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02/10/08, 7:44 PM
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#26
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Von Kaiser
Night Elf Druid
Silvermoon (EU)
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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.
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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.
Last edited by Batguus : 02/10/08 at 7:53 PM.
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02/10/08, 7:46 PM
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#27
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King Hippo
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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.
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02/10/08, 7:48 PM
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#28
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Von Kaiser
Night Elf Druid
Silvermoon (EU)
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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.
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GetUnitManaRegenRateFromSpirit("unit") doesnt get mana/tick but mana/sec, so 67.6*5=338 Mp5.
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02/10/08, 7:54 PM
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#29
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King Hippo
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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.
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02/10/08, 8:05 PM
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#30
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Von Kaiser
Night Elf Druid
Silvermoon (EU)
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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.
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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.
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02/10/08, 8:36 PM
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#31
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Don Flamenco
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Is the data suggesting that the formula is the same regardless of class? If so that's fairly significant.
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02/10/08, 9:11 PM
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#32
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Pities the fool
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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.
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02/10/08, 9:12 PM
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#33
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Von Kaiser
Night Elf Druid
Silvermoon (EU)
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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.
Last edited by Batguus : 02/10/08 at 9:32 PM.
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02/10/08, 9:34 PM
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#34
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Don Flamenco
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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.
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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)?
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02/10/08, 9:35 PM
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#35
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Von Kaiser
Night Elf Druid
Silvermoon (EU)
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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.
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Kavan's formula gives mana per second, I simply multiplied his "constant" by 5 to get mp5.
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02/10/08, 9:36 PM
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#36
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Von Kaiser
Human Warrior
Earthen Ring (EU)
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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?
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02/10/08, 9:36 PM
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#37
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Pities the fool
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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.
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02/10/08, 9:37 PM
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#38
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Glass Joe
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Is the data suggesting that the formula is the same regardless of class? If so that's fairly significant.
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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.
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02/10/08, 9:40 PM
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#39
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Pities the fool
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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. 
Last edited by constantius : 02/10/08 at 9:52 PM.
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02/10/08, 9:48 PM
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#40
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Von Kaiser
Night Elf Druid
Silvermoon (EU)
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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.
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02/10/08, 10:12 PM
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#41
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Piston Honda
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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.)
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02/10/08, 10:15 PM
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#42
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Pities the fool
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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.
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02/10/08, 10:17 PM
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#43
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Long Time Reader, First Time Toaster.
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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.
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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.
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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?
Last edited by Pintofbrew : 02/10/08 at 10:28 PM.
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02/10/08, 10:36 PM
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#44
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Piston Honda
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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.
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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.
Last edited by Ulthwithian : 02/10/08 at 10:51 PM.
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02/10/08, 10:42 PM
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#45
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Long Time Reader, First Time Toaster.
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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.
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02/10/08, 10:46 PM
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#46
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Don Flamenco
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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.
Last edited by Alvira : 02/10/08 at 10:52 PM.
Reason: acknowledge a prior post
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02/10/08, 10:53 PM
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#47
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Piston Honda
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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.
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02/10/08, 11:34 PM
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#48
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Always carry a white flag
Undead Death Knight
Twisting Nether (EU)
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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.
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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).
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02/10/08, 11:52 PM
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#49
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King Hippo
Gnome Warlock
Spinebreaker
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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.
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That seems to be a fairly mundance mistake, if instead of tick you had second it would make perfect sense.
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02/11/08, 12:40 AM
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#50
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Honorary Toastr
Night Elf Priest
Dragonblight
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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).
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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.
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