I've heard that, statistically speaking, the highest casualty rate of any modern war the US has been in (civil war), was 1/15. It makes sense then to say your chances of actually killing someone are about the same.
However I was curious if this would hold true to a medieval soldier, someone on the front lines. For simplicities sake, in one battle, what would your chances be of actually killing an enemy soldier?
Unfortunately, medieval record-keeping was absolutely not up to the sort of standards that would be required to provide a definitive answer to this question. There's practically no consensus on the number of combatants fighting on either side in even the best-known battles of the period (Hastings may come closest to a battle in which there is at least close-ish agreement on numbers among historians), nor on the number of casualties inflicted in these battles, much less on how and by whom the majority of the killing was done.
It's also worth mentioning that some interesting claims were made after World War II regarding the proposal that the majority of killing in modern wars is done by a relatively small group of efficient and experienced soldiers, while the great majority, even among infantry, actually have a low likelihood of killing anybody. This suggestion, if true, would somewhat undermine the links between total deaths and the likelihood of killing someone in combat that you draw in your question.
While hopefully some of our medieval military flairs may be able to expand on this response, I did write a detailed assessment of a recent claim on the proportion of violent deaths recorded in this period, and the thread includes some further discussion of specifics that may be of some interest to you while you await some fresh responses: