Mathematical function for weighting football results Let's assume team A has scored x goals, and team B has scored y goals in a match.
I'm trying to find a function that returns a number between 0 and 1 based on the goals from the match.
Ideally, the function would reach 1 when y is 0 and x approaches infinity.
I have a very simple function that works almost entirely as desired, and that is x/(x+y).
The problem with this function is that 1-0 gives the same function output as 10-0, 1.

One possibility is
$$f(x,y)=\frac{x+1}{x+y+2}$$
This never equals $1$ or $0$, but the more lopsided the win for $x$ the closer it gets to $1$. This also is symmetric in $x$ and $y$, as you said you wanted in a comment.
The score $1-0$ gives a value of $\frac 23$, while $10-0$ gives a value of $\frac{11}{12}$. This seems to meet all your criteria. Ties give the value $\frac 12$, which makes sense. This does show, however, that you can get the same result for differing scores. Is this acceptable?
