Yeah... the more battle advantage you have, the more troops you will have on the battlefield (relative to the enemy).
Battle advantage appears to be determined by two factors:
1) The size of your army. Obviously, if your army is ten times the size of the enemy army, you'll have more troops on the field.
2) The amount of tactics skill you have. I think the only effect of tactics is to increase your battle advantage, and thereby increase the percent of troops on the battlefield that belong to your army.