Congrats on winning!
You're right: battles are not deterministic and in fact follow the rules of the original Risk board game. There are dice involved (up to 5 of them, actually) and we compare the rolls in pairs, from the highest to the lowest. Would it help if we logged what numbers rolled on the dice?
As for the stats, do you mean army strength and health? Or perhaps whether an army has moved this turn or not yet?