So now you know what stats and roles do and how armour fits in. Now we get to the meat of the game: the core dice mechanic.
At the heart of the way actions are resolved is a single mechanic that covers the vast bulk of dice usage in DB. There are a couple of other things that dice are used for: launching the ball, scattering the ball, doing Ref checks and so on, but these are less common and are simple cases of form following function.
DreadBall designer talks about the dice system in the game
DreadBall still chugging along on Kickstarter. Here's a look at the dice system for the game from one of the game designers.