I was asked how jousts were structured around 1345. Since I'm answering, I'll share the answer.
It's understandable for a modern reader to think that the winner was chosen by something like the modern elimination tree or round robin tournament.
Understandable, but wrong.
Here's what we know.
Although jousts were individual contests, the contestants were always divided into two sides, typically called dedans and dehors, literally within and without but perhaps best translated as the home team and visitors. 15th and 16th century English joust announcements would refer to challengers and comers.
The traditional division dated back to the time when jousts were preliminary events attached to mounted melee tournaments between two teams, and persisted when jousts became independent contests in their own right.
Once jousts became an independent event, the sizes of the two teams were often asymmetrical: the home team was often determined in advance, but the visitors were who turned up on the day of combat.
Each visitor could run some number of courses, that is to say attack runs with the mounted lance, against a defender.
At the end of the jousts, winners were chosen.
We have one set of rules for scoring a joust from Spain ca. 1330. Different regions almost certainly ran jousts somewhat differently. Geoffroi de Charny's Questions suggest that choosing a winner in a French joust was somewhat more subjective, although it probably followed a roughly similar ranking of achievements.
Charny's Questions, translated in Steven Muhlberger's Jousts and Tournaments, is a valuable but frustrating source on French jousts and tournaments around 1350: frustrating because Charny lists various debatable questions about the martial sports without providing answers.
Still, his questions make it clear that in some, but not all, French jousts a man who unhorsed an opponent would win his horse, and that there were jousts for knights and jousts for squires, and that they involved different equipment. It seems likely that as at the later Smithfield jousts of 1390, the knight's joust was run in full armor and the squire's joust used a saddle that protected the legs and made leg armor unnecessary. Flemish records from the 1340s list prizes given to the best knight and best squire on each team.
Interestingly, Charny examines the question of a squire entering a knight's tourney and vice versa. He regards this as somewhat irregular, but not so much so that the interloper would clearly forfeit his winnings. He might or might not: he thought the question worth debating
Often the home team would be dressed in matching livery.
Charny describes a very informal process for assigning opponents: the visitors would line up on one side of the field and as soon as one of the home team rode forward one of the visitors would charge him. Because of their limited visibility with helmets on, sometimes two visitors would unintentionally charge at once.
The biographer of the Castillian knight Pero Niño noted the same informality when he jousted in France around 1405, contrasting it with what was presumably Spanish custom. "There is neither one that holds the lists, nor joust of one man against another by champions assigned"
There seems to have been a general agreement that someone that killed or injured another's horse usually owed compensation. For Charny, the possible exceptions seem to have been insufficient promtness in presenting a claim, the injuring party possibly acting as an agent for another person, damage to a borrowed horse, and damage from a dropped lance the jouster no longer controlled.