I am creating a Matchmaking ranking structure where players have a value to determine their skill level. If I win I get points, say $X$ points and if I lose then I win $Y$ points.
I am playing around with the values in a spreadsheet to see long term where players will fit into.
How can I calculate the breakeven point for $X$ and $Y$?
For example, if I have a $50\%$ win ratio then $X = Y$
However, how do I calculate what will be the win percentage to retain your position if, for example, $X$ is $6$ and $Y$ say $-4$?
To retain position simply means that wins and losses should compensate, i.e. $6X-4Y=0$.
You can solve this for $Y$ and get $Y=\frac{3}{2}X$.
Win ratio is defined of the fraction of wins divided by the total number of games, i.e. $R=\frac{X}{X+Y}$. You can now insert the formula for $Y$ to get
$R=\frac{X}{X+\frac{3}{2}X}=\frac{2}{5}=40\%$.
That means, you should win 40% of all games top keep position.