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You have a few choices in the type of tournament you can run but there are myriad possibilities in how to structure your "seasons". Some group admins go for the simple cup structure, like the Blutballas Cup. Some go for the simple league season. Many choose to have a league season which qualifies the best-performing teams for an elite end-of-season cup, just like finals in the modern NFL.
This is a basic scheduled everyone against everyone else tournament. The matches are completely predetermined and has to be played in order.
Leagues in groups of 16 or more are usually broken up into divisions. There are several excellent reasons for splitting into divisions. You can't play a round-robin match until your next opponent has played all of his games up to that round, which means that the more players in a round-robin tournament, the more potential there is for one or two lazy players to hold up the entire league. Another good reason for divisions is that when there is a drop-out, it will affect fewer other teams. Also, starting a tournament is quicker when you can start it one division at a time.
IMHO, eight is the ideal number of teams in a division - big enough to have a diversity of teams and coaching styles, but not too big that you lose a sense of community. Six would be the workable minimum, and twelve would be the highest.
Divisional groupings can be determined in many ways. Randomly assigning teams to each division is the easiest way. Your divisional structure might be dictated by your group theme, e.g. single-race divisions, or each division has one team from each allowed race. Perhaps the smartest way is to group coaches from the same time-zone, so that you would have an American division, a Euro division, an Oceania division and so on. This would ensure that coaches in each division would be online at around the same time.
This is a loose form of the Round-Robin type. It allows games to be played in any order and there is consequently nothing that ensures that teams have played an equal number of games.
This type can be used in tournaments where you want to give a degree of freedom to the coaches, allowing them to pick the order of games themselves. This allows coaches to play a recovery game against an elf team before taking on that bashy chaos team.
The number of teams in each grouping can be higher than in the strict round-robin as the matches that are easy to schedule will be played quickly, without having the slower coaches block the tournament.
A basic single elimination tournament type. Teams that lose games get eliminated and the ones that win go on to the next round. This type is also called "single elimination" or "cup".
The knockout type tournaments can be seeded*, which means that the initial round is set up in various ways. There are a number of seeding options available:
The seeding is done* so that assuming no upsets (lower seed beats a higher one), the final will be between the first and the second seeded teams. The semis will involve the first four teams and so on. This should ensure that games get gradually harder as you advance in the rounds.
(* Typically highest seed v. lowest seed, 2nd highest v. 2nd lowest, etc etc.)
The number of participants need to be a power of two (4, 8, 16, 32, etc) in this type and overtime will be enforced when playing since there cannot be any draws. The overtime will be resolved by 'Golden Score', that is the first who scores gets the win and the game finishes immediately. If overtime ends in a draw, both teams roll 1d6 and add their remaining team re-rolls (automatically done by the client) to decide who moves on to the next round. Highest result wins.
These tournaments are essentially the same as Knockout Tournament, the only difference is - in King of The Hill tournaments each round of games is drawn after the previous round has been completed. This means that if you win in your first round match you will not know which team you will be playing in the next round until all the other first round matches are finished and the draw has been made.
This format is an extension of the knockout format and is very popular in tabletop tournaments. The basic idea is that all teams play the same (predetermined) number of rounds. A team gets 2 points for a win and 1 for a tie (thus, no need for overtime) and will play games against opponents with a score as close to their own as possible. An attempt is made to avoid scheduling the same two teams against eachother in the same tournament.
The first round is scheduled by seeding just like in knockouts and allows the same seeding options. The following rounds are determined by the following system:
In case of ties, teams are ordered by Touchdown difference+Casualty difference/2 (descending), followed by Raw Touchdowns+Casualties/2.
The benefits of the Swiss system is that it lets everyone play the same number of games and all games should (at least theoretically) become more even as you progress through the rounds.
There has to be at least 8 participants and the number of teams must be even in this format.