I need an S-curve equation that looks at two numbers

[RockandGrohl]

I've been reading more about the problem I describe here:

I need to examine the relationship between two parameters and allocate points to them.


I think what I need is actually a formula that result in an S-curve, like this:

Some Basics on the Value of S Curves and Market Adoption of a New Product

An ongoing challenge for any firm is estimating demand for new products. This is especially true when the product has new technology or is replacing an existing product and the additional function in the new product is limited. Often a mathematical constructed called an S curve is helpful. This...

blog.arkieva.com

To be clear, I'm not trying to make a graph, but if you imagine the Y-axis of the graph runs from -50 to +50, then the result of the formula would be within that range.

There are four inputs:

1) The Ratio, or "r"
2) The number of advertisements, or "a"
3) The average ratio, 0.2
4) The average advertisements, 20

What I'd like to do is input the r and a and have it compare against the average inputs.

If the average ratio is 0.2, and the advertisements is 20, then parameters that exceed this should be weighted higher up the S curve in points to an upper limit of +50 points. And the inverse is true.

Does anyone know of a formula where I can just jiggle the parameters around? Thanks.