Int:Spellcrit Ratio

• Slake · 05/09/07, 3:15 PM

I tried a search and nothing immediately jumped out at me, so I'll see if anyone else has looked into this. This arose when I was trying to figure out how much intellect it takes to get 1% spellcrit; common knowledge says that it's a fixed amount, but the evidence (as measured by my character sheet on my 70 undead warlock) says otherwise; not only is it not a fixed amount, it's not even a linearly increasing amount!

Intellect	Crit Rating	Crit Chance	Crit% due to Int	Int:Crit%
131		0		3.30%		3.30%			39.7
137		0		3.37%		3.37%			40.65
138		0		3.38%		3.38%			40.83
139		30		4.75%		3.39%			40.97
141		0		3.42%		3.42%			41.23
144		24		4.54%		3.45%			41.69
146		19		4.34%		3.48%			41.95
147		14		4.13%		3.50%			42.04
148		0		3.51%		3.51%			42.17
150		19		4.39%		3.53%			42.49
152		14		4.19%		3.56%			42.74
153		0		3.57%		3.57%			42.86
156		18		4.42%		3.61%			43.27
158		14		4.26%		3.63%			43.57
160		28		4.92%		3.65%			43.8
163		15		4.37%		3.69%			44.16
168		29		5.06%		3.75%			44.83
175		14		4.47%		3.84%			45.61
177		0		3.86%		3.86%			45.85
215		46		6.41%		4.33%			49.67
254		61		7.56%		4.80%			52.92
283		89		9.18%		5.15%			54.92
301		147		12.03%		5.38%			55.96
386		226		16.65%		6.42%			60.09

The curve from this data is certainly nonlinear; the best equation I've been able to find for it is:

int/1%crit = 0.0002*(int)^2 + 0.1833*(int) + 19.52

Which is neither clean nor satisfying. I understand why they increase the amount of intellect required per 1% spell crit, clearly for the same reasons they introduced the rating system; otherwise eventually everyone would have 100% crit just from intellect.

Any thoughts on the data or a better/cleaner equation would be nice.

Kytrarewn · 05/09/07, 3:25 PM

The main issue that I can see is, perhaps, the lack of a usable "base crit at 0 int" Y-intercept, which has been found for different classes recently. Try finding warlocks of other races with different "base int at 70" samples, and have them do similar studies of their own crit/int equations.

Also, the increase of crit rating at the same time as int at a fairly rapid rate provides compounding factors toward the far end of the scale, as it's possible though not likely, that the spell crit rating ratio increases at high levels.

I know from experience that you've got more gold than the catholic church... you can afford tests with green level 70 Of Intellect pieces and re-enchanting items with 3, 5, 7, 9 int.

Also: The character sheet display might very well be borked. Try screwing around with actual tests on dr. boom or somesuch.

• frmorrison · 05/09/07, 3:35 PM

I always thought is was around 83 int per 1 spell crit for a Warlock.

From your data, looking at the last six pieces of data (where there is a noticable difference between int numbers) supports that int:crit ratio.

◊ Shalas · 05/09/07, 3:49 PM

All Class Level 70 Stat conversions

Balkoth · 05/09/07, 4:07 PM

Assuming his data is correct, you DO realize that this indicates that it ISN'T a flat amount of int for spell crit? IE the data in the other thread is wrong, the part about "1% spell crit = 83.33 Intellect --- Confirmed."

So no, this doesn't appear to be covered in the other thread.

• Slake · 05/09/07, 4:08 PM

Originally Posted by frmorrison

always thought is was around 83 int per 1 spell crit for a Warlock.

From your data, looking at the last six pieces of data (where there is a noticable difference between int numbers) supports that int:crit ratio.

Yes yes I realize that current knowledge says that ~80 int:spellcrit at 70 for warlocks is the correct amount, and indeed the result of (386-131)/(6.42-3.30) = 81.73, which is close.

The question is, why the reported variation in amount of intellect required per spellcrit? Is it actually 83.33 int per crit? If it is, why does the display give differing numbers?

◊ zeidrich · 05/09/07, 4:33 PM

Naw, it's linear.

Take your 2 closest numbers there:

301 int = 5.38 spell crit
138 int = 3.38 spell crit

301 - 138 = 163 int per 2 spell crit, 81.5 per spell crit.

Solve for base spell crit at 0 int:

3.3 - 131/81.5 = 1.693%

So you have a base 1.693% crit chance at 0 int, and gain 1% crit per 89.5 int.

Check a few values:

141/81.5+1.693% = 3.42%
160/81.5+1.693% = 3.65%
386/81.5+1.693% = 6.43%

Now that's only slightly off due to rounding error.

81.5% crit per int.
Base crit of 1.69% at 0 int.

• Arawethion · 05/09/07, 4:36 PM

It's 80.0 Int for Mages.

◊ zeidrich · 05/09/07, 4:40 PM

Plugging into excel gives me this

int		sp crit		char sheet crit	calc'd int crit	Expected
131		0		3.30%		3.30%		3.300
137		0		3.37%		3.37%		3.374
138		0		3.38%		3.38%		3.386
139		30		4.75%		3.39%		3.399
141		0		3.42%		3.42%		3.423
144		24		4.54%		3.45%		3.460
146		19		4.34%		3.48%		3.484
147		14		4.13%		3.50%		3.497
148		0		3.51%		3.51%		3.509
150		19		4.39%		3.53%		3.533
152		14		4.19%		3.56%		3.558
153		0		3.57%		3.57%		3.570
156		18		4.42%		3.61%		3.607
158		14		4.26%		3.63%		3.632
160		28		4.92%		3.65%		3.656
163		15		4.37%		3.69%		3.693
168		29		5.06%		3.75%		3.754
175		14		4.47%		3.84%		3.840
177		0		3.86%		3.86%		3.865
215		46		6.41%		4.33%		4.331
254		61		7.56%		4.80%		4.810
283		89		9.18%		5.15%		5.165
301		147		12.03%		5.38%		5.386
386		226		16.65%		6.42%		6.429

Which looks pretty good.

◊ Shalas · 05/09/07, 4:42 PM

If you graph spell crit from int vs. int with those numbers you get a straight line with a lot of bumps due to rounding issues. I'm not quite sure why you think it's non-linear.

• Chicken · 05/09/07, 5:56 PM

There's a certain base value for each stat which doesn't get taken into account for purposes of derived stats. The easiest one to spot this with is the health increase from Stamina (Or the Mana increase from Intelligence).

These are generally small little things, but could account for a fair amount of variance when trying to figured out how some other stats are derived. For a Blood Elf Paladin for example, the following amounts of Strength, Stamina and Intelligence don't seem to get counted for Attack Power, Health and Mana respectively (And thus presumably for other things as well).

Strength: 10
Stamina: 18
Intelligence: 18.66

The same is probably true for all races/classes, and is probably to account for racial stats or somesuch.

I'd suggest that instead when trying to derive stat formulas you assume that your stats naked are 'zero' and than attempt to figure out the rate of increase each point gives from there. In your above table, that'd basically mean reducing all Intelligence values by 131 and all Crit% due to int values by 3.30%. That way you also make sure your values don't get muddied by any base crit values you'd have even with no intelligence.

There's no need for more intelligence being needed for more spellcrit in the system either; the ratings scale with level, the amount of intelligence you need for spellcrit does as well.

As I'm bored, here's the table as revised according to my suggestion (I've removed the crit rating and normal crit chance as they don't matter):

Intellect	Crit% due to Int	Int:Crit%
0		0%			 0.00
6		0.07%			85.71
7		0.08%			87.50
8		0.09%			88.89
10		0.12%			83.33
13		0.15%			86.67
15		0.18%			83.33
16		0.20%			80.00
17		0.21%			80.95
19		0.23%			82.61
21		0.26%			80.76
22		0.27%			81.48
25		0.31%			80.65
27		0.33%			81.82
29		0.35%			82.85
32		0.39%			82.05
37		0.45%			82.22
44		0.54%			81.48
46		0.56%			82.14
84		1.03%			81.55
123		1.50%			82.00
152		1.85%			82.16
170		2.08%			81.73
255		3.12%			81.73

Note particularly that apart from the first 15 Intellect, the variance in the last 240 Intellect could easily be attributed to rounding and the Int:SpellCrit% ratio is quite close for all those values.

tedv · 05/10/07, 10:29 AM

Originally Posted by Chicken

Note particularly that apart from the first 15 Intellect, the variance in the last 240 Intellect could easily be attributed to rounding and the Int:SpellCrit% ratio is quite close for all those values.

That wouldn't be the first time that a stat scaled differently at lower stat values than higher. Most people quote the spirit regen function as something like (spirit/4) + 13. But in reality, it works like this, at least for priests:

Spirit 0-50: Every 2 spirit = 1 mana per 2 seconds
Spirit 51+: Every 4 spirit = 1 mana per 2 seconds

So technically it's a piecewise linear function. It sounds like Spell Crit from Intellect might also be piecewise linear.

Athinira · 05/10/07, 10:36 AM

Originally Posted by tedv

That wouldn't be the first time that a stat scaled differently at lower stat values than higher. Most people quote the spirit regen function as something like (spirit/4) + 13. But in reality, it works like this, at least for priests:

Spirit 0-50: Every 2 spirit = 1 mana per 2 seconds
Spirit 51+: Every 4 spirit = 1 mana per 2 seconds

So technically it's a piecewise linear function. It sounds like Spell Crit from Intellect might also be piecewise linear.

But in reality? Care to back it up, i have never seen anything that shows it works differently.

tedv · 05/10/07, 10:53 AM

Originally Posted by Athinira

But in reality? Care to back it up, i have never seen anything that shows it works differently.

By "it", which do you mean?

A) Spirit below 50 regenerates mana at 2 spirit => 1 mana/2 sec
B) Int below X provides a*Int spell crit and Int above X provides a*(Int-X) spell crit

For the former, I ran tests on both a hunter and a paladin that were below level 30 (less than 50 base spirit with all gear off) and tested regeneration rates as I added gear. In both cases, I saw 2:1 efficiency below 50 spirit and 5:1 above 50 spirit. Most people test regen rates on their high level mains, but they have base spirit above 50 already, so they never see the different linear rate at lower spirit levels.

For the latter, I have no evidence except what's already posted in the thread.

Dwarphro · 08/03/07, 3:33 PM

I was curious about this as well. I originally posted the answer here:
HonorBound Forums - GuildPortal Guild Hosting

Quote follows (leaving out a couple of wrong guesses about other stuff):

I have finally battled this windmill into submission.

The short version: For ALL casters, it takes 80 (eighty!) Int for 1% spell crit at level 70.
The only difference is where each class starts.

There was a blue post a while back that explained that the base spell crit chance is 5%. This is modified by the difference between the character's Int and the "expected" Int for that level applied at some mystical ratio. The infamous 59.5 Mage number came from this at level 60. There are other modifiers for target level difference, etc., but the fundamental one we all look for is "How much spell crit will this much Int give me?"

Through the magic of The Armory™, I have derived the formula:

The basic equation is: Spell Crit % = 5 + (Int - expected Int)/80

At level 70, the expected Int values are as follows:
Druid 252
Mage 327
Paladin 133
Priest 301
Shaman 224
Warlock 273

Go ahead, run your own numbers. You'll see.

For the purists that must have the spell crit % at level 70 in y=mx+b format (1/80 = .0125):
Druid .0125*Int + 1.85
Mage .0125*Int + 0.91
Paladin .0125*Int + 3.34
Priest .0125*Int + 1.24
Shaman .0125*Int + 2.20
Warlock .0125*Int + 1.59

PS I also verified that 80 is not level+10.

rochan · 08/03/07, 4:04 PM

I was curious about this too, thanks for sorting that out. I suppose another useful conversion from this information is ~3.6 int = 1 spell crit rating.

Drundia · 08/03/07, 5:29 PM

You use GetSpellCritChanceFromIntellect('player') to get full precision amount of spell crit from intellect. Warlocks gain 1% spell crit from 81.967 intellect or 0.0122% spell crit from 1 Intellect (81.967173816175 and 0.012200005849203 are exact numbers obtained). Warlocks are in fact 1 level ahead of other classes in int per crit (80 int for 1% at 69, other classes have it at 70) and have 1.7% ground crit.

But I would argue with Dwarphro about mythical ratio. Ground spell crit (at 0 int) is same for any level. As for "expected" Intellect, for Warlocks it seems to be close to 2 times white Intellect. From those 2 numbers and 5% base crit int per crit may be obtained, but I see expected Intellect of 270.5 rather disturbing...

• frmorrison · 08/03/07, 7:06 PM

Originally Posted by Drundia

I see expected Intellect of 270.5 rather disturbing...

How so? I have 340 int on my PvP gear, where Int as a stat is pretty low on the priority list.

270 is like a Warlock with full AH greens at 70.

Drundia · 08/04/07, 5:53 PM

Do you see that decimal point in "270.5"? That is most disturbing part of it. As for it being low, of course that value is "expected" intellect of a character that isn't stuck at that level because it's max. Why would expected intellect not be integer?

galzohar · 08/06/07, 2:09 PM

When you try figure out the increase in 1 stat as a result of another stat increasing the starting point is completely irrelevent. For example if stat Y = a*X+b where X is the other stat you'll just get a different 'b' but the 'a' will be the same, which is what matters.