[@King Cosmos] and anyone else it may concern, the ranking works like this:

[u][b]Global[/b][/u]

Every dorm gets a flat rating at the start of the year (let's say 10,000). This rating goes up or down with a ranked challenge between members of opposing dorms. In order to start one, you have to verbally announce your intent to have a ranked duel with the other person. Regular students can initiate these at any time, as their Duel Disk will track the data for them automatically after their announcement and send it to the staff. For top students, though, it has to be played in a public arena so people can anticipate 'dream matches' and come watch. This doesn't prevent people from having regular duels, though. It just has to be clear that they're not being played for rankings.

The amount the rating going up and down depends on the rankings of the challenged and challenger. Winning with a huge difference in favor of you will make little to no impact to the global ranking, while about even will create the most normal numbers. The year of admission and amount of rating the duelists have also matters, as two equal rated people of high rating and second or third year will have much more impact on it than two low rated people of the first year. It's to prevent a complete curbstomp. Win/loss streaks and other factors are also taken into account.

Synchro and Xyz need to pair with someone to start having their rating go up and down. Inherently, if nobody did pair up, they'd remain stagnant. However, teachers make sure to encourage people to team up with them as neither dorm is particularly weak and can help a lot with the ranking shifts.

There are also three week-long periods that double the impact of global rankings while scheduling forced matches between top students.

[u][b]Individual[/b][/u]

Individual rankings work mostly the same way. First and second years share a bracket and get a flat rating at the start of the year (say 1000), with their ranking changing upon the conclusion of announced ranked matches (which does not prevent casual dueling). The ranking of the third years is decided by the end-year ranking of them as second years. They get spots 1-? depending on their rating, with the highest rating automatically becoming champion. If the ratings are tied, however, they will have to duel until one of them wins over the other. The last two weeks of the year is a blitz period for most students, as everyone is desperately dueling each other to secure their spot for next year.

Being inactive will cause you to take penalties to your rating, but this does not apply to the top 5 because of their position. They may, however, be asked to duel each other from time to time by the principal to show they still deserve their rank, but I don't think this should be relevant in the story as I expect character development to happen throughout it and rankings to not be set in stone forever (even if the number 1 might stay that way start to finish).