Help with a 9 Variable Equation

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jewish_scientist
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Help with a 9 Variable Equation

Postby jewish_scientist » Mon Feb 27, 2017 6:51 pm UTC

X is a pseudo-random number between 85 and 100. All other letters are variables.
H = ((((2 * L / 5 + 2) * A * P / D) / 50) + 2) * S * W/R * X / 100
H = (((( 2L/5 + 2) AP/D) /50) + 2) SWX/100R
H = ((( 2APL /5D + 2AP/ D) / 50) + 2) SWX/100R
H = (( 2APL /250D + 2AP/ 50D) + 2) SWX/100R
H = ( APL /125D + AP/ 25D + 2) SWX/100R
H = APLSWX/12,500DR + APSWX/ 2500DR + 2SWX/100R
H = APLSWX/12,500DR + APSWX/ 2500DR + SWX/50R
H = ( APL/250D + AP/50D + 1) SWX/50R
H = ( AP/50D( L/5 + 1) + 1) SWX/50R

If I made a mistake somewhere up there, I think that I may just explode. If I did not, then we can move on to the next part. I want to figure out the proportion between each variable and H. Here is a far as I could go:
H ∝ S
H ∝ W
H ∝ X
H ∝ 1/50R

Here is where I run into a problem:
H ∝ AP/50D( L/5 + 1) + 1

Now that there is a constant, I am fairly sure that I need to do calculus here. Unfortunately, I have never done calculus with proportions or with more than 2 variables. My guess is that calculus works for equations and proportions identically; I am not sure what to do in a 5 variable calculus problem. Thanks in advance for any help.
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>-)
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Re: Help with a 9 Variable Equation

Postby >-) » Mon Feb 27, 2017 7:10 pm UTC

what exactly do you mean by proportion of a variable and H? is it the ratio?

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LaserGuy
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Re: Help with a 9 Variable Equation

Postby LaserGuy » Mon Feb 27, 2017 7:31 pm UTC

I don't think you need calculus for this, unless I'm grossly misunderstanding what you're trying to do here. Would you be differentiating or integrating? Why?

The short answer is that H is not directly proportional to A, P, D, or L. If you have some information about the size of H, you can make some approximations--if |H| >> 1, then you can ignore the constant, for example. But if H is small compared to 1, then you don't have a proportionality.

Personally, if I were approaching this, I would simplify my life by making some composite variables. Starting from your first line, let a = L/5 + 1, b = AP/(50D), c = SWX/(200R), then we just get:
H = (ab + 1)c

Even better, let d = ab

H = (d + 1)c
So H is proportional to (d+1) and to c.

jewish_scientist
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Re: Help with a 9 Variable Equation

Postby jewish_scientist » Wed Mar 01, 2017 6:22 pm UTC

>-) wrote:what exactly do you mean by proportion of a variable and H? is it the ratio?

Iff A/B = C, where C is a constant, then A ∝ B.

LaserGuy wrote:I don't think you need calculus for this, unless I'm grossly misunderstanding what you're trying to do here. Would you be differentiating or integrating? Why?

I thought that you would need calculus because differentiating an equation removes any constants and it is the constants that are messing me up.

The short answer is that H is not directly proportional to A, P, D, or L.

Then there has to be something that identifies the relationship A, P, D, and L have with H. I refuse to believe that me, some random guy on the internet, is the first person in human history to try and remove a constant from a proportion.

LaserGuy wrote:If you have some information about the size of H, you can make some approximations--if |H| >> 1, then you can ignore the constant, for example.

How big does |H| have to be before it is considered much greater than 1?

Personally, if I were approaching this, I would simplify my life by making some composite variables.

Yeah, but then you would need to substitute the composite variables back out at the end, so no real problem has been solved.


Maybe I should rephrase my question. If I wanted to maximize H, should I double S or triple A.
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RCT Bob
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Re: Help with a 9 Variable Equation

Postby RCT Bob » Wed Mar 01, 2017 7:41 pm UTC

That's the pokémon damage equation right?

The true answer is, it depends. For high enough L and H, you can pretty much assume H to be proportional to A and P, and inversely proportional to D. In earlier game at lower levels the approximation goes off. What I mean is that at high levels, when pokémon have strong attacks, the proportion L*A*P/(D*50) is much larger than 2 so the +2 part does not have much influence and can be neglected.

The point is that it is not exactly proportional, and no kind of algebraic or calculus manipulation is going to change that fact. You can differentiate, integrate, rewrite all you want, but if it's not proportional, it's not proportional.

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LaserGuy
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Re: Help with a 9 Variable Equation

Postby LaserGuy » Wed Mar 01, 2017 9:50 pm UTC

jewish_scientist wrote:Maybe I should rephrase my question. If I wanted to maximize H, should I double S or triple A.


I'll start with my equation H = (d + 1)c, where c is proportional to S, and d is proportional to A. If 0 < d < 1/3, then (3d + 1) < 2. So doubling S is better. If d > 1/3, then 3d+1 > 2, so you're better off tripling A.

[edit]More accurate: doubling S is better for -2/3 < d < 1/3; tripling A is better for d < -2/3 or d > 1/3, and they're the same at -2/3 and 1/3.

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Xenomortis
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Re: Help with a 9 Variable Equation

Postby Xenomortis » Wed Mar 01, 2017 10:22 pm UTC

jewish_scientist wrote:Maybe I should rephrase my question. If I wanted to maximize H, should I double S or triple A.

X-Y problem?

Look, if you have a Shuckle (very low Attack) attacking a Steelix (very high Defense) with a physical move, there's less point in using Shell Smash (doubling A) - the A/D term is still going to be really small, meaning the "+2" in that equation is going to be quite significant. So the effect of STAB or type-modifiers matters a lot more (the S term in your equation).

On the other hand, if you have something like a Breloom, with a much better Attack stat (making the +2 far less significant), then the using Sky Uppercut (85 Base Power, but also doubling the S term (super-effective against Steelix)) is going to be very similar to using Seed Bomb (80 base power) after a Swords Dance (doubling A).
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