Best way to format data for supervised machine learning ranking predictions
This problem looks like a lot with the problem of ranking college football teams. I have never worked on this ranking problem, but I believe you can borrow some tools used there to build your model.

Here goes a couple of references:

Colley Matrix Rankings - This was one of computer rankings used by the BCS. It is also the only one that shared their methodology.

An example of the Colley Matrix Rankings - An easy example to follow.

The Perron-Frobenius Theorem and the Ranking of Football Teams - A well known reference that presents some ranking methods. This paper also shows how to assess the probability of winning a game based on the rankings of the teams.