I love questions like this, mainly because it gives me the opportunity to dispel a myth about pre-modern warfare: battles with pirouetting swordsmen flailing widely are an invention of Hollywood film directors.

By and large, pre-modern battles were fought between tight formations with polearms. I'm most familiar with high medieval Italian militias, but by and large, medieval battles were characterized by infantry slowly grinding each other out while opposing cavalry engaged each other on the wing. A more open melee would only ensue if one of the two infantry formations broke and fled, or if one side's cavalry was able to encircle the opposing infantry.

With a few very notable exceptions like Swiss Pikemen, massed polearms are very difficult to advance with. And even the Swiss, who were well trained enough to keep a compact formation when moving forward, fought by mowing over opponents by crushing them under a wall of spears. There were very few individual fights with individual soldiers cutting through the lines.

In fact, in medieval Italy you sometimes see untrained urban militias sent into battle. The remedy was to place sergeants (servants of an aristocrat trained in warfare) at regular intervals along the line of battle so that they could push against the shoulders of their companions and pack them tight. This works if you're on the defensive, like when the Lombards trapped Emperor Barbarossa at Legnano and forced him to stage repeated cavalry charges against massed pikes (incidentally, the best way to lose a medieval battle) but was not viable on the offensive, like at Mount Porzio, where the Roman Urbis' militia attacked Barbarossa's lieutenant Reinald of Dassel's flying column. That battle saw what Sicard of Cremona called "The greatest army which Rome had sent into the field in centuries" engage about about 700 Brabantines from the front, unwilling or too undisciplined to screen their flanks as the compact imperial soldiery stood compact and unmoving right in front of them. The Brabantines would not have to stand fast for long, a detachment of German cavalry quickly overcame the mounted Roman aristocracy on the flank. The Roman army soon routed as another wing of cavalry rounded them and fell upon their rear. Rainald chased them all the way back to Rome, where the Pope and Oddo Frangipani locked themselves inside the Colosseum (which was still intact and fortified at the time) and Rainald sent word to the Emperor that the city of Rome was his.

So in short, battlefields were gruesome places to be sure, but the real horror only started when one side broke and ran.