Given two values, I'm trying to come up with a formula that will return 50% if both values are equal, 25% if the first value is half the second, 75% if the second is half the first. In other words:
given (a=3,b=12) returns .125
given (a=3,b=6) returns .25
given (a=3,b=3) returns .5
given (a=6,b=3) returns .75
given (a=12,b=3) returns .875
(a and b will always be positive)
... the idea being that if a is half of b, it's 25%, if it's half of half, it's 12.5% or half of 25%, if it's half of half of half, etc - the numbers go down if a is greater, but up in the same way if b is greater.
I'd love to know what that equation would look like - I don't really know enough about how this stuff fits together to do much more than fiddle with it on my own. (not even sure what tags to apply to this)
This function will reproduce your numbers (at least if $a$ and $b$ are positive):
$$f(a,b)= \frac{a}{2b} \text{ when } a \le b$$ $$f(a,b)= 1- f(b,a) \text{ when } a \gt b$$
You can write the latter case as $f(a,b)= \dfrac{2a-b}{2a}$ when $a \ge b$.
You can write both as $\dfrac{1}{2}+\dfrac{(a-b)\times \min(a,b)}{2ab}$.