你如何创建一个收益递减的公式？ [英] How do you create a formula that has diminishing returns?

问题描述

我想这是一个数学问题，而不是一个编程问题，但创建一个收益递减公式的好方法是什么？

下面是一些例子指出我希望曲线如何。

  f（1）= 1 
f（1.5）=。 98 
f（2）= .95 
f（2.5）= .9 
f（3）= .8 
f（4）= .7 
f（5）=。 6 
f（10）= .5 
f（20）= .25 
  

请注意，随着输入量的增加，百分比迅速下降。有没有什么方法可以模拟一个非常平滑和准确的曲线来表示这个功能？

另一种说法是使用一个真实的例子。你在Diablo II中知道他们有Magic Find吗？魔法发现的收益递减。如果你得到100％，真正的魔法发现仍然是100％。但越多，你的实际魔法发现就会下降。这么多说，如果你有1200，你真正的魔术发现可能是450％。所以他们有一个像这样的函数：

pre $ actualMagicFind（magicFind）= //减少魔法的一些方法find
code $ <$ $ p


解决方案

f（x）= f（0）e -rx < sup>

其中r是复合递减率

这只是指数衰减

I guess this is a math question and not a programming question, but what is a good way to create a formula that has diminishing returns?

Here are some example points on how I want the curve to look like.

f(1) = 1
f(1.5)= .98
f(2) = .95
f(2.5) = .9
f(3) = .8
f(4) = .7
f(5) = .6
f(10) = .5
f(20) = .25 

Notice that as the input gets higher, the percentage decreases rapidly. Is there any way to model a function that has a very smooth and accurate curve that says this?

Another way to say it is by using a real example. You know in Diablo II they have Magic Find? There are diminishing returns for magic find. If you get 100%, the real magic find is still 100%. But the more get, your actual magic find goes down. So much that say if you had 1200, your real magic find is probably 450%. So they have a function like:

actualMagicFind(magicFind) = // some way to reduced magic find

解决方案

f(x) = f(0)e^-rx

Where r is the rate of compounded diminishing return

This is just exponential decay

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