[top] 125(50), 189 spi, 150 int

constantius · 02/10/08, 4:44 PM

Here's my current model for Intellect -> Spirit regeneration.

First off, assume it doesn't matter whether you are a priest or a druid: the modification is made to the SCALING FACTOR. Everything you compute must be based on that fact.

Druids:
(spirit / x + 14) * 2.5 = regen OO5SR from spirit

Priests:
(spirit / x + 12.5) * 2.5 = regen OO5SR from spirit

If you're computing anything, take off static Mp5, ignore every factor but intellect, spirit, and regen ignoring static factors.

Now, having said that, I used Bekah's numbers for priests for the majority of my high intellect computations, and numbers that Shadowed and I (The World of Warcraft Armory) came up with using his character transferred to the PTR. I'm not going to post all the details for now; I have a spreadsheet I'll try to clean up and post later.

Basically, here's the conclusions:
1) Relationship of intellect to spirit is logarithmic. If you have under 300 intellect, you will LOSE regen. If you have over 300 intellect, you GAIN regen.
2) Relationship of factor is quadratic in scaling, to prevent over-scale at the high end.

To find your regen, do the following:

L = - log (int/300)

Factor = Base_factor + (6 L^2 + 7.2 L)

Then (spirit/factor+12.5)*2.5.

I'm not completely happy with the regression curve at the moment, but I'm almost 100% positive that the factor WILL be -log(int/300). The only question is how that factor merges into the actual conversion from your base spirit factor to your actual PTR spirit factor.

The only way to get it more precise is to get a *ton* more data in the range around 300 intellect and down. We need a couple of hundred points in the 110 -> 330 intellect range. Go go.

There's a conversion which seems 99% accurate, computed by Kevan:
Regen_mp5 = 5*0.00932715221261 * sqrt(Int) * Spirit

This computation doesn't come at the problem from a Mana/Tick angle like normal, but does fit extremely accurately. It rides roughshod over the spirit/x+y formula, and remains a reduction in regen for sub-300 int cases.

Example: 200 intellect, 300 spirit. Live regen (for priest/mage): 218.8 Mp5.
By Formula: 197.9 Mp5.

constantius · 02/10/08, 4:47 PM

Looking for Data Points:

If you want to submit data points to aid in this theorycrafting, here are the requirements:
- intellect value
- spirit value
- OO5SR regen value with STATIC VALUES STRIPPED
- class (druid, priest, mage, etc)
- specification of your talents -- SoR, Intensity, etc..

Example (data set from Shadowed and myself):

Base Int: 115
Base Spirit: 155
Base regen: 77 (23) [121(36)]

Shimmer-pelt : 35 int, 30 spi, 18 mp5

[top] 125(50), 189 spi, 150 int

107(32) -- should be 140(42) -- 6.56

Grove-Bands : 14 int, 21 spi

[top] 94 (28), 129 int, 179 spi

94(28) -- should be 134(40) -- 7.59

Khaarma's : 15 int, 6 Mp5

[top] 88 (30), 130 int, 155 spi

82(24) -- should be 121(36) -- 8.24

Vindicator's Pendant : 16 int, 6 Mp5

[top] 88 (30), 131 int, 155 spi

82(24) -- should be 121(36) -- 8.24

Cord of Braided Troll Hair : 34 int, 9 Mp5

[top] 97 (35), 149 int, 155 spi

88(26) -- should be 121(36) -- 7.31

Jade Ring of the Everliving : 12 Mp5

[top] 89(35), 115 int, 155 spi

77(23) -- same as base -- 9.23

Voodoo Shaker only : 20 int, 25 spi

[top] 99(29), 135 int, 183 spi

99(29) -- should be 137(41) -- 7.15

Vindicators Neck, Khaarma's, Vindicator's MH, Vindicator's Legs, Vindicator's Boots, Signet of Ancient, Troll Hair : 56 Mp5

[top] 179(93), 308 int, 155 spi

123(37) -- should be 121(36) -- 4.40

Vind Neck, cloak, MH, legs, boots, ring, gloves, Signet, Troll, S1 shoulders : 56+12+8+6 = 82

[top] 220(123), 369 int, 155 spi

138(41) -- should be 121(36) -- 3.76

Vind Neck, cloak, MH, legs, boots, ring, Signet, Troll, S1 shoulders : 56+12+6 = 74

[top] 206(113), 335 int, 155 spi

132(39) -- should be 121(36) -- 3.99

Note that the values of regeneration at the far left are including static, and the = x(y) are the refactored ones. The "should be" are what the current live values would be, and the final number is what the scaling factor on spirit would have to be to get that value as an output. You don't need to include the final 2 if you are just grabbing raw data; I can compute it easily.

This data in simplified form:

(factor) (int)
6.56	150
7.59	129
8.24	130
7.31	149
9.23	115
7.15	135
4.4	308
3.76	369
3.99	335

If you're submitting a large data set, I highly suggest using PvP gear, especially of the Gladiator variety. It has almost no spirit, static Mp5, and high values of intellect.

constantius · 02/10/08, 4:48 PM

Bekah's Data: (converted) [priest data]

(factor) (int)
2.53	555
2.54	552
2.55	551
2.57	550
2.56	544
2.57	538
2.58	536
2.59	531
2.60	527
2.61	526
2.61	524
2.64	516
2.64	515
2.65	512
2.65	511
2.66	509
2.66	508
2.67	504
2.67	500
2.69	498
2.69	496
2.70	494
2.73	484
2.75	479
2.76	476
2.76	473
2.79	469
2.79	468
2.80	464

Ripman · 02/10/08, 5:01 PM

Originally Posted by constantius

Druids:
(spirit / x + 14) * 2.5 = regen OO5SR from spirit

According to my memory and this wowwiki page, Druid regen is spirit/4.5 + 15. I've never seen the 14 number before, are you sure?

Ulthwithian · 02/10/08, 5:05 PM

Okay, I'm interested in this more from a Mage standpoint than anything else (specifically, Arcane). My 61 Arcane Mage has 467 Int and 199 Spr. Using the formulas known (and provided above), his current base regen OO5SR should be 155.625 mp5. He also has 467 Int. So in 2.4 he'll have 206.554 mp5 with the same gear, for a net gain of ~51mp5 OO5SR. This is 15.3mp5 added from talents, and another 15.3 mp5 added from Mage Armor, correct?

From a theory standpoint, can the balance point be found where increasing Int is more profitable than Spr for mana regen purposes?

constantius · 02/10/08, 5:05 PM

14 is what naked-base on live was coming up as for the two druids I asked. It could just be a rounding issue; if it's 15, that'll tweak the numbers in a *small* way. I can easily correct for this.

As far as a balance point for increasing intellect vs spirit, it's almost a moot point. The only thing this does is allow you to justify taking a piece of gear with intellect vs no intellect. You will still *never* 'stack' intellect. We all get it for free, and it's semi-useless (mana pool size, crit %) -- they're just making it slightly more valuable by giving it an actual scaling factor. I have a feeling (gut only) that you'd have to do 50%+ on intellect to balance something small like 30 or 40 spirit. So 5:1 or more. I'll work more on this later today.

giansm · 02/10/08, 5:10 PM

It's 15 if you believe the character screen (the Spirit tooltip that says "increases mana regeneration by xxx"). It uses ( Spirit / 4.5 + 15 ) * 2.5, and rounds down.

constantius · 02/10/08, 5:11 PM

Confirmation that it does indeed use a floor function on spirit, and not a classic decimal rounding proceedure?

Ulthwithian · 02/10/08, 5:19 PM

While I see your point, Constantius, certain classes and talent specs (Arcane Mage, Moonkin Druid) can make more use out of Intellect than the norm. As it is, I must admit my question was more of a thought exercise than anything else. I'll see what I can do with your formulae. Thank you _very_ much for this; I've been looking for data on this since it was announced.

Irise · 02/10/08, 5:36 PM

I don't buy this formula yet.

I plugged Bekah's data into a spreadsheet and I ran a linear regression of Bekah's regen against the results from your formula the slope was 1.08 (not 1.00 as expected) with a std. deviation of 0.02.

Bekah's data only shows one side of the picture because of the fixed spirit value. I think we need some more data with varying value of spirit before we can settle on a formula.

XP-Dolphin · 02/10/08, 5:54 PM

The complete formulas use to be exposed in the lua code released with 2.0 and 2.1. They have since hidden it behind a function called GetUnitManaRegenRateFromSpirit("unit"). However, the old formula still held. It worked like this.

For the first 50 spirit, everyone would gain 0.25 mana/sec per spirit.

For all spirit after this, Mages/Priests would get 0.125 mana/sec per spirit. Druids would get 0.1125 mana/sec per spirit. Everyone else would get 0.1 mana/sec per spirit.

Hopefully this helps people work out more of the new formula.

Nenormalen · 02/10/08, 5:55 PM

Basically we have SpiritRegen(Spirit, Int), TotalRegen=(SpiritRegen, Mp5). dTR=(deltaSR/deltaS)*dS+(deltaSR/deltaI)*dI+1*dMP5 should be the total differential about regeneration. deltaSR/deltaS =2.5/(Base_factor + (6 L^2 + 7.2 L)). deltaSR/deltaI=2.5S/[6*((-2lnI+4.94)/I+7.2*(2.47-1/I)).

so dTR=[2.5/(Base_factor + (6*((-ln(I/300))^2 + 7.2*(-ln(I/300)))]*dS + [2.5S/[6*((-2lnI+4.94)/I+7.2*(2.47-1/I)]]dI +dMP5. Or did I understand you wrong?

Quoting myself from the other thread, since the discussion ended there.

edit: think I got an inner derivative wrong somewhere, will check tomorrow perhaps.

Starfire · 02/10/08, 5:56 PM

Originally Posted by Ulthwithian

While I see your point, Constantius, certain classes and talent specs (Arcane Mage, Moonkin Druid) can make more use out of Intellect than the norm. As it is, I must admit my question was more of a thought exercise than anything else. I'll see what I can do with your formulae. Thank you _very_ much for this; I've been looking for data on this since it was announced.

Dreamstate Restoration Druids, Holy Paladins/Shockadins, Restoration Shamans.

But I think we need to work on that later, solving for the formula is the first priority ~ then we can nitpick the finer details. On that note, I am personally interested in knowing what this means for flasking/potting.

65 intellect vs. 25 mp5 vs 45 intellect/45 spirit/15 stamina vs. 50 healing/30 intellect/30 spirit vs 50 healing/16mp5 vs. 15 intellect/15 spirit/16 mp5.

Without actually running numbers, kinda look for endurance high mana fights, 45 int/45 spi/15 stam combo will be pretty sweet.

Ulthwithian · 02/10/08, 6:02 PM

For a Priest, put in 400 Spr and 200 Int into the formula. If you then increment each by 1 separately, you should see (if I did my math correct) that 400Spr/201Int > 401Spr/200Int in terms of Spirit-based Regen. (I get 215.3 vs. 215.1 mp5.)

A little more research reveals that it seems that the inflection point isn't static, but can be quantified. For a Priest or Mage, once Spr+50~=Int, adding to either stat is equivalent. If the difference between the two stats is on the order of 100 or more, adding to whichever stat is lower will increase spirit-based regen.

I guess what this means in game terms is that if you have high-Spr/low-Int itemization, adding Int will not only increase your mana pool, but also your mana regeneration.

Pagaen · 02/10/08, 6:12 PM

Can we get a condensed, human-readable formula where we just plug in our SPI and INT numbers and get a number? Obviously, logs and stuff aren't a problem, but I think I see some calculus and that flys over my head.

Lord BEEF · 02/10/08, 6:13 PM

Moved per request.

Originally Posted by constantius

Bekah's Data: (converted) [priest data]

(factor) (int)

2.67	500

Could you explain this to me? Does this mean at 500 intellect the spirit formula is spirit / 2.67 instead of the normal spirit / 4 for priests?

Faxmonkey · 02/10/08, 6:24 PM

I was going to try tackling this problem myself, logged onto the PTR for the first time and got the "Sever is restarted in 4:45" message. I did jot down a few quick data points, but probably not enough to be useful. I'm curious as to whether this change effects pet mana regeneration as well -- though frankly I'm not quite sure I'm fully aware of the mechanics behind pet mana regen on live . . . Just to throw these out here, even though there's only a few that I managed to grab before the server went down:

with 300 spirit (0 mp5, 0 talents to impact result):
512 int = 316
489 int = 306
473 int = 304
426 int = 288

Sorry it's not much . . .

Pagaen · 02/10/08, 6:40 PM

This is what I put together:

2.5(class_base + (spirit/(class_factor + 6(-log(int/300)^2) + 7.2(-log(int/300)))

Anyone agree? Disagree?

Kavan · 02/10/08, 6:53 PM

Just a dump of my data points so far (arcane mage), using GetUnitManaRegenRateFromSpirit.

int spi spi regen (279)
675 279 67.60899408
677 279 67.70908411
683 279 68.00845392
693 279 68.50450952
701 279 68.89877374
712 279 69.43724115
723 279 69.97155817
int spi spi regen (256)
463 256 51.37843759
466 256 51.54461725
472 256 51.87538202
482 256 52.42202051
490 256 52.85525949
501 256 53.44522913
512 256 54.02875574
841 256 69.24464471
844 256 69.36804254
850 256 69.61417444
859 256 69.98174341
868 256 70.34738977
879 256 70.79172571
890 256 71.2332998
int spi spi regen (145)
185 145 18.39583261
187 145 18.49499757
193 145 18.78934915
203 145 19.2699476
211 145 19.64596231
222 145 20.15152986
233 145 20.64471872
int spi spi regen (214)
407 214 40.2683378
409 214 40.36715753
415 214 40.66216333
425 214 41.14913995
433 214 41.53461511
444 214 42.05886896
455 214 42.57666452
int spi spi regen (314)
498 314 65.35712488
501 314 65.5536886
507 314 65.94504602
517 314 66.59220941
525 314 67.10543878
536 314 67.80480249
547 314 68.49700983
789 314 82.26506097
792 314 82.42130334
798 314 82.73291071
808 314 83.24967249
816 314 83.66077478
827 314 84.22277887
838 314 84.78104456

constantius · 02/10/08, 6:55 PM

Originally Posted by Lord BEEF

Could you explain this to me? Does this mean at 500 intellect the spirit formula is spirit / 2.67 instead of the normal spirit / 4 for priests?

Yes. That's the basic idea.

For those who are mathematically inclined, I'll explain why it *has* to be based on a logarithm, and then we can work together to figure out exactly how.

Things we know:
1) Intellect less than 300 has a reducing effect on spirit regen. Proved via Shadowed values produced on today's push of the PTR.
2) Intellect greater than 300 has an increasing effect. Proved via Bekah and Shadowed values.
3) It is unlikely that Blizzard set two separate formulae based on value of intellect. If they did, all bets are off. But let's assume it's one formula.

Hence, we require a function of intellect that can be both positive and negative, depending on what value of intellect you put in, with a 0-crossing at 300. The easiest way to model this is with a logarithm, hence the log(int/300).

Additionally, people may question why this formula has to modify the factor (the 4.0 and 4.5 numbers). Basically, it comes down to how to compute the factor. We know it's a scalar multiple of the spirit, so is it possible to do something like:

(spirit/4 + spirit*(new_scaling_int_factor) + static_base_factor) * 2.5

vs

(spirit / new_scale_factor_2 + static_base_factor) * 2.5

We would need new_scaling_int_factor = 0 for int = 300, negative for int < 300, and positive for int > 300. This is entirely possible using a logarithm. However, the same could be said for new_scale_factor_2.

However, the two methods are functionally identical. If we let:

new_scaling_int_factor = x
new_scale_factor_2 = y

then

0.25*spirit + x*spirit = spirit / y => y = 1/(x+0.25).

Accordingly, I just went with the first method.

Now, as far as the actual *fit* goes, that's where it gets squirrely. I'm perfectly willing to acknowledge a lack of good fit with my 6L^2 - 7.2L. I'm not happy with it. I just don't have enough data to refine it yet.

Pagaen: that's my formula. So ... yes. I agree. For now. :p

Norfair · 02/10/08, 7:02 PM

Originally Posted by Pagaen

This is what I put together:

2.5(class_base + (spirit/(class_factor + 6(-log(int/300)^2) + 7.2(-log(int/300)))

Anyone agree? Disagree?

If I put these numbers in my Excel sheet I get:

ORIG.	CALC.
313,00	315,721117
312,00	314,6535819
311,00	314,2965646
308,00	313,9389626
310,00	311,7811264
308,00	309,6024828
307,00	308,8716809
306,00	307,0347169
305,00	305,5549696
304,00	305,1836281
304,00	304,4392668
301,00	301,4396025
301,00	301,0621628
300,00	299,9265613
300,00	299,5469371
299,00	298,7860599
299,00	298,4048092
298,00	296,8744192
297,00	295,3354654

Where "ORIG." is the original mana regen and "CALC." is it calculated through your formula. So even though it's close, it's still off.

constantius · 02/10/08, 7:03 PM

The formula is rounded. Sheesh!

Also, remember that Mp5 is limited to the nearest Mp5, so a little loss of precision isn't going to cause your world to come to an end.

I'll post a "this is accurate to 400 decimal places" formula in a minute.

Kavan · 02/10/08, 7:36 PM

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

Batguus · 02/10/08, 7:38 PM

The Data Ive seen so far, I substracted the mp5 on gear, so it is: Int, Spi, mp5 from spi

Bekah, Priest
555	285	313
552	285	312
551	285	311
550	285	308
544	285	310
538	285	308
536	285	307
531	285	306
527	285	305
526	285	304
524	285	304
516	285	301
515	285	301
512	285	300
511	285	300
509	285	299
508	285	299
504	285	298
500	285	297
498	285	296
496	285	296
494	285	295
484	285	292
479	285	290
476	285	289
473	285	289
469	285	287
468	285	287
464	285	286
544	337	366

Aristiri, Druid
605	386	443

Faxmonkey, Mage
512	300	316
489	300	306
473	300	304
426	300	288

Kavan, Mage
675	279	338,0449704
677	279	338,5454206
683	279	340,0422696
693	279	342,5225476
701	279	344,4938687
712	279	347,1862058
723	279	349,8577909
841	256	346,2232236
844	256	346,8402127
850	256	348,0708722
859	256	349,9087171
868	256	351,7369489
879	256	353,9586286
890	256	356,166499
185	145	91,97916305
187	145	92,47498785
193	145	93,94674575
203	145	96,349738
211	145	98,22981155
222	145	100,7576493
233	145	103,2235936
407	214	201,341689
409	214	201,8357877
415	214	203,3108167
425	214	205,7456998
433	214	207,6730756
444	214	210,2943445
455	214	212,8833226

constantius · 02/10/08, 7:43 PM

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

Edit: Kevan, are your numbers matching up with your character screen? Because atm, they don't seem to work at all with the data I gathered together with Shadowed. Example:

Intellect: 675
Spirit: 279
Live_regen: 205.6 Mp5 (or 69.75 spirit_val / tick)
Your number: 67.6

Bekah Value:
Intellect: 555
Spirit: 285
Number: 313 Mp5

As far as I can tell, mages are identical to priests for regen values: spirit/4+12.5. Any ideas?