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SinisteRing
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PostSubject: Mathematical Problems   Sat Feb 14, 2009 12:29 pm

I bet Pythagoras would love to solve this one, but he's currently on the love boat. So, I'm going to post it here and see what people come up with:

I'm looking for mathematical expressions that rely on 2 variables for the output. The first variable will be a stat, either Physical, Mental, or Soul. They start at 1 and remain integers at all times. The second will be an attribute within them, such as Physical Strength, Physical Speed, etc. These 2 variables shall be labelled:

A = Stat (Physical, Mental, Soul)
B = Attribute (The sub-stats within them)
Z = The increment/answer of the expression.


Therefore...

{MATHEMATICAL WITH A AND B} = Z

Now, here's what needs to happen during the mathematical equation:

    1. As A goes up, Z goes up.
    2. As B goes up, Z goes down.
    3. Z cannot be negative.
    4. Z cannot be zero.


Well, since this is slightly complex, I'll give you an example as to how you should present your equation and prove it works:

A / B = Z
This works because of the following:
  • If A = 4 and B = 4, then Z = 1.00
  • If A = 8 and B = 4, then Z = 2.00 (A goes up, Z goes up)
  • If A = 2 and B = 4, then Z = 0.50 (A goes down, Z goes down)
  • If A = 4 and B = 8, then Z = 0.50 (B goes up, Z goes down)
  • If A = 4 and B = 2, then Z = 2.00 (B goes down, Z goes up)


These are the types of equations that are able to be used. Get nifty, and use things such as square roots and such if you'd like, as they are all the better for my needs.
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kuro
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PostSubject: Re: Mathematical Problems   Sat Feb 14, 2009 4:36 pm

First of all, if you have more physical strength/speed why does your cumulative stat go down? Shouldn't it go up? (higher net strength = more powerful)



If A = 4 and B = 4, then Z = 1.00
If A = 8 and B = 4, then Z = 2.00 (A goes up, Z goes up)
If A = 2 and B = 4, then Z = 0.50 (A goes down, Z goes down)
If A = 4 and B = 8, then Z = 0.50 (B goes up, Z goes down)
If A = 4 and B = 2, then Z = 2.00 (B goes down, Z goes up)

(((A^2 / B^2)+3)^2 / 5

eh.

I really don't know what you're looking for... like what Z would do exactly.
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SinisteRing
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PostSubject: Re: Mathematical Problems   Sat Feb 14, 2009 5:11 pm

Z is the increment to the skill after a certain action. If your strength is 200, you shouldn't be gaining more strength more rapidly... you should be gaining it slower. However, if you're stronger physically, your potential rises.

A = Potential
B = Limiter of that Potential
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Coverzin
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PostSubject: Re: Mathematical Problems   Mon Feb 16, 2009 1:55 am

So... What's the problem with A/B=Z? A and B will always be positive because all you will do is at to them from their starting point of zero or one. So, Z will allways be postive and nonzero. All that's left to do is add functions to define a scaling rate, which you can just play around with on a graphing calculator application on your computer.
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Jay.J
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PostSubject: Re: Mathematical Problems   Mon Feb 16, 2009 11:12 am

What if b=0. MIND BLOWN.

Seriously though, not sure what Sin wants here...?

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SinisteRing
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PostSubject: Re: Mathematical Problems   Mon Feb 16, 2009 5:25 pm

Nevermind. I over-explained it, confusing you guys. Just forget it.

I was basically looking for a formula that will lower stat gain as it gets higher.
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Lagger09
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PostSubject: Re: Mathematical Problems   Mon Feb 16, 2009 6:45 pm

use a root or logarithmic funtion.
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Coverzin
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PostSubject: Re: Mathematical Problems   Mon Feb 16, 2009 8:06 pm

Lagger09 wrote:
use a root or logarithmic funtion.

Yeah, this would work. Every time you chop wood you increase X by whatever ammount and Y=X^1/2 or 1/3 2/3 etc, just however you want it to scale.
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SinisteRing
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PostSubject: Re: Mathematical Problems   Mon Feb 16, 2009 9:07 pm

You guys are still confused as to what I wanted. Smile
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Lagger09
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PostSubject: Re: Mathematical Problems   Mon Feb 16, 2009 9:41 pm

both a logarithmic and root funtion have a decreasing slope but still positive for all of infinity contiuing toward a positive X.

K(a)^1/G(b)=z
K&G being constants
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AquaAscension
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PostSubject: Re: Mathematical Problems   Tue Feb 17, 2009 2:33 am

Then please, with your infinite wisdom, tell us what you are looking for with this amazing code! I'm sure once it is done, it will be able to train dogs, solve fractal geometry, and finally provide the question to the answer: 42!

And don't assume that we're retarded. I may be an English major, but, damn it! I can understand mathematics*

Spoiler:
 
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Piddagoras
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PostSubject: Re: Mathematical Problems   Sat Feb 21, 2009 10:16 pm

You're talking about diminishing returns. Your Z would basically represent the derivative of your actual function that you need. The problem is that it varies with two quantities so it would be graphically represented by a surface, not a line.

Lets let F(A, B)=final "position" of your "power" derived from the statistics, in whatever the action or passive may use this sense of "power" for.

Let FA=the rate of change of F with respect to the A attribute, at any given point on the surface

Let FB=the rate of change of F with respect to the B attribute at any given point on the surface

As I understand it, this is what you require:
Quote :
As B approaches infinity and A remains constant, FB approaches zero but never reaches zero.
As A approaches infinity and B remains constant, FA diverges (also approaches infinity)
FB must contain an instance of the A variable, such that F cannot be the addition of two functions g(A)+h(B)

One such function that serves your purposes would be F(A, B)=ln(B)A2, which would make FB=A2/(B) and FA=ln(B)A

Sadly, you cannot use natural logarithms, or any kind of logarithms for that matter with any reasonable speed in WC3.

An alternative function would be F(A, B)=BA2 so FA=AB and FB=A2/B

Note: Raising a number to the power of 0.5 is the equivalent of taking the square root of that number. The constant coefficients can be tweaked as you see fit, so can the degree of the A variable, as long as it is greater than 1.

Basically when you want to compute how powerful something will be based on those stats, use
BA2
and then multiply or add that to whatever you want to use it for.

I hope this post was enlightening, and hopefully it met all your specifications. Let me know if you're unsatisfied, we can get more specific and complex if you'd like.

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