Yeah I would say it looks like it's based on the relative strength in favor of or against you, as the game calculates and displays on that balance bar before the fight. This notion is somewhat reinforced by the game files, where various triggers utilize the battle odds as opposed to the hard numbers of troops, IIRC. While I'm thinking about it, I also notice that we have determined very little about how the game determines those odds and the relative strength value of any given troopy types, or armies as a whole.
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