When I first joined the Society for Creative Anachronism in 1975, the default tournament format was a double-elimination tournament tree based entirely on modern sports events. Each round ended with a clear winner, based on the somewhat stylized standard rules for Society combat at that time. All blows counted as light (ignored), "kills" (powerful enough to end the fight even against an armored opponent) and "wounds"(blows that incapacitated an arm or leg, while leaving the victim otherwise unimpaired.)
In the late 1980s, I started trying to understand how medieval deeds of arms were actually structured., and how medieval armored combats were won or lost. I wasn't the first to attempt this: I know that David Friedman tried to recreate combats for an agreed number of blows much earlier.
It took about two decades to work out more realistic sets of combat conventions that were still acceptable variants of SCA rattan combat, and formats for deeds of arms that better reflected how they were actually fought in the 12th-16th century.
Here is one set of combat conventions for armored combat from 2008. This focused on armored combat on foot in the late 14th and the 15th century, either singly or in small groups. We've used other conventions to recreate large melees in the 12th and 15th century, combat over the barriers in the 16th century, and recreate 16th century unarmored longsword sport combat with rattan weapons.
One key insight was figuring out that that in combats for a previously agreed number of blows, the sequence normally ended as soon as *either* champion had thrown that number. This avoided the unrealistic artifact of previous reconstructions when one fighter could hoard his last few blows until his opponent had thrown all of his, and then go on the offensive knowing that his opponent could do nothing but defend.
Another thing important thing I learned in the two decades after 1990 was that there were several different formats for consensual deeds of arms in the Middle Ages, and none of them were much like a modern double or single elimination tournament.
The third was that the classic default rules for SCA armored combat didn't recreate actual medieval armored combat well at all. Fortunately, the Society was willing to accept variant rules as acceptable variations for specific contests on a case-by-case basis.
The best and most authentic recreations of medieval combat and deeds of arms within the SCA have improved a lot since ca. 1990.