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Thread: Requesting Help with Diminishing Returns

  1. #1
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    Requesting Help with Diminishing Returns

    Hello,

    I am a new user to this forum and I have come here to request assistance from more powerful brains than my own. I am designing a "game", so to speak, and I have an issue regarding diminishing returns of a certain statistic.

    In my games, the "players" are rated by a certain "Power", we will call it. As this "Power" increases, the players have a "Factor" that increases alongside it. This "Factor" is just what it sounds like. It is a multiplier for all of their actions. So, essentially, as players desire a higher Power in order to increase their Factor so they will perform better in the game.

    Here is the catch: I want Power to increase at a steady amount, for the most part, but I want Factor to actually have a lower rate of increase than Power, but I am having difficulty modeling this in the game so that it is consistent. There must be a mathematical formula I can use?

    Here is an example:

    Let's say Person A has a "Power" of 200. Person B has a "Power" of 400. So, it could be implied that Person B is twice as effective as Person A (400 vs. 200). But, as I discussed above, I simply want Power to influence "Factor", so Person B might have a Factor of x3.5, and Person A might have a Factor of x2. So, in reality, Person B is only 1.75 times more effective than Person A. And, as players progress in "Power", I want this effect to continue.

    Later on, if Person A has a "Power" of 2,000, and Person B has a "Power" of 4,000, we could give Person A a Factor of x10, and Person B a Factor of x13 (these are just examples and not exact numbers). So, even though they are both ten times more effective than they were previously (respectively) Person B is now only 1.3 times more effective than Person A.

    Is there a way to model this mechanically on a graph or curve somehow?
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  2. #2
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    Re: Requesting Help with Diminishing Returns

    What you are describing is a logarithmic relationship between power and factor. A quick curve fit to the four data points you provided yields a relationship close to this:

     F=3.75 \times  \ln(P) -18.4

    It's not exact, but pretty close. One thing to be careful of is how to handle the calculation of force when the value of power is very low - for values of P below 135 you get a negative value for F. At P = 176 you get F=1.0, so perhaps you want to use that as your starting point for the game.

    Requesting Help with Diminishing Returns-power.jpg
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  3. #3
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    Re: Help with Diminishing Returns (Re-Posted into correct Forum)

    Quote Originally Posted by Indie1388 View Post
    Hello,

    I am a new user to this forum and I have come here to request assistance from brains more powerful brains than my own. I am designing a "game", so to speak, and I have an issue regarding diminishing returns of a certain statistic.

    In my games, the "players" are rated by a certain "Power", we will call it. As this "Power" increases, the players have a "Factor" that increases alongside it. This "Factor" is just what it sounds like. It is a multiplier for all of their actions. So, essentially, all players desire a higher Power in order to increase their Factor so they will perform better in the game.

    Here is the catch: I want Power to increase at a steady rate, for the most part, but I want Factor to actually have a lower rate of increase than Power, but I am having difficulty modeling this in the game so that it is consistent. There must be a mathematical formula I can use?

    Here is an example:

    Let's say Person A has a "Power" of 200. Person B has a "Power" of 400. So, it could be implied that Person B is twice as effective as Person A (400 vs. 200). But, as I discussed above, I simply want Power to influence "Factor", so Person B might have a Factor of x3.5, and Person A might have a Factor of x2. So, in reality, Person B is only 1.75 times more effective than Person A. And, as players progress in "Power", I want this effect to continue.
    That appears to be the opposite of what you are saying above. If person A has power 200 and a factor of 2 then the "effectiveness" of A should be 2(200)= 400. If person B has power 400 and a factor of 3.5 then the "effectiveness" of B should be 3.5(400)= 1400. So the relation is 1400/400= 3.5 which is larger than 2, not less, as 1.75 is.

    I thought perhaps that your factor was actually a "divisor". In that case, a power of 200 with a factor of 2 would give an "effectiveness" of 200/2= 100. And a power of 400 with a factor of 3.5 would be given an "effectiveness" of 400/3.5= 114.3 (approximately). That gives 114.3/100= 1.14, not 1.75.

    Later on, if Person A has a "Power" of 2,000, and Person B has a "Power" of 4,000, we could give Person A a Factor of x10, and Person B a Factor of x13 (these are just examples and not exact numbers). So, even though they are both ten times more effective than they were previously (respectively) Person B is now only 1.3 times more effective than Person A.

    Is there a way to model this mechanically on a graph or curve somehow?



    [/QUOTE]
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    Re: Requesting Help with Diminishing Returns

    Thank you for your help!
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    Re: Requesting Help with Diminishing Returns

    Tinkering with this a bit I find the function

    $factor = power^{0.344971}-4.21678$

    to be a pretty good fit to the numbers you gave.
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