After all most of these "Barbarian" armies were composed of professional soldiers, at least in their cores. All their commanders would have been experienced officers that knew their trade and were in no way inferior to their Greek and Roman counterparts (just imagine men like Ariovist or Arminius in charge of Antigonos' or Mithradates' army).
The armies would have had division of several kinds; divisions by tribe for example are recorded - what would also include division by traditional waeponary and way of combat. There would have also been divisions by troop type or quality. There was a developed chain of command as well as a way to communicate orders.
What they were lacking, and in what they would have been inferior to the Greeks and Romans, was personal discipline. Each individual ranker seemed to be very eager to gain personal fame in a battle. That would have made it difficult for a commander to keep control over his troops once battle was unleahsed.
To make matters even worse, the leaders themselves would have charged ahead of their men into close combat to proof their bravety; and there is hardly anything more useless on a battlefield than a fighting general. A Roman or Greek general watching the show from a distanced point and not busy fighting for his very live would have been more able to give the right command at the right moment.
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