During the time of battle where infantry fought and clashed with swords, or other melee weapons, how often was it that they fought an opponent one on one? If the idea of the battle is to survive, and win, how often (or not), would a soldier kill an enemy who is occupied fighting someone else, or distracted in some other way?
There are two things to clear up here. First of all, if we're discussing formation warfare, you shouldn't get stabbed in the back because the only one behind you should be your friends. An enemy should only be on one side, the front.
However, if the formation breaks or you're fighting in a different scenario, say defending the wall during a siege or fighting a skirmish in an urban environment. Really fighting anywhere unsuited to rigid formations you're in a very different scenario. This is life and death scenarios, if you can get a gang up on someone, stab him in the back or get any dirty edge at all, you're going to do it because the alternative is death. So how often did it happen? As often as is humanly possible one would assume.
That said, to my knowledge there has never been a comprehensive study of how all mortal wounds inflicted in a battle.
I will be specifically talking about the late/high medieval period because a lot of the information we have on the topic is from the various primary sources ranging from the Hundred Years War to the War of the Roses that followed.
The average casualties of a battle were surprisingly low, most being only around 10% of the fighting force which was fielded (Bennett, Burn 1991)and the majority of these casualties were typically when the losing side was Routed, meaning that they broke formation and were fleeing the field.
A text book example of this is the Battle of Towton, which was known now and in it's contemporary for having an exceptionally large number of casualties, the majority of which occurred when the losing Lancastrian army was routed and was subsequently slaughtered on their retreat. (Gavett 2003)
So to answer your question, most armies fought in tight formations, with slightly looser formations being skirmishes, but formations none-the-less. When these formations failed and the ranks broke, the fleeing side would turn their back and run. During this point when the line was being overrun you would have people being ganged up on if they did not flee or attacked in the back if they were attempting to flee.
Bennett M., Burn J. Agincourt 1415: Triumph Against the Odds, Osprey Publishing Ltd., Oxford, 1991
Gravett, Christopher. Towton 1461—England's Bloodiest Battle. Campaign. Osprey Publishing Ltd., Oxford, 2003