I don't know a whole lot about medieval duels, but they definitely were not like fencing. I just used that term because it has a similar physical setup, with both fighters starting in the middle, and people spar forward and backward without variation to either side. That's easy to keep track of in a numerical system.

An alternative to dueling that might get used a bit more would be drinking challenges. Have an argument? Settle it by drinking your opponent under the table.