I'm back again, on the topic of mana regen for the new patch. despite all my work I didn't make it any farther then anyone else. There's no "set in stone" stat that is superior. But the crew of Priestly Endeavors came to the same conclusions as I did.
The inflection point is where your Spirit is twice that of your Intellect. So if you have twice your Intellect in Spirit, an even 400/800, one point in Spirit will do the same thing as a point of Intellect to increasing your mana regen.
If the balance is upset, moving back toward balance will be more rewarding then skewing the stats even moreso. But it's not like you don't get regen either way, just more of it per point.
I figured less math in this post would make up for the over-abundance of Math in the last one. Hopefully this post makes more sense!
~Because my Brain Hurts now.
Bob
Thursday, February 14, 2008
Wednesday, February 13, 2008
My Turn. Theorycrafting 2.4 Regen.
You saw it coming, I'd hope. Intellect shall cause Spirit to scale mana regen as of Patch 2.4. Bloggers are going crazy. I'm sure there's more, but I didn't want to elongate that sentence any moreso then neccesary.
So, I stole the basic formula from the Elitist Jerks, and went to town. I figured there's gotta be some way to compare Spirit and Intellect in a general manner, and that I might as well put my Calculus II classes to work.
If you want to know the nit-picky numbers and details, read on. Otherwise... Well, you've been warned!
The basic formula they dug up for active mana regen (PER SECOND):
.009327[ (.001 + SPIRIT) (INT^.5) ] = X
Removing the constant from the variables side (Int and Spirit):
(.001 + SPIRIT) (INT^.5) = 107.2156106 X
Now this is where I'm trying something new, atleast from what I've seen. I'm going to solve for Spirit and Intellect in respects to each other, then plug in one value in the formula for the other. It's the same method used to solve intersection points between graphs with two variables, exactly what we have here. Just not in simple non-classroom Math X and Y.
This is what I came up with...
SPIRIT = (107.21561x / INT^.5) - 0.001
And because Intellect is never used in it's full form in this formula, it says as a square root (^.5 is a square root without the powers of drawing), I'm just solving for INT^.5
INT^.5 = 107.21561x / (SPIRIT +.001)
Now, if you were to try and plug one of those in to the other formula right now, you'd end up just solving for INT = INT or SPIRIT = SPIRIT. Wanna know why? This is a tri-linear function. X is still a value, so we need to remove the X values from these two formulas. How, you may ask? By substituting it with our starting function. This step stumped me for a bit, but just bear with me on this.
*Wipes Dry-Erase board clean, begin page 2*
... It was at this point I realized you can't ACTUALLY do this. You can plug in one value and see where the inflection points would be for the other when one value is constant, but you most certainly can't find ALL points of inflection without any set values, on both sides. My Math was clean, but my logic and memories of RULES of Math were certainly faulty. And for that I paid about 2 hours of my time. But it was totally worth the mental sweat I broke!
So, I spin off on a new tangent, basing numbers off of base points. Let's test this formula with some numbers and see what this does to my regen! I'm assuming you can add in the MP5 from gear directly, because I'm not picking gear in particular; just random numbers from the air.
I'm just going to scale from 300 to 450 for this example, but it'll work with ANY numbers. This is just to get a feel for what the graph would do. If you've followed this all the way to here A) I applaud you; and B) you need to multiply the number you get by 5 for the actual Mp5 value. This base formula determines Mana per second. I'm just going to multiply for Mp5 for common comparison values.
INT 300, SPIRIT 300. MP5 = 242.32
INT 300, SPIRIT 350. MP5 = 282.71
INT 300, SPIRIT 400. MP5 = 323.09
INT 300, SPIRIT 450. MP5 = 363.48
INT 350, SPIRIT 300. MP5 = 261.74
INT 350, SPIRIT 350. MP5 = 305.36
INT 350, SPIRIT 400. MP5 = 348.98
INT 350, SPIRIT 450. MP5 = 392.61
INT 400, SPIRIT 300. 279.81
INT 400, SPIRIT 350. 326.44
INT 400, SPIRIT 400. 373.08
INT 400, SPIRIT 450. 419.71
INT 450, SPIRIT 300. 296.78
INT 450, SPIRIT 350. 346.25
INT 450, SPIRIT 400. 395.71
INT 450, SPIRIT 450. 445.17
So what's better? Spirit of Intellect? To be honest, all this work I've just done shows me that you can sacrifice a fair chunk of mana to increase you mana regen by even more then the buff it's already going to get. Is it worth it? I'll leave that much up to you. Do some number-crunching, Planeteers; The power is yours!
Going from 400 INT, 300 Spirit to 300 INT, 400 Spirit is a change of 73 MP5 non-casting. a fair chunk of regen, but you're also LOSING 1500 mana. There's the plus damage and healing, to account for as well, but I'm not going QUITE that in detail at this time of night. I've been at this for nearly 3 and a half hours now. Perhaps some music and WoW to soothe my now-running brain?
~And people say I think too much!
Bob.
So, I stole the basic formula from the Elitist Jerks, and went to town. I figured there's gotta be some way to compare Spirit and Intellect in a general manner, and that I might as well put my Calculus II classes to work.
If you want to know the nit-picky numbers and details, read on. Otherwise... Well, you've been warned!
The basic formula they dug up for active mana regen (PER SECOND):
.009327[ (.001 + SPIRIT) (INT^.5) ] = X
Removing the constant from the variables side (Int and Spirit):
(.001 + SPIRIT) (INT^.5) = 107.2156106 X
Now this is where I'm trying something new, atleast from what I've seen. I'm going to solve for Spirit and Intellect in respects to each other, then plug in one value in the formula for the other. It's the same method used to solve intersection points between graphs with two variables, exactly what we have here. Just not in simple non-classroom Math X and Y.
This is what I came up with...
SPIRIT = (107.21561x / INT^.5) - 0.001
And because Intellect is never used in it's full form in this formula, it says as a square root (^.5 is a square root without the powers of drawing), I'm just solving for INT^.5
INT^.5 = 107.21561x / (SPIRIT +.001)
Now, if you were to try and plug one of those in to the other formula right now, you'd end up just solving for INT = INT or SPIRIT = SPIRIT. Wanna know why? This is a tri-linear function. X is still a value, so we need to remove the X values from these two formulas. How, you may ask? By substituting it with our starting function. This step stumped me for a bit, but just bear with me on this.
*Wipes Dry-Erase board clean, begin page 2*
... It was at this point I realized you can't ACTUALLY do this. You can plug in one value and see where the inflection points would be for the other when one value is constant, but you most certainly can't find ALL points of inflection without any set values, on both sides. My Math was clean, but my logic and memories of RULES of Math were certainly faulty. And for that I paid about 2 hours of my time. But it was totally worth the mental sweat I broke!
So, I spin off on a new tangent, basing numbers off of base points. Let's test this formula with some numbers and see what this does to my regen! I'm assuming you can add in the MP5 from gear directly, because I'm not picking gear in particular; just random numbers from the air.
I'm just going to scale from 300 to 450 for this example, but it'll work with ANY numbers. This is just to get a feel for what the graph would do. If you've followed this all the way to here A) I applaud you; and B) you need to multiply the number you get by 5 for the actual Mp5 value. This base formula determines Mana per second. I'm just going to multiply for Mp5 for common comparison values.
INT 300, SPIRIT 300. MP5 = 242.32
INT 300, SPIRIT 350. MP5 = 282.71
INT 300, SPIRIT 400. MP5 = 323.09
INT 300, SPIRIT 450. MP5 = 363.48
INT 350, SPIRIT 300. MP5 = 261.74
INT 350, SPIRIT 350. MP5 = 305.36
INT 350, SPIRIT 400. MP5 = 348.98
INT 350, SPIRIT 450. MP5 = 392.61
INT 400, SPIRIT 300. 279.81
INT 400, SPIRIT 350. 326.44
INT 400, SPIRIT 400. 373.08
INT 400, SPIRIT 450. 419.71
INT 450, SPIRIT 300. 296.78
INT 450, SPIRIT 350. 346.25
INT 450, SPIRIT 400. 395.71
INT 450, SPIRIT 450. 445.17
So what's better? Spirit of Intellect? To be honest, all this work I've just done shows me that you can sacrifice a fair chunk of mana to increase you mana regen by even more then the buff it's already going to get. Is it worth it? I'll leave that much up to you. Do some number-crunching, Planeteers; The power is yours!
Going from 400 INT, 300 Spirit to 300 INT, 400 Spirit is a change of 73 MP5 non-casting. a fair chunk of regen, but you're also LOSING 1500 mana. There's the plus damage and healing, to account for as well, but I'm not going QUITE that in detail at this time of night. I've been at this for nearly 3 and a half hours now. Perhaps some music and WoW to soothe my now-running brain?
~And people say I think too much!
Bob.
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