Reverse Formula

It appears to me that you are looking to use the formula based on the score to compute a number to multiply some other number by. That is a score of minus 1 means that you will mutiply something by 0.7 and thereby reduce it. A score of plus 1 means that the formula will generate a number greater than 1 and thereby increase what is being multiplies. If a score of minus 1 generates a 30% decrease, do you want a score of plus 1 to generate a 30% increase?

If that guess is correct, I suggest that the formula generate 1 for a score of zero. That way whatever you are multiplying wont change at all with a zero score.
 
JeffM said:
It appears to me that you are looking to use the formula based on the score to compute a number to multiply some other number by. That is a score of minus 1 means that you will mutiply something by 0.7 and thereby reduce it. A score of plus 1 means that the formula will generate a number greater than 1 and thereby increase what is being multiplies. If a score of minus 1 generates a 30% decrease, do you want a score of plus 1 to generate a 30% increase?

If that guess is correct, I suggest that the formula generate 1 for a score of zero. That way whatever you are multiplying wont change at all with a zero score.
Click to expand...

Yes, so basically it's to reduce or increase damage in a game.

So, like for example Pokémon; types have advantages and do increased or reduced damage based on the moves type used against the Pokémon's type. But in my case there's more than simply "super-effective" or "not very effective" and so I used a point system. So each time something's effective it adds a point, and when it's not effective it loses a point. If the result is 1 or more points I want the damage to increase based on the points. But if the result is -1 or less I want the damage to decrease based on the points.

But as I said before I want the increase/decrease to be less effective per point (this is my way of balancing it, so too much, or too little effectiveness doesn't make a move too strong or too weak).
 
OK, I think cubist or I can give you something that works, but I am busy right now. Probably tomorrow sometime.
 
Working on a sigmoid function for you. Look it up on wikipedia. It has the general shape I think you want.
 
I do not know whether you are calculating things by hand, on a hand calculator, or by computer. Implementing this may differ on different machines.

I have tried to give you values that look like the ones you used. If you want different values, I shall have to recompute the constant used in the formula.

I am assuming that points accumulate and can be positive or negative. I am also assuming that we are calculating a multiplier based on points so with no points (zero), we multiply by 1. This formula does not duplicate yours. It is similar to yours in general shape, but covers any score and is symmetric, which your formula does not do.

Here is the formula, where m is the multiplier and p is the number of accumulated points.

[MATH]m = 1 + \dfrac{e^{(0.25p)} - e^{(-0.25p)}}{e^{(0.25p)} + e^{-(0.25p)}}.[/MATH]
A good hand calculator will give you the value of e as will excel's exp function if you enter a value of 1. It is a little bigger than 2.7.

Here are the approximate results

-9 points gives a multiplier of approximately 0.022
-8 points gives a multiplier of approximately 0.036
-7 points gives a multiplier of approximately 0.059
-6 points gives a multiplier of approximately 0.095
-5 points gives a multiplier of approximately 0.15
-4 points gives a multiplier of approximately 0.24
-3 points gives a multiplier of approximately 0.36
-2 points gives a multiplier of approximately 0.54
-1 points gives a multiplier of approximately 0.76
0 points gives a multiplier of exactly 1
1 points gives a multiplier of approximately 1.24
2 points gives a multiplier of approximately 1.46
3 points gives a multiplier of approximately 1.64
4 points gives a multiplier of approximately 1.76
5 points gives a multiplier of approximately 1.85
6 points gives a multiplier of approximately 1.91
7 points gives a multiplier of approximately 1.94
8 points gives a multiplier of approximately 1.96
9 points gives a multiplier of approximately 1.98

What do I mean by symmetric? Notice that m for +4 points is 0.76 greater than 1 and m for - 4 points is 0.76 below 1.

There is no problem with 0.

Try it yourself. Let me know if you see a problem.

EDIT: If you are using a sophisticated programming language you can use the following formula to get the same result.

[MATH]m = 1 + tanh(0.25p).[/MATH]
 
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