Percentages of percentages

Question

I do not even know how to title this question, or the name of the thing i'm looking for, but here's an example:

1. there's N participants
2. we'll take just three into account, but i need a formula for N participants
3. A has x% to win B, B has y% of winning C .. x% and y% are known
4. since A hasn't competed with C .. i want to guess what % of A winning against C would be, based on their percentages against B.
5. there could be N participants between A and C, not just 1 as in the example

how would i calculate this? Thanks for your time!

Answer 1

This is how I reflected on your question

I will assign a number that represent how much an participant $A$ is skilled in comparison with his opponent $A'$. ( note that by $\alpha_{A,A'}$)

For example if $A$ has $x\%$ to win $B$. So, $A \equiv \frac{x}{100-x} B$ ( in this case $\alpha_{A,B} = \frac{x}{100-x}$)

and $B$ has $y\%$ of winning $C$. So, $B \equiv \frac{y}{100-y} C$ ( we have $\alpha_{B,C} = \frac{y}{100-y}$)

$A \equiv \alpha_{A,B} B$ and $B \equiv \alpha_{B,C} C$ this implies that $ A \equiv \alpha_{A,B} \alpha_{B,C} C $ ( so $\alpha_{A,C}= \alpha_{A,B} \alpha_{B,C} $)

you can follow the same method if you have more elements in your chain, but, it's important to suppose that there isn't a 100 percent of win in your chain between A and C.

after recovering $\alpha_{A,C}$, by a simple equation you can get the percentage.