In Rise of Nations when looking at the scores chart you sometimes see in the linear timeline a "Battle Won" or "Battle Lost". What is needed for the game to classify an attack as a battle?
I tested this once, and found some interesting results.
The comments on your question are correct; When armies collide, and units die, the army which took the most casualties loses the battle. Loss is calculated as a number of units rather than the cost of the units.
Additionally, the amount of unit casualties needed for an engagement to be classified as a battle varies, throughout the game. I was not able to determine the exact function, but it seems to be a combination of age in which the battle was fought, and the ratio of troops involved in the battle/overall troops in the empire.
I don't remember the exact number of troops required to qualify as a "battle", but I believe it was >5 in the earliest age, rising to >25 in later ages.