How to automate the rendering of all possible combinations of a composition in Adobe After Effects? I have a composition used to display current scores for a match on a tournament. It shows the two teams banners on both sides and their current scores underneath them. The scene also has various animations and effects.

The rounds are best of three so the different combinations of scores are 0-0, 1-0, 2-0, 0-1, 0-2, 1-1, 2-1, and 1-2. So the way I'm doing it now is: change the numbers, render composition, and repeat for all combinations.

As you can see, this can get tedious and time consuming as it has to be done for every combination of teams as well.

I would like to know if there is a way to automate this process or a more efficient way of carrying out these steps.
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.