Intellect -> Spirit Conversion on the PTR : Theorycrafting HQ - Page 3

Grayson Carlyle · 02/10/08, 11:44 PM

Originally Posted by constantius

This may actually indicate that Blizzard has fully abandoned their former "mana-per-tick" model and moved to a per-second value which can be used by the per-tick regen calculator.

That would be a fairly significant step for them to have taken, since we're 3 years and counting on the per-tick model.

Uh... this was patched in, and in the patch notes for... 2.2? It went with the rogue energy change that made energy an energy/second count, but would only give the energy on the old tick time, but at a now-fixed rate. All regen was changed to this same model so that over the entire length of combat, mana and energy gained was an exactly calculated value, and didn't depend on when you got out of casting/used a skill to know how much you would regen.

Originally Posted by Starfire

Holy priests can also clear cast/inner focus and do not ever spend 100% of the time inside the FSR.

How sure are you of this? Just measured in-FSR time for our resident CoH priest on Naj'entus, Akama, Teron, Gurtogg, RoS and Mother this week. Naj'entus was 87%, the rest were all >99% in FSR. HS also is just as high except on Anatheron where there's no point to heal while you're debuffed, and Archimonde with all the running. If you're much better geared than we are, then I can see it being quite a bit lower (unless you're also dropping healers for DPS to get fights over quicker), but perhaps you should run a mod to track your in-FSR% so you know just how much mp5 converts to spirit for you.

Starfire · 02/10/08, 11:46 PM

Originally Posted by Grayson Carlyle

Uh... this was patched in, and in the patch notes for... 2.2? It went with the rogue energy change that made energy an energy/second count, but would only give the energy on the old tick time, but at a now-fixed rate. All regen was changed to this same model so that over the entire length of combat, mana and energy gained was an exactly calculated value, and didn't depend on when you got out of casting/used a skill to know how much you would regen.

Didn't they do this to address innervate/evocate/adrenaline rush sometimes giving considerably less mana/energy than at other times? If I remember, in the case of evocate/innervate, it was a full tick difference depending on when it was cast.

Grayson Carlyle · 02/10/08, 11:52 PM

Originally Posted by Starfire

Didn't they do this to address innervate/evocate/adrenaline rush sometimes giving considerably less mana/energy than at other times? If I remember, in the case of evocate/innervate, it was a full tick difference depending on when it was cast.

Yes, that was the reason.

XP-Dolphin · 02/11/08, 12:46 AM

I wrote a data collection mod to pick up mana/sec regen values for different int/spi values automatically. It could speed up the efforts to see what the formulas are. It seems so far that for a given static int value, the mana/sec gains per spirit is linear. However, given that, it seems that the mana/sec/spirit value goes down as int increases. Would fit with the non-linear formulas given for that so far.

http://72.36.128.2/isc.zip

Feel free to use this mod. The variables will be saved in the saved variables lua. The ManaRegenArray is stored as an array of ManaRegenTable[class][int][spi] = manaregenfromspirit/sec. /intspicalc calc will let it go through all int values that you have 2 or more spirit entries in and figure out how much mana/sec 1 spirit will give and save that as well. It will also share data with guild automatically, so if many in 1 guild are running it, 1 person can collect all the data to be posted. Feel free to examine the code (it is short and simple) to verify if you are not the trusting type.

Whitetooth · 02/11/08, 12:50 AM

Hello,
I'm the author of RatingBuster, so naturally I started working on the formula the moment test servers went up too.

So after 6 hours of work, the new mana regen formula is a function of spi, int and level(class is no longer a parameter), the following data and formula is 100% accurate:

ManaRegen(SPI, INT, LEVEL) = (0.001+SPI*BASE_REGEN[LEVEL]*(INT^0.5))*5

BASE_REGEN[LEVEL] = { -- parsed from game files
[1] = 0.034965
[2] = 0.034191
[3] = 0.033465
[4] = 0.032526
[5] = 0.031661
[6] = 0.031076
[7] = 0.030523
[8] = 0.029994
[9] = 0.029307
[10] = 0.028661
[11] = 0.027584
[12] = 0.026215
[13] = 0.025381
[14] = 0.0243
[15] = 0.023345
[16] = 0.022748
[17] = 0.021958
[18] = 0.021386
[19] = 0.02079
[20] = 0.020121
[21] = 0.019733
[22] = 0.019155
[23] = 0.018819
[24] = 0.018316
[25] = 0.017936
[26] = 0.017576
[27] = 0.017201
[28] = 0.016919
[29] = 0.016581
[30] = 0.016233
[31] = 0.015994
[32] = 0.015707
[33] = 0.015464
[34] = 0.015204
[35] = 0.014956
[36] = 0.014744
[37] = 0.014495
[38] = 0.014302
[39] = 0.014094
[40] = 0.013895
[41] = 0.013724
[42] = 0.013522
[43] = 0.013363
[44] = 0.013175
[45] = 0.012996
[46] = 0.012853
[47] = 0.012687
[48] = 0.012539
[49] = 0.012384
[50] = 0.012233
[51] = 0.012113
[52] = 0.011973
[53] = 0.011859
[54] = 0.011714
[55] = 0.011575
[56] = 0.011473
[57] = 0.011342
[58] = 0.011245
[59] = 0.01111
[60] = 0.010999
[61] = 0.0107
[62] = 0.010522
[63] = 0.01029
[64] = 0.010119
[65] = 0.009968
[66] = 0.009808
[67] = 0.009651
[68] = 0.009553
[69] = 0.009445
[70] = 0.009327
}

Now to start working on RatingBuster...

How I obtained the formula and data

• constantius · 02/11/08, 1:02 AM

Glad you confirmed the results from the other findings. Since your numbers match with ours within 4 decimals, it's basically derived. I'm not sure you need the 0.001 intercept factor, since it works out to less than round-off error on your Mp5, but your call.

Whitetooth · 02/11/08, 1:12 AM

Originally Posted by constantius

Glad you confirmed the results from the other findings. Since your numbers match with ours within 4 decimals, it's basically derived. I'm not sure you need the 0.001 intercept factor, since it works out to less than round-off error on your Mp5, but your call.

Its needed for 100% accuracy, in 2.4 mana users have a 0.001 mana/sec with 0 spirit, this is from data I obtained on test server.

XP-Dolphin · 02/11/08, 1:22 AM

Originally Posted by constantius

Glad you confirmed the results from the other findings. Since your numbers match with ours within 4 decimals, it's basically derived. I'm not sure you need the 0.001 intercept factor, since it works out to less than round-off error on your Mp5, but your call.

The mp5 value listed on the character sheet may be rounded off, but it still works it out internally to great precision. You can determine this with the API function that gives the mana regen/sec from spirit. I am sure that is what he did to get that value. That is why ticks will sometimes give like say 200 mana back and others will give 199. It is the internal rounding working out to the real exact value.

Arthian · 02/11/08, 1:35 AM

Originally Posted by Grayson Carlyle

How sure are you of this? Just measured in-FSR time for our resident CoH priest on Naj'entus, Akama, Teron, Gurtogg, RoS and Mother this week. Naj'entus was 87%, the rest were all >99% in FSR. HS also is just as high except on Anatheron where there's no point to heal while you're debuffed, and Archimonde with all the running. If you're much better geared than we are, then I can see it being quite a bit lower (unless you're also dropping healers for DPS to get fights over quicker), but perhaps you should run a mod to track your in-FSR% so you know just how much mp5 converts to spirit for you.

I'm dragging this a little off topic. In the holy priest thread it was estimated an average OO5SR of about 70%. If you're hitting 100% I5SR then I'm guessing your COH priest is cross healing.

Good post is [Priest] Holy Raiding Compendium (2.3.x) Post #636

Muphrid · 02/11/08, 1:36 AM

Originally Posted by Ulthwithian

Granted, but again, I'm more concerned with what happens with mages. Unfortunately, I checked my math again so that I can use an inequality. (I'd like to apologize if my math skills are not too honed for the company I'm in.)

s*√i*k

(s+1)*√i*k>s*√(i+1)*k

(s+1)*√i>s*√(i+1)

〖(s+1)〗^2*i>s^2*(i+1)

(s^2+2s+1)*i>s^2 i+s^2

(2s+1)*i>s^2

i>s^2/(2s+1)

This means that if your Int is greater than the given number (related to your spirit), adding Spirit will increase your mana regen better than Int. So, let's pick a number. Say, 400. That's your Spirit. This means that if you have greater than 199.75 Int, it is better to put one point of Spirit on than one point of Intellect, for purposes of mana regen.

Thus, this change does not really benefit Mages at all, but it might have implications for very high-Spirit casters. It seems the rule of thumb would be that if your Intellect is less than half your Spirit, increasing your Intellect to the point that it is half of your Spirit would yield better regeneration than simply stacking Spirit.

Edit: Another statement you can derive is how much Int you would need to match the mana regen increase of 1 additional Spirit for any combination of Intellect and Spirit. The formula is

x (the required increase in Int) = i(2s+1)/s^2

For my own mage with 467 Int and 199 Spr, it comes out to 4.7 Int.

Actually it's more useful to consider any abstract change in the stats.

$\Delta{i} = i \left ( 1+\frac{\Delta{s}}{s} \right)^2 - 1$

$\Delta{s} = s \sqrt{1+\frac{\Delta{i}} {i}}$

Its needed for 100% accuracy, in 2.4 mana users have a 0.001 mana/sec with 0 spirit, this is from data I obtained on test server.

How did you obtain 0 spirit?

◊ Lord BEEF · 02/11/08, 1:52 AM

Originally Posted by Pyros

I thought the whole point of knowing the formula and what not was to find out at what point does spirit become better than mp5 on items(respecting ilvl weight). I don't think anyone thought of stacking int, but if spirit becomes better than mp5, it makes a big difference, for druids and priests at least, because we both benefit from spirit based talents/skills(well not sure about holy priests, might be disc only? resto druid have tree of life and innervate tho). In the current situation, even when grouped often in tank group, there's really no point in stacking spirit over mp5 because the gains from the aura are low enough, and mp5 is straight out better for mana usage.

I can't help much since my druid hasn't copied, and I suck at math anyway, but like everyone else, I'm interested in the effects on my char, and indirectly in the loot I can get right now that will be better when 2.4 goes live(even tho with all the new easy to get gear, that might not be necessary).

For druids in 2.3, if you have blessing of kings, living spirit, and innervate yourself, spirit is as good as mp5 even if you're in the five second rule 100% of the time.

This change if the formula stays the same makes spirit massively better, almost to the point of absurdity and I expect it to be toned down somewhat.

Whitetooth · 02/11/08, 1:52 AM

Originally Posted by Muphrid

How did you obtain 0 spirit?

Raw data from test server(I have lots of these):
INT SPI MANA_REGEN
19 25 3.811222864
19 20 3.049178196

Its calculated by 3.811222864 - (3.811222864 - 3.049178196) / 5 * 25

Muphrid · 02/11/08, 1:57 AM

Originally Posted by Whitetooth

Raw data from test server(I have lots of these):
INT SPI MANA_REGEN
19 25 3.811222864
19 20 3.049178196

Its calculated by 3.811222864 - (3.811222864 - 3.049178196) / 5 * 25

Fair enough. Although with that many places, I'm rather...surprised I don't get .001 exactly.

Pintofbrew · 02/11/08, 5:56 AM

I'm a little confused with how the per-sec regen compared to the per-tic model. When will the actual OO5SR pulse tic? The exact instant 5.0sec have gone past last cast-end or next tic after that time? Also, will it pulse every second after that, or every subsequent tic?

The reason I'm asking is in arcane it is often the case rotations are used to the tune of: 5sec channel, then 1.5sec cast. This results in 6.5sec between mana spending, so getting 1 pulse worth of "2-sec OO5SR" or 2 pulses of "1-sec OO5SR" makes a signifficant difference to how much haste one can stack before this effect starts to be diminished.

Batguus · 02/11/08, 8:22 AM

Whitetooth, might I ask how you came up with the BASE_REGEN[LEVEL] numbers? The formula seems (near) perfect for lvl70 at least, but just curious what kind of formula you found for level -> base regen.

Mearis · 02/11/08, 8:24 AM

This change makes spirit and int utterly absurd, it might make gemming completely different. I am going to play around and see if you can make some absurd human priest with int and spirit gems getting 350+ mana/5 in combat.

djmcave · 02/11/08, 9:04 AM

You mean raid buffed or normal....
normal I am already at
270+ unbuffed and 380 raid buffed.
and looks like i'll be adding about 60 regen to the casting figure.

Check Seersage on Grim Batol EU.
Been away for a few so dont mind part of the gear

Mearis · 02/11/08, 9:36 AM

Here is a simple surface plot of the spirit/intelligence gains at level 70:

[img=http://img513.imageshack.us/img513/9263/spiritintat70gb0.th.jpg]

Pintofbrew · 02/11/08, 10:11 AM

Seems like there's a distinct inflation on the intellect side of things compared to spirit. This bodes well for arcane mages as stacking huge intellect seems infinitely more viable/useful than stacking spirit. Looks like it's shaping up to be "get gear with spirit, and gem for max int" might be possible as an AB-feeding method. Kavan suggests 1int->1.5spell given his AB-heavy rotations andraid conditions; whether this is accurate or not in TC terms remains to be analyzed.

Mithos · 02/11/08, 11:29 AM

Originally Posted by Whitetooth

Raw data from test server(I have lots of these):
INT SPI MANA_REGEN
19 25 3.811222864
19 20 3.049178196

How do you get this Mana_Regen of 3.811222864 (Int 19, Spi 25)

With your formula:
ManaRegen(SPI, INT, LEVEL) = (0.001+SPI*BASE_REGEN[LEVEL]*(INT^0.5))*5 ?

Because if i calculate backwards i come to:

ManaRegen(SPI=25, INT=19, LEVEL=?)=3.811222864

3.811222864 = (0.001+25* X *(19^0.5))*5 ?
3.811222864/5 = 0.001+25* X *(19^0.5)
3.811222864/5 - 0.001 =25* X *(19^0.5)
(3.811222864/5 - 0.001) =25* X *(19^0.5)
(3.811222864/5 - 0.001)/25 = X *(19^0.5)
(3.811222864/5 - 0.001) /25 / (19^0.5) = X

X = 0.0069856592929...

This is not a value of BASE_REGEN[LEVEL]

If i fill out the formula with those values we come to:

ManaRegen(SPI=25, INT=19, LEVEL=70) = (0.001+25*0.034965*(19^0.5))*5
= 5.086931306 instead of 3.811222864

Where is my fault?

• constantius · 02/11/08, 11:39 AM

I'm not sure whether the image above actually shows anything new -- mostly, it looks like regen is proportional (which, from the formula, it is) to both intellect and spirit. This makes sense. You can also see the curve of the power of 0.5 along the intellect portion of the curve.

For those interested in computing the deflection point at which intellect makes your post-2.4 (current PTR) regen *higher* than 2.3.2 values (Live), here's a quick reformulation of the equation:

Explanation

For any level of spirit, there will be a value of intellect that is a deflection point. On one side, Live values are greater, on the other, PTR values are greater. You can fairly easily determine these values.

sqrt(Int) =670/Spi + 13.4

Fix spirit, and you'll find Int. Fix Int, and you can solve for spirit. 300 int was roughly the value I found (not using this method) where there was a deflection point for values of spirit under 200 - i.e. spirit =155, int = 300 to improve on results.

As an example:
- 325 int, 155 spirit (PTR) = 130 Mp5
- 300 int, 155 spirit (Live) = 128.1 Mp5
- 300 int, 155 spirit (PTR) = 125.2 Mp5
- 275 int, 155 spirit (PTR) = 119.9 Mp5

Since my original formula was not an accurate model, this deflection point shifted around. As spirit gets very high, it becomes quite low, and at 600 spirit, you only need 210 intellect to have a better PTR result.

As an aside, for most of us, 155 spirit is basically unbuffed. So if you have absolutely no spirit at all (unlikely, but theoretically possible), you need only 314 intellect to *still* gain more benefit from spirit than you currently do. Since 314 intellect is a mana pool of ~ 8500, and can easily be gained from raid buffs, even a new-to-70-in-blues priest should be gaining a benefit from this change. Those of us in T6 ... yowza.

Mearis · 02/11/08, 11:44 AM

Originally Posted by constantius

I'm not sure whether the image above actually shows anything new -- mostly, it looks like regen is proportional (which, from the formula, it is) to both intellect and spirit. This makes sense. You can also see the curve of the power of 0.5 along the intellect portion of the curve.

For those interested in computing the deflection point at which intellect makes your post-2.4 (current PTR) regen *higher* than 2.3.2 values (Live), here's a quick reformulation of the equation:

Explanation

For any level of spirit, there will be a value of intellect that is a deflection point. On one side, Live values are greater, on the other, PTR values are greater. You can fairly easily determine these values.

sqrt(Int) =670/Spi + 13.4

Fix spirit, and you'll find Int. Fix Int, and you can solve for spirit. 300 int was roughly the value I found (not using this method) where there was a deflection point for values of spirit under 200 - i.e. spirit =155, int = 300 to improve on results.

As an example:
- 325 int, 155 spirit (PTR) = 130 Mp5
- 300 int, 155 spirit (Live) = 128.1 Mp5
- 300 int, 155 spirit (PTR) = 125.2 Mp5
- 275 int, 155 spirit (PTR) = 119.9 Mp5

Since my original formula was not an accurate model, this deflection point shifted around. As spirit gets very high, it becomes quite low, and at 600 spirit, you only need 210 intellect to have a better PTR result.

As an aside, for most of us, 155 spirit is basically unbuffed. So if you have absolutely no spirit at all (unlikely, but theoretically possible), you need only 314 intellect to *still* gain more benefit from spirit than you currently do. Since 314 intellect is a mana pool of ~ 8500, and can easily be gained from raid buffs, even a new-to-70-in-blues priest should be gaining a benefit from this change. Those of us in T6 ... yowza.

It isn't anything new, it is just more intuitive to understand I think than formulas - it is also handy to follow the equipotential lines to see the equivalence and what stat is worth more.

It would be quite easy to find now at any given point, as a function of itemization costs what stat is best to boost. This mostly makes gemming extremly interesting.

bowbaq · 02/11/08, 12:22 PM

What about hunters, since we do have mana, int and spirit and in some way are casters

?

I don't have my char on the PTR because EU PTR copy is down, but I just use the formula from Whitetooth.
I have on live 277 int, 96 spi, resulting in a 85 mp5. According to Whitetooth, my OO5SR would be 74.5 mp5 ?

I'd have to yell for a new nerf for hunter :p

I do not have my OO5SR on live full buff, but I can calculate my int and spi : That'd be 397 int and 209 spi, meaning a 194 mp5 on PTR.

Wondering if this could help

When I get my char on PTR (and if you want it), i'll make some tests.

• Playered · 02/11/08, 12:49 PM

This brings up an interesting change to Innervate.

#1 Priests/Druids should yield around a 50-100% increase in return unless I am mistaken.

#2 It should work for Paladins and Shamans too? They should have around 200 Spi buffed.
I've estimated an OOC regen for one of our Paladins being around 240~, which with an Innervate thrown ontop should result in a 4-4.5k mana regeneration over its duration.

It wouldn't be amazing but still.

Also this will change the Innervate rule of Spi*14 for mana returned as far as im aware.

Batguus · 02/11/08, 12:57 PM

To find what kind of boost 1 Spirit or 1 Intellect will give you in terms of mp/5 you can use this (for lvl70):

+1 Spi = 0.046635*(Int)^0,5
+1 Int = ((Int+1)^0,5-(Int)^0,5)*0.046635*Spi

Here's a very ugly table from excel, look up your Intellect at the top, your Spirit at the left, and you will get 2 values.

The value you find at the left is the Mp5 gain from 1 Spi, the value at the right is the Mp5 gain from 1 Int (the green part is where Spi>int, blue is Int>Spi).