Well I gave you a comprehensive definition.
Basically balance is where winrate = 1/#offactions for all players where all sets of players who win together and don’t win with the other factions is considered a faction. You can just declare an arbitrary team to be a faction so long as they share a win so as to let that work.
In the event that the game is not faction based this breaks down. For example in DBD you technically have no factions since all wins are both individual and not always mutually exclusive, if they were mutually exclusive then we could call them 1 person factions like in a battle royal but they aren’t. You need a different formula for those games.
Regardless for ToL this works.
What’s your definition? Just whatever your intuition says or something more specific?