Intellect -> Spirit Conversion on the PTR : Theorycrafting HQ - Page 2

Batguus · 02/10/08, 7:44 PM

Originally Posted by Kavan

My current findings suggest the actual formula is of the form regen(int,spi)=f(spi)*sqrt(int). More analysis to follow.

Yes as I posted alot earlier, a formula involving sqrt(int) seems to fit the data very well, Ill add two extra columns to my previous data, the 4th is sqrt(int) the 5th is (Sqrt(int)*SPI)/Mp5

Bekah, Priest
555	285	313	23,55843798	21,45097388
552	285	312	23,49468025	21,46148677
551	285	311	23,47338919	21,51098366
550	285	308	23,45207880	21,70078720
544	285	310	23,32380758	21,44285536
538	285	308	23,19482701	21,46274577
536	285	307	23,15167381	21,49259620
531	285	306	23,04343724	21,46202488
527	285	305	22,95648057	21,45113758
526	285	304	22,93468988	21,50127176
524	285	304	22,89104628	21,46035589
516	285	301	22,71563338	21,50815785
515	285	301	22,69361144	21,48730651
512	285	300	22,62741700	21,49604615
511	285	300	22,60530911	21,47504366
509	285	299	22,56102835	21,50465913
508	285	299	22,53885534	21,48352432
504	285	298	22,44994432	21,47058433
500	285	297	22,36067977	21,45721797
498	285	296	22,31591360	21,48660600
496	285	296	22,27105745	21,44341680
494	285	295	22,22611077	21,47268329
484	285	292	22,00000000	21,47260274
479	285	290	21,88606863	21,50872262
476	285	289	21,81742423	21,51545296
473	285	289	21,74856317	21,44754500
469	285	287	21,65640783	21,50549209
468	285	287	21,63330765	21,48255290
464	285	286	21,54065923	21,46534224
544	337	366	23,32380758	21,47574632
605	386	443	24,59674775	21,43192919
512	300	316	22,62741700	21,48172500
489	300	306	22,11334439	21,67974940
473	300	304	21,74856317	21,46239787
426	300	288	20,63976744	21,49975775


Aristiri, Druid
605	386	443	24,59674775	21,43192919


Faxmonkey, Mage
512	300	316	22,62741700	21,48172500
489	300	306	22,11334439	21,67974940
473	300	304	21,74856317	21,46239787
426	300	288	20,63976744	21,49975775


Kavan, Mage
185	145	91,97916305	13,60147051	21,44195662
187	145	92,47498785	13,67479433	21,44196203
193	145	93,94674575	13,89244399	21,44198144
203	145	96,349738	14,24780685	21,44200945
211	145	98,22981155	14,52583905	21,44203097
222	145	100,7576493	14,89966443	21,44205782
233	145	103,2235936	15,26433752	21,44208377
407	214	201,341689	20,17424100	21,44259143
409	214	201,8357877	20,22374842	21,44259059
415	214	203,3108167	20,37154879	21,44259470
425	214	205,7456998	20,61552813	21,44260135
433	214	207,6730756	20,80865205	21,44260408
444	214	210,2943445	21,07130751	21,44261091
455	214	212,8833226	21,33072901	21,44261914
675	279	338,0449704	25,98076211	21,44280573
677	279	338,5454206	26,01922366	21,44280490
683	279	340,0422696	26,13426869	21,44280761
693	279	342,5225476	26,32489316	21,44280791
701	279	344,4938687	26,47640459	21,44281089
712	279	347,1862058	26,68332813	21,44281203
723	279	349,8577909	26,88865932	21,44281518
841	256	346,2232236	29,00000000	21,44281347
844	256	346,8402127	29,05167809	21,44281234
850	256	348,0708722	29,15475947	21,44281243
859	256	349,9087171	29,30870178	21,44281434
868	256	351,7369489	29,46183973	21,44281684
879	256	353,9586286	29,64793416	21,44281996
890	256	356,166499	29,83286778	21,44282007

That last value seems to be VERY close to a constant.

edit: rearranged Kavan's data so int and spi increases from top to bottom, seems like the "constant" increases very slightly when int increases.

Kavan · 02/10/08, 7:46 PM

The numbers reported by GetUnitManaRegenRateFromSpirit arein mana per second.

I found spiregen=0.009327*spi*sqrt(int) to be a very good fit to the data, the coefficient could use a bit more precision though, but it gets results correct up to 2 decimal points.

Batguus · 02/10/08, 7:48 PM

Originally Posted by constantius

Your Kevan numbers are *way* off. Not sure how you went from 67.6 M/Tick -> 338 Mp5. The Bekah ones look good.

GetUnitManaRegenRateFromSpirit("unit") doesnt get mana/tick but mana/sec, so 67.6*5=338 Mp5.

Kavan · 02/10/08, 7:54 PM

Using 0.00932715221261*spi*sqrt(int) gives up to 3 decimal points correct. From here it's just about what kind of rounding and precision Blizzard is using, but I think this is the correct formula, at least for mage data.

Batguus · 02/10/08, 8:05 PM

Originally Posted by Kavan

Using 0.00932715221261*spi*sqrt(int) gives up to 3 decimal points correct. From here it's just about what kind of rounding and precision Blizzard is using, but I think this is the correct formula, at least for mage data.

Yes this seems to be very close. Your formula gives mana/sec so 5*0.00932715221261*spi*sqrt(int) gives Mp5.

And 1/(5*0.00932715221261)=21,44277218
Which is basically the (Sqrt(int)*SPI)/Mp5 value in my table above, but there seem to be very small deviations depending on the int.

Muphrid · 02/10/08, 8:36 PM

Is the data suggesting that the formula is the same regardless of class? If so that's fairly significant.

constantius · 02/10/08, 9:11 PM

Well, there are only 2 basic formulas for regen for mages/priests/druids: mages/priest & druid. Druid is different for no apparent reason.

What really interests me is that this formula gives precise (accurate) values regen values OO5SR without factoring in the 12.5 / 15 that is normally added. Naked, with 115 int and 155 spirit, this formula actually *predicts* the precise value of regen OO5SR for the PTR build. 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.

Batguus · 02/10/08, 9:12 PM

Indeed, and there does not seem to be any base regen anymore either. I still dont have a lvl70 on the ptr, but I made a couple of lvl1s and this is what I got:

Class	Int	Spi	Mana/sec	(Sqrt(int)*SPI)/Mp1
Priest	22	23	3,773009134	28,59244667
Druid	22	22	3,609008623	28,59210312
Mage	24	24	4,112027718	28,59307274
Paladin	21	23	3,686284615	28,59226891

So it seems like Blizzard has indeed removed the class differences with regard to mana regenerated from a point of spirit. And the formula is:

Mana per 5 seconds from spirit outside casting rule @ lvl70: 0,046636*Sqrt(Int)*Spi.

At lvl1 it is 0.17487*Sqrt(Int)*Spi.

Muphrid · 02/10/08, 9:34 PM

Originally Posted by constantius

Well, there are only 2 basic formulas for regen for mages/priests/druids: mages/priest & druid. Druid is different for no apparent reason.

What really interests me is that this formula gives precise (accurate) values regen values OO5SR without factoring in the 12.5 / 15 that is normally added. Naked, with 115 int and 155 spirit, this formula actually *predicts* the precise value of regen OO5SR for the PTR build. 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.

Well, what it would indicate is that base mana regen has been eliminated. You must have non-zero spirit and intellect to have non-zero regen.

As for the tick model, the only difference between ticks and mana/sec. values is proportionality. As it is, mana/5 sec. doesn't give mana "every 5 seconds," but rather it adds to your two-second ticks by the correct ratio. I expect this is no different, and ultimately, to ensure compatibility between two-second ticks and mp5, Blizzard probably keeps all the values measured in units of mana/sec.

Now let me repeat my question: we have the constant of proportionality of 9.327E-3 mana/sec. for mages and priests, and it seems that this is holding for druids and paladins as well. Am I correct in gathering that? That is, we can conclude mana regeneration formulas are the same for all classes (or at least all 4 examined here)?

Batguus · 02/10/08, 9:35 PM

Originally Posted by Kavan

Using 0.00932715221261*spi*sqrt(int) gives up to 3 decimal points correct. From here it's just about what kind of rounding and precision Blizzard is using, but I think this is the correct formula, at least for mage data.

Kavan's formula gives mana per second, I simply multiplied his "constant" by 5 to get mp5.

Sapphidia · 02/10/08, 9:36 PM

Not wishing to derail what's an otherwise fascinating bunch of numbers, but have tests been done to check whether it's definitely Intellect rather than Total Mana Pool that determines this? Of course in the vast majority of cases mana pool will be int*15 and they scale identically with only a small constant value from the lower levels making a difference... but my sideline question is whether talents like the 10% Mana discipline priests have (which has no effect on Int) will affect it.

Ie, is spirit now returning effectively a percentage of total pool, and if so, would talents like the Disc one, or 5% mana in the shammy enhancement tree, have a corresponding boost to regen? Or is the formula definitely only being affected by boosts to Int alone?

constantius · 02/10/08, 9:36 PM

The biggest thing is that 12.5 and 15 (for constants) and /4 and /4.5 are functionally the same when it comes to large calculations. There MAY be some variance hidden in the 1% regression error at the moment, so we can't be sure this is true for all classes.

We really need a couple of hundred values for *each class*, then we can be sure.

Edit: prediction: it's done by Intellect only. It's too accurate to not be. I'll confirm this with a respec to Discipline when I get on the PTR, but I'm not expecting a change at all.

jaedan31 · 02/10/08, 9:37 PM

Is the data suggesting that the formula is the same regardless of class? If so that's fairly significant.

The data is suggesting that the formula for mages and priests is the same, but that was already well known.

Over what range are you finding 0.00932715221261*spi*sqrt(int) to be applicable? Does it predict regeneration at both low spirit (<300) and high spirit (>300)?

We know the old formula was 0.25*spi + 12.5 for mp2. What happened to the 12.5 in your formula? It should appear as a 6.25 additive factor Try fitting "Constant*spi*sqrt(int) + 6.25" instead of what you have. It may come out better. The 6.25 is nearly negligible, but over large ranges of intellect it will have a noticeable impact.

constantius · 02/10/08, 9:40 PM

The formula fits within 0.5% at sub-300 and post-300 values. I think you're probably right that the 6.25 / second would improve precision slightly. Checking now.

Checked: no, the 6.25 doesn't improve things. It looks like it's straight-up gone. Here's 90 points from druid/priest/mage all plotted on the same axis.

X-axis is spirit * sqrt(Int), Y-axis is char-screen (or function-return) MP5.

Additionally, due to reporting issues (rounded Mp5), there's a high likelihood that the level of statistical variation we're seeing is entirely due to the coarseness of the reporting medium. Only the one set of mage data was reported accurate to more than 0 decimals.

Batguus · 02/10/08, 9:48 PM

I doubt it look at this:

Int	Spi	Ingame value	Value formula	Difference*1000000
185	145	18,39583261	18,39513293	699,6762
187	145	18,49499757	18,49429879	698,7806
193	145	18,78934915	18,78865626	692,8943
203	145	19,26994760	19,26926216	685,4397
211	145	19,64596231	19,64528321	679,0989
222	145	20,15152986	20,15085851	671,3477
233	145	20,64471872	20,64405593	662,7930
407	214	40,26833780	40,26799835	339,4480
409	214	40,36715753	40,36681567	341,8556
415	214	40,66216333	40,66182678	336,5517
425	214	41,14913995	41,14881212	327,8281
433	214	41,53461511	41,53428951	325,6046
444	214	42,05886890	42,05855258	316,3212
455	214	42,57666452	42,57636064	303,8802
675	279	67,60899408	67,60909987	-105,7903
677	279	67,70908411	67,70918742	-103,3056
683	279	68,00845392	68,00856627	-112,3502
693	279	68,50450952	68,50462366	-114,1357
701	279	68,89877374	68,89889813	-124,3867
712	279	69,43724115	69,43737017	-129,0246
723	279	69,97155817	69,97169850	-140,3262
841	256	69,24464471	69,24477803	-133,3164
844	256	69,36804254	69,36817244	-129,9021
850	256	69,61417444	69,61430511	-130,6706
859	256	69,98174341	69,98188100	-137,5888
868	256	70,34738977	70,34753628	-146,5069
879	256	70,79172571	70,79188344	-157,7349
890	256	71,23329980	71,23345887	-159,0739

The fit is very close but higher int seems to mean the constant must be a tiny bit lower.

Ulthwithian · 02/10/08, 10:12 PM

So, given this new formula, I find the point where you achieve equal gains from Int and Spr to be

i =

s^2

-----

2s+1

(This was found by taking the formula, incrementing a given value for s and i by 1, and then equating and reducing.)

constantius · 02/10/08, 10:15 PM

I'm fairly certain no-one will intentionally stack intellect to take advantage of this. Healers have a lot already (most of us are over 600 raid-buffed), so we'll just benefit passively, and ignore it.

Pintofbrew · 02/10/08, 10:17 PM

Originally Posted by constantius

Edit: prediction: it's done by Intellect only. It's too accurate to not be. I'll confirm this with a respec to Discipline when I get on the PTR, but I'm not expecting a change at all.

It's also possible to get/remove a +mana chest enchant to affirm this.

Originally Posted by constantius

I'm fairly certain no-one will intentionally stack intellect to take advantage of this. Healers have a lot already (most of us are over 600 raid-buffed), so we'll just benefit passively, and ignore it.

Kavan already has all his gear stacked to the hilt with int gems; while I'd question the sanity of any mage prefering int over spelldamage the fact remains that at 860 int his enormous manapool seems to be enough to feed his amazing mana-habit of AB spam. Parsings showing him at a consistently high standard were enough to cause me to wonder: With utterly mad intellect levels could we see a major benefit? Will there even be a point to wearing the rather underwhelming +14dmg +2%int meta?

Ulthwithian · 02/10/08, 10:36 PM

Originally Posted by constantius

I'm fairly certain no-one will intentionally stack intellect to take advantage of this. Healers have a lot already (most of us are over 600 raid-buffed), so we'll just benefit passively, and ignore it.

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.

Pintofbrew · 02/10/08, 10:42 PM

That falsely assumes you only gain mana regen from int. For an arcane spec you would clearly not stack spirit over intellect.

What it technically means for mages, is now we're getting a slight increase in spirit-from-gear value given that we can dump the mana. Effectively, this only means one thing: Arcane mages, stack more int, get more AB time through enhanced mana regen.

How much this regen will be and how exactly significant it'll end up being remains to be seen. If >75% AB can be possible perhaps we'll have a shift in the power ballance. This becomes doubly true now given we can maintain 2/5 T5 and 4/8 T6 at the same time.

Alvira · 02/10/08, 10:46 PM

For arcane mages its a bit different. We have talents that incease our damage as our Int goes up. Plus Int also contributes some aount of crit rating as well. So, this idea that Int becomes the primary stat for arcane mages is not that far fetched. Its just that I am bulking at the idea of regemming every single one of my sockets and reenchanting my gear. (faints at the thought).

But Kavan's numbers are very tempting. Some of these changes also make me wonder if with enough haste gear stacked on, would a pure AM build be possible again? (AM has no pushback while arcane blast does, that is quite big for certain fights with lots of pushback).

Pintofbrew posted just before I did.

BTW, I agree with him. I am just hoping against hope that just perhaps with these changes, arcane will again be competitive.

Ulthwithian · 02/10/08, 10:53 PM

Pint/Alvira: I certainly agree that Int has other benefits for an Arcane mage than regen. I guess my point was that, for Mages, stacking Int for purposes of mana regen will never be as good as stacking Spr for those same purposes. I apologize if this was not clear.

Edit: Something I might work on now is to see how Int and Spr compare for Moonkin, considering that they get both spellpower and mp5 from Int.

Pyros · 02/10/08, 11:34 PM

Originally Posted by constantius

I'm fairly certain no-one will intentionally stack intellect to take advantage of this. Healers have a lot already (most of us are over 600 raid-buffed), so we'll just benefit passively, and ignore it.

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).

Darkmantle · 02/10/08, 11:52 PM

Originally Posted by constantius

Your Kevan numbers are *way* off. Not sure how you went from 67.6 M/Tick -> 338 Mp5. The Bekah ones look good.

That seems to be a fairly mundance mistake, if instead of tick you had second it would make perfect sense.

Starfire · 02/11/08, 12:40 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).

Disc priests have more spirit than holy priests, but holy priests convert 25%-35% of spirit to +heal. Holy priests can also clear cast/inner focus and do not ever spend 100% of the time inside the FSR.

As far as "healing" priests in general go, trend seems to be a very large portion (and imo the majority) of T6 priests have lots of spirit, though there is a significant amount of us that stack mp5.

My concern is not to figure out if spirit > mp5, for me an equivilent amount of spirit always is, it is to figure out how to balance intellect vs. spirit.