There is an upcoming contest to write an AI for an (American) football based board game, Bloodbowl. The players have different stats as you describe, and the teams can be asymmetrical (though for the competition, both teams select 11 players from a fixed 12 player roster, so not too asymmetrical).

Here is a link to the competition: https://njustesen.github.io/ffai/bot-bowl-ii

(As an aside, just wanted to mention that the original article is actually about soccer, rather American Football. The comment I'm replying to is certainly about American football, so I feel my comment here is fair.)