In 415, a coalition of Athenians and their allies fought a battle against the Syracusans and their allies near the city of Syracuse. The Athenians and their allies numbered 5100, but were divided into two elements: one who advanced to attack the Syracusans, and one which remained to guard the camp and act as a reserve or a fallback position, depending on how the battle turned out. The number of the Syracusans isn't given but, as their formation was twice the depth of the Athenian line and presumably matched it in length, it's likely they had around 5000 men.
The Athenians advanced, much to the surprise of the Syracusans, some of whom had even gone home to the city, but there was a sufficient period in which the light armed men (slingers, archers and javelin men) skirmished for those who had gone off to return. Once the skirmishers had beaten each other up enough, sacrifices were made and then the two hoplite forces charged each other and engaged in hand-to-hand combat. It was not an easy battle for the battle-hardened Athenians, and they had a lot of trouble breaking the Syracusan lines. As Thucydides says:
The armies met, and for a long time the issue was doubtful. During the battle there came on thunder and lightning, and a deluge of rain; these added to the terror of the inexperienced who were fighting for the first time, but experienced soldiers ascribed the storm to the time of year, and were much more alarmed at the stubborn resistance of the enemy.
Eventually, though, both wings of the Syracusan army were driven back and the route began. However, while the Syracusan hoplites had been defeated, their cavalry had control of the field and, while not able to charge a formation of hoplites directly, were perfectly capable of killing any who were foolish enough to break formation. As a result, there was almost no pursuit of the Syracusans and they were able to reform and present enough of a barrier that the Athenians decided to return to the battlefield and raise a trophy in memory of their victory.
After the battle, a count was made of the dead. No more than fifty Athenians had been killed, and these were burned on a pyre that night, while about 260 Syracusans had been killed, and these were given back the next day. These were probably just the hoplites, as the light-armed troops weren't always included in the count.
I've gone into so much detail about this battle because it was the best example I know of that demonstrates how non-lethal the actual fighting in pre-modern warfare was. No more than 2% of the Athenians and 5% of the Syracusans were killed during both the main phase of the battle and the initial pursuit before the cavalry intervened. While the Athenian casualties were somewhat lower than average for hoplite battles (Peter Krentz calculates the range as 2-10% and the average as 5%, which is also the mode), the Syracusan numbers are only one third of the average number of dead on the losing side (range of 3-20%). In fact, only one other Classical Greek battle (Coronea) had fewer than 10% dead on the losing side.
The total percentages of casualties in Classical Greek warfare isn't something that can be applied to all premodern battles, since each period has its own character. Richard Garbiel and Karen Metz, for instance, have calculated a 5.5% death rate for victorious armies, which is in line with the Greek numbers, but found the losing side would lose 37.7% of its men. Less reliable information is available for the Middle Ages - and the information that Gabriel and Metz use might not be 100% reliable in any case, especially for the Hellenistic battles - so far less can be said for the casualty rates in those battles. Some outliers, such as Crecy and Agincourt, though, suggest that the victors could expect less than 2% casualties and the losers more than 20% casualties.
However, caveats about applying this information outside of its context aside, what the Battle of Syracuse in 415 demonstrates is that most of the killing was done in the pursuit. Comparatively few of the combatants would have been killed in direct combat, with perhaps the numbers being roughly equal on both sides until one side finally broke and fled, whereupon the victors would pursue and kill as many men as they could. Medieval authors were just as aware of this as the Greeks were. Jean Froissart, for example, wrote that "in flight there is more danger than in the heat of battle, for, when anyone flies, a pursuit is made, and, if overtaken, he is slain". Similarly, Alfonso VIII wrote to Pope Innocent III about the Battle of Las Navas and said that, after the battle, the Christian forces "followed up the pursuit till nightfall, and killed more in that rout than we had in the battle."
The question now becomes: why did the armies rout so quickly when so few men (comparatively speaking)? This isn't a question that can be fully answered, because those writing about combat in the ancient and medieval world already assumed that their audience would have a degree of familiarity with hand-to-hand combat that we just don't have. A couple of different explanations have been proposed, such as the idea that the rout started once the battle line had been broken, but I'm personally a believer in what I'd called the Ardant du Picq model, which is based around the work of a 19th century French army officer and which holds that morale is key.
Ardant du Picq's model of combat, which serves as the basis for the more recent "pulse" model of pre-modern combat, holds that during combat there will come a time when the rear rank believes that they have lost and that their only chance of survival is to flee. du Picq gives the example of late Republican warfare in Rome, where swords were employed as the primary offensive weapon, and suggests that, after being pushed back too long without an advance by the men in front, the man in the rear will begin to look at the empty space behind him and, when terror pushes him over the edge, he will run.
This is supported by a degree of circumstantial evidence from ancient Greek sources. Xenophon in his Memorabilia (3.1.6-9) has Socrates explaining that the best and bravest men must be at the front and the rear of a phalanx in order to prevent the rear ranks from fleeing. This is an idea that would be echoed in the Hellenistic military manuals and their successors, right down to Maurice's Strategikon in the late 6th century AD.
In addition, we also have some examples of flight being contagious that, while not specifically mentioning the rear ranks, do suggest that routs tended to occur because of one or more individuals who flee in fear rather than from a break through. Xenophon in his Hellenica (7.5.24-25) credits Epaminondas with a plan to ensure the Athenian cavalry would be defeated early in the battle so that the rest of the force would loose moral and run. In a similar incident, Roger II of Sicily lost the Battle of Nocera, just as he was on the cusp of winning, because a wounded knight fled the attack of Count Ranulf and others, seeing him go, were afraid they had lost and fled as well. Finally, Froissart, speaking of the Battle of Aljubarrota, provides an excellent description of his behaviour:
When once an army is broken, that that are defeated are so much frightened, that if one fall, three follow his example, and to these three ten, and to ten thirty; and, also, should ten run away, they will be followed by a hundred."
All these factors, combined with the men in the rear being the only ones who have enough mobility to run away in any case, lend credence in my opinion to du Picq's model. As the fighting went on in waves, each side advancing or retreating as they succeeded in their attack, failed in their defence or became too tired to continue fighting, those in the rear suffered a lot of uncertainty and, not being able to tell what was going on in front except by the motion of the formation and perhaps the wounded leaving the formation, eventually reached the point where they were convinced that the battle was already lost and fled.
TL:DR
Long story short, the majority of pre-modern combat deaths were not sustained in hand-to-hand fighting, but during the pursuit after one side had broken. The casualties on the winning side could be less than a percent if they had enough of the odds stacked in their favour, but even in a straight up fight they were unlikely to suffer more than 10% dead. In most cases, it was probably 3-7%, as opposed to in excess of 10% dead - and often very much higher figures - for the defeated.
While the evidence is not sufficient to say with 100% certainty, there is good circumstantial evidence that most of the time the loosing side broke and fled from a loss of morale well before their lines could be penetrated and that this happened from the rear of the formation rather than those in the front.
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