I'm currently reading "How Great Generals Win" by Bevin Alexander (great book, recommended by someone on this sub). Towards the end of the chapter about Hannibal and Scipio, Alexander states that in encounters of ancient armies, by far the most casualties occurred not during the actual fighting, i.e. exchange of missiles, projectiles, direct confrontation of infantry or cavalry charge, but instead as a result of unorganized retreat and the routing by enemy cavalry.
The confrontation after which he makes this observation is the Battle of Zama, which constitutes the end of the Second Punic War. He explains the battle was in terms of infantry more or less even - while the Roman drives the Carthaginian cavalry of the field - and attributes the massive differences in loss of lives, around 20-30k of the Carthaginian army opposed to 2-3k on the Roman side, to the aftermath of the battle, that is the slaughter of the fleeing troops by the Roman cavalry.
Now, I understand Hannibal had a number of less well trained soldiers, which were overpowered, and thus make a fairly large contribution to his high death rate. However the question I'm trying to arrive at is, were the deaths in ancient (hand-to-hand) combat indeed not quite as numerous as commonly believed/pictured; and what would be a realistic assumption of the ratio of casualties during and after battle?
Throughout ancient times, casualty rates for the loser of pitched battles were significantly higher than those of the winner. The losing side having 5 to 10 times the casualties of the winning side would not be uncommon. At Cannae, a battle which was especially bloody, Carthaginian losses numbered 6000 to 8000 (12 to 16% of the army), whereas the Romans suffered about 50k deaths (60% of their army).
The difference in casualty rate is almost entirely due to the aftermath of the battle. To flee from the battle, combattants literally had to turn their back to the enemy. Exposing your back is never a good idea, but it also reduced the effectiveness of the fighting formation of the army. Much of the protection a soldier had was from being in pretty tight formation with other soldiers at his side and right behind him. Turning tail would reduce the pressure on the enemy and might leave gaps in the formation. Furthermore, in order to run faster fleeing soldiers would often drop their heavy shields, reducing whatever protection they had left even further.
John Lazenby mentions in his article The Killing Zone that fugitives might even trample each other in their desperation to get away. Most casualties will have been inflicted by a pursuing enemy though. A fleeing army could easily be run down by cavalry, or parts of the now mostly defenseless army might be surrounded by light infantry and massacred. Wounded enemies left on the battlefield would be killed. Overall, the winning army would suffer only few additional losses in the process of pursuit and mopping up.
The answer to your question then is perhaps more simple than you thought. The casualty ratio of combat to rout is approximately the difference between the casualties of the winner and the casualties of the loser. The winning army will have suffered nearly all of its losses in the actual combat. The losing army will have suffered about that (perhaps slightly more, they were losing after all) in the actual combat and the rest afterwards.
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