
The intellect to spirit ratio is
1Spirit : 2+Intellect
Considering that 1/(21.45*5) is very close to 0.00932715221261, you're talking about the same formula.
As for the correct ratio, if you try to stack to stack spirit that much with your gear, you're going to find yourself using inferior gear. It's better to stack gear for 3:2, then gem to bring yourself closer to 2:1.
Considering that 1/(21.45*5) is very close to 0.00932715221261, you're talking about the same formula.
As for the correct ratio, if you try to stack to stack spirit that much with your gear, you're going to find yourself using inferior gear. It's better to stack gear for 3:2, then gem to bring yourself closer to 2:1.
It's the same basic formula, except it has rounding errors present in it that can add up given the right set of comparisons.
Though comparing the numbers between Whitetooth's formula(with the +0.001 added in) which track with the reported regen numbers from the client(rather than the character sheet) out to the 6th decimal place with 520 int, 494 int being the numbers I used... (the error I came up with was +0.0000032256297, though I might have been doing something wrong)
That alternate formula was off by -0.1734488262888 mana per 5 versus the in game client... Which for the majority of players won't really concern them too much when they're just doing mp5 comparisons on a single five second interval. It gets problematic when people start using it to model regen over a much longer duration.
Basically, it's good enough for shorthand calculations, particularly when dealing with the character sheet stats, as they're already riddled with rounded values. But for more detailed work, the longer formula is the better one to use.
Considering that 1/(21.45*5) is very close to 0.00932715221261, you're talking about the same formula.
As for the correct ratio, if you try to stack to stack spirit that much with your gear, you're going to find yourself using inferior gear. It's better to stack gear for 3:2, then gem to bring yourself closer to 2:1.
This isn't what i am talking about at all.
Stacking spirit can be good, but you must keep it to some kind of pattern. For me, I break down an item as its stats pertain to regen (ex. in 2.3, spirit/2.7=1mp5 for me) and then compare from there.
In this intence, I can convert any gained intellect to spirit, using the formula, and then convert spirit to MP5.
If you approach comparing gear this way, you can fool proof yourself against getting a downgrade. Since for the most part on items spirit and intellect are given the same weight, you aren't gonna find a 2:1 ratio, and lucky if you find a 3:2 ration. Also gems give spirit and intellect the exact same weight, so you cannot find a 2:1 ratio of gems(basically a 8spirit gem will always > a 8 intellect gem). I don't know how anyone else does gear comparisons, but when you can convert 5 stats down to 1 or 2 its much easier to compare.
The BASE_REGEN[LEVEL] in my original post on the formula is actually rounded to 6th decimal places, because that seems to be a logical thing to do when I looked at the raw data.
So I thought I should also post the raw data for those that care to experiment with it, see if it gives less error and what not, the raw data has a full 16 decimal places but most is rounding error from decimal -> binary -> decimal.
Looks like elixir of mastery + elixir of draenic wisdom = win
All of that work you are doing has already been done Ackis. Your revisions have already been done
The "Looks like elixir of mastery + elixir of draenic wisdom = win" is old news.
All of that work you are doing has already been done Ackis. Your revisions have already been done
The "Looks like elixir of mastery + elixir of draenic wisdom = win" is old news.
Nemockulous: you're right that the stated ratios that are "optimal" are also difficult to achieve. It's mostly of theoretical interest, I think.
Thus, your approach to stat equivalence is basically the way I would do things, just in a more formalized fashion. We can use algebra to generalize.
Given , we have...
We can compute various deltas...
Which allows us to convert freely between int, spirit, and mp5. Converting int and spirit to equivalent mp5 is done by setting these expressions equal.
These are, in essence, first-order approximations. You'll note that if one increases both int and spirit at the same time, one gets...
We can subtract out the one-variable gains of just int and spirit to figure out what the non-linear ("quadratic") gain is.
This is, of course, of even less practical use, merely theoretical interest. Indeed, for a change of +10 spirit and +10 int at 300 spirit and 400 int, we get a paltry .116 mp5 from the non-linear term (compared to 12.8 mp5 from the linear terms, a less than 1% difference).
Nemockulous: you're right that the stated ratios that are "optimal" are also difficult to achieve. It's mostly of theoretical interest, I think.
Thus, your approach to stat equivalence is basically the way I would do things, just in a more formalized fashion. We can use algebra to generalize.
Given , we have...
We can compute various deltas...
Which allows us to convert freely between int, spirit, and mp5. Converting int and spirit to equivalent mp5 is done by setting these expressions equal.
These are, in essence, first-order approximations. You'll note that if one increases both int and spirit at the same time, one gets...
We can subtract out the one-variable gains of just int and spirit to figure out what the non-linear ("quadratic") gain is.
This is, of course, of even less practical use, merely theoretical interest. Indeed, for a change of +10 spirit and +10 int at 300 spirit and 400 int, we get a paltry .116 mp5 from the non-linear term (compared to 12.8 mp5 from the linear terms, a less than 1% difference).
Well, I don't think that this type of calculation is all that theoretical. In the computations that are being performed, there are really no assumptions being made, which basically removes the theory factor to the calculations. When analyzing Intellect V Spirit from a purely regeneration standpoint, you carry no assumptions. When you compare that to say a regeneration model based on %inside the five second rule, that is more of a theoretical model.
I however do like your approach of removing all the numbers to create a generic equation, because the way i performed the calculation was a tad crude (I have since made a excel spreadsheet that i will post if i get a chance).
On a side note, what did you use to get all of your equations in such a nice looking format?
Well, I say it's of theoretical interest because a spreadsheet or tool would probably just want a master formula and calculate numerical equivalences rather than using the derived equivalences.
Now, to go more along the lines of what you're saying, it would be more "theoretical" to introduce another constant multiplier to account for the five-second rule and the percent of regeneration allowed while in it. If you wanted to be really technical, you could introduce a function as a multiplier (perhaps a function of time, even?). No idea how useful that would be, though.
And the boards have LaTeX built in, which is quite convenient for me to learn the language while avoiding a lot of the compromises usually associated with posting algebra.
I wonder if they realy intended it to be this major of a buff, or well, yes they want to make spirit better, aswell as making intellect worthwhile. that's good. But giving a druid/priest ~50 while casting mp5 for free? just out of nowhere? hmm seems to be little too much imho, neither paladins or shamans gain from this buff.
I like the buff though, realy makes spirit better and could even make arcane visiable ^_^
I wonder if they realy intended it to be this major of a buff, or well, yes they want to make spirit better, aswell as making intellect worthwhile. that's good. But giving a druid/priest ~50 while casting mp5 for free? just out of nowhere? hmm seems to be little too much imho, neither paladins or shamans gain from this buff.
I like the buff though, realy makes spirit better and could even make arcane visiable ^_^
Well they have done it before. Remember I believe it was 2.2 or 2.3 when the increased meditation and the druid talent to give 30% regen while casting. I think in large part this change could have to do with the shift away from regen on items, and towards spell haste. By increasing the regen model, you can allow for less regen stats on an item and increase its other stats, i.e. spell haste.
It does seem a bit of a huge buff. Like I mentioned, I gained about 40-50mp5 for doing nothing but keeping the gear/gem set I have. There is a bit of shift towards spell haste, which I imagine is to offset the mana gains (no mp5 on a lot of spell haste pieces) but this seems to be quickly contradicted by the set pieces (boots, bracers, belt) as they have both spell haste, healing, and mp5.
I keep telling myself it's not a joke, I was excited when flexing like 500 OOFSR and nearly 320 within, now with 2.4 it's up to nearly 800-1000 ooFSR and close to 450-500 within. (all theorycrafting of course)
From most of my time on the PTR I've gathered at least this for druids.
Red = Teardrop Crimson Spinel
Blue = Sparkling Empyrean Sapphire
Yellow = Luminous Pyrestone
However a though that comes across my mind, with spirit such an assest, innervating that shadow priest becomes infinitely more viable.
I don't know if it's me, but does 2.4 seem like it spells the end of the hybrid gems for healers? (Goodbye shadowsong?)
Well, I don't think that this type of calculation is all that theoretical. In the computations that are being performed, there are really no assumptions being made, which basically removes the theory factor to the calculations. When analyzing Intellect V Spirit from a purely regeneration standpoint, you carry no assumptions. When you compare that to say a regeneration model based on %inside the five second rule, that is more of a theoretical model.
I however do like your approach of removing all the numbers to create a generic equation, because the way i performed the calculation was a tad crude (I have since made a excel spreadsheet that i will post if i get a chance).
On a side note, what did you use to get all of your equations in such a nice looking format?
Regarding the "ideal" ratio of Spirit:Intellect in 2.4, after reading a thorough article on the subject posted yesterday at the Resto4Life blog (link below), it occurred to me that the ratio analyses in this thread have been assuming a fight of infinite duration. As Resto4Life points out, the raw chunk of additional mana provided by Intellect has an MP5 value that varies with the fight length; ergo, the ideal ratio actually varies with the fight length. And as the chart in the article demonstrates, the variation in the ratio is very substantial moving from a 4 minute to an 8 minute fight.
Since the 3:2 ratio (when accounting for item budgeting) and 2:1 ratio (when not accounting for it) assume an infinite fight length, they cannot be the "ideal" ratios for any encounter the game has or ever will have. The ideal ratios will necessarily favor Intellect more. Resto4Life tentatively concludes that a ratio around 7:5 is ideal, but her conclusion is limited to Resto Druids under a specific trinket itemization. She also does not account for item budget costs (so her Resto ideal ratio may actually end up close to 1:1 when choosing gear sans gems). However, her general reasoning makes obvious that this thread has yet to arrive at the true, actual-gameplay ideal ratio for a typical-length boss fight (say 8 minutes). My calculus has been long forgotten, so I'll just throw the computation of that down as a challenge to the posters here....
Regarding the "ideal" ratio of Spirit:Intellect in 2.4, after reading a thorough article on the subject posted yesterday at the Resto4Life blog (link below), it occurred to me that the ratio analyses in this thread have been assuming a fight of infinite duration. As Resto4Life points out, the raw chunk of additional mana provided by Intellect has an MP5 value that varies with the fight length; ergo, the ideal ratio actually varies with the fight length. And as the chart in the article demonstrates, the variation in the ratio is very substantial moving from a 4 minute to an 8 minute fight.
Since the 3:2 ratio (when accounting for item budgeting) and 2:1 ratio (when not accounting for it) assume an infinite fight length, they cannot be the "ideal" ratios for any encounter the game has or ever will have. The ideal ratios will necessarily favor Intellect more. Resto4Life tentatively concludes that a ratio around 7:5 is ideal, but her conclusion is limited to Resto Druids under a specific trinket itemization. She also does not account for item budget costs (so her Resto ideal ratio may actually end up close to 1:1 when choosing gear sans gems). However, her general reasoning makes obvious that this thread has yet to arrive at the true, actual-gameplay ideal ratio for a typical-length boss fight (say 8 minutes). My calculus has been long forgotten, so I'll just throw the computation of that down as a challenge to the posters here....
You're correct, and the model here also doesn't factor in the bonus spell crit for all caster, spell damage and Mp5 for Moonkins, etc, all of which provide a benefit from int, or the extra healing for tree druids, spell damage under the effects of Imp. DS, or healing for priests. All of these are much more case-by-case problems without an easy closed-form solution. However, if your intent is simply to maximize your regen, then barring Dreamstate these calculations work pretty well.
You're correct, and the model here also doesn't factor in the bonus spell crit for all caster, spell damage and Mp5 for Moonkins, etc, all of which provide a benefit from int, or the extra healing for tree druids, spell damage under the effects of Imp. DS, or healing for priests. All of these are much more case-by-case problems without an easy closed-form solution. However, if your intent is simply to maximize your regen, then barring Dreamstate these calculations work pretty well.
The examples you mention are clear "case-by-case problems," and they are nontrivial to the extent they involve damage/healing --> mana conversions peculiar to a class. In contrast, 1 Int = 15 more mana at the fight's commencement for all casters.** The effective regen rate of that 15 mana over an x-minute fight is the same for all casters. It would thus seem to make some sense to include that in a base general formula that is the starting point for all the subsequent case-by-case analyses.
In any event, the point is moot because the formula already has been published. I overlooked that Resto4Life included it and its derivation in an appendix to her post. She says it is:
S = 2I - 30√I / (t * 0.046635) where t = number of ticks in the fight.
This adjusted formula does indeed present a character-by-character element because the ratio now varies not only with the fight length, but also with the character's actual amount of Int. The effect of differing Int levels is less than the effect of the t variable; here are some example ratios calculated with this formula:
Character with 400 Int, 300 tick (10-minute) fight: 1.892:1
600 Int, 10 min fight: 1.912:1
400 Int, 5 min fight: 1.786:1
600 Int, 5 min fight: 1.824:1
Now if only someone could adjust her formula to account for item value budgeting...
Speaking from an end-game perspective, there will be functionally *zero* cases where I will care to compare the amount of intellect on an item. Zero. Zip. Zilch. I just functionally do not care.
I will (and do, currently) have over 700 intellect raid-buffed on my gear. I will not stack it. I will not care about it. It's there, it's free, it's meaningless. Given that regen is going to scale with the square root of intellect, stacking it makes absolutely no sense as a priest, given that I get nothing from it but that scaling and spell crit. Stacking spirit on the other hand ... gives linearly increasing regen results and gives 35% as +heal.
The constant arguments over what ratio to aim for are, to be frank, silly, when taken in the context of priests and druids. We really should *not* be caring about 'stacking intellect'. It's a dumb idea. Don't even care about your ratio, either. It's not like we have multiple sets of gear sitting around with identical stats except for the amount of intellect/spirit on them. There are a maximum of 2 items per slot in 2.4 that are 'best-in-game'. They basically differ in the amount of spirit they have on them (spirit and haste, to be precise). That's it. You pick the one you want more of, and you get intellect for free.
Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house. - R.A. Heinlein
Yeah, look, the math doesn't say more than what it says. Optimizing the spirit regen function on the item point allocator, well, just doesn't tell you very much when there are other factors at play. Yes, we can make more complicated models to find better optimizations, but the majority of such work is best done by spreadsheets and tools, not by symbolic math.
It does not seem accurate to value all gem colors the same (@18 points for example). Instead, the stat point values should be based on what is entered for each gem choice and your stat point values. Red > Blue > Yellow.
I found a number of items missing from the spreadsheet that may be helpful for the community. I added these items to my own version, but I thought it might be helpful if they were added to the "master" version being distributed.
Light-Collar of the Incarnate
Light-Mantle of the Incarnate
Masquerade Gown
Trousers of the Incarnate
Gloves of Saintly Blessings
Vindicator's Mooncloth Cuffs (competative if socketed with red +healing gem)
Anveena's Touch (version 2.4 60 Badges Ring)
Earring of Soulful Meditation (estimate stats: 75 spirit, 66 healing)
Essence of the Martyr (estimate stats: 134 healing)
Fel-Reaver's Piston (estimate stats: 75 healing, 16 Mp5)
Lower City Prayerbook (estimate stats: 70 healing, 12 Mp5)
Ribbon of Sacrifice (estimate stats: 98 healing)
Gavel of Pure Light (Sha'tar Exalted)
Vengeful Gladiator's Baton of Light
Carved Witch Doctor's Stick
Blue Diamond Witchwand
03/01/08, 10:17 PM
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