How to automate the rendering of all possible combinations of a composition in Adobe After Effects?
I hope there is a better answer, but my similar case is making lower thirds where I have to change out the name.  In that case, I have a static composition with the title that I use as a source in other compositions.  I then create a text layer for each name, hide all but one, click through to the final render comp (using the parent/child links) and start a generation for each.

It's still manual, but it is a relatively quick way to get them dumped out.  In your case, you could do one comp for the team logos and one for the scores (or just do two sets of layers in the same comp.)

Alternately, you may be able to render the background blank and then render the text and graphics layer's being animated without the background render.  This can save time if the background animation is difficult to render and the composition allows for alpha blending to meet the needs.  I wouldn't generally bother with that added complexity unless the background being pre-rendered would save a lot of time though.