Design for a short-form competition

This is a description of a possible short-form competition. It was originally published as a post on the All About Petanque site, with a request for comments. Some of the most useful comments have been appended to the bottom of the original post.

GOAL: A competition format for a friendly competition to be held in conjunction with a large family picnic. We expect 12-14 teams to compete. Teams have not been seeded (ranked for relative skill) before the competition. We want the competition to allow most teams to play several games, but not to be too grueling. We want the competition to fit into a specified time frame consisting of three or four hours for qualifiers, approximately one hour for (two simultaneous) semi-final games, and an hour or more for the final game.

PROPOSAL: A two-part competition. In the first part teams compete in short-form games. By “short-form games” we mean games limited to a 6 ends. (Note that at the end of 6 ends the teams may have the same score. It is also possible for a team to score more than 13 points in a game.) A game of 6 ends should take approximately 30-40 minutes to play. Planning for 5 short-form rounds guarantees each participating team about 2.5-3 hours of playing time. Scheduling short-form rounds at 45-minute intervals allows all games in a round to finish and for players to have 5-10 minutes of R&R time between games. Scheduling 30-minute breaks at 90-minute intervals also allows for a certain amount of slop and over-run in the schedule.

08:00‑08:45am team registration and check-in
9:00‑09:45 short-form round 1
9:45‑10:30 short-form round 2
[30 min break]
11:00‑11:45 short-form round 3
11:45‑12:30 short-form round 4
[30 min break] LUNCH BREAK
1:00‑1:45 short-form round 5
1:45‑2:00 assess the results of the short-form rounds and pick the teams to play in the semifinals
2:00‑3:00? two simultaneous semifinal games are played to 10
[15 min break]  
3:15-4:30? final game played to 13
4:30 congratulations and prizes to the winners
NOTE that ad hoc changes to the schedule are possible. For example short-form round 5 could be eliminated

For each short-form round, the games will be played between teams paired at random by the competition organizer, except that no team shall play a team that it has already played, and no team shall be forced to sit out a round more than once. A team may drop out of the short-form competition after any round. Teams that drop out of the competition are encouraged to organize friendly games among themselves.

The results of the short-form games will be determined using the following procedure. After a short-form game finishes, each team calculates its “margin”, the number of points by which it beat, or was beaten, by the other team. (Note that a margin may have a negative value. If team A beats team B with a score of 9-6, team A’s margin is 3 and team B’s margin in -3.) After all short-form rounds have been played, an “average margin” is calculated for each team (the sum of the team’s margins, divided by the number of games that it played). Team rankings are determined by the teams’ average margins. The team with the highest average margin is ranked #1; the team with the second highest average margin is ranked #2, and so on. In the semi-finals, team #1 plays team #3, and team #2 plays team #4.


COMMENTS ON THE ORIGINAL POST


Why not use the proper Swiss System instead?
The main answer to your question is that our casual players simply do not have the experience or equipment to be able to use the Swiss system. We need something really easy that can be administered with simple paper forms and a pencil. There is also a more theoretical answer…

Let’s assume that every team has a certain skill level to which we can assign a numerical value. In a worst-case scenario, the only way that you can be sure of sorting all of the teams in order by skill level is via a round robin. A round robin tournament takes a lot of time: for n teams, each team must play n-1 games. That means n! (n factorial) games. It you have more than a few teams, this is a huge number of games.

To avoid this problem, especially in large competitions, the Swiss system is a sort of truncated round robin. It works, but it has its own set of limitations and costs. (1) You must abandon the goal of assigning ALL teams ranking position. (Since we’re interested only in identifying a handful of the highest-ranking teams, this is acceptable.) (2) In order to reduce the possibility that the second-best team will be eliminated in the first round by the best team, before the competition begins the teams need to be “seeded”, so that we can make sure that the first seed and the second seed don’t play each other in the first round. That’s the purpose of the “qualifying rounds” of a competition– to seed a previously unseeded bunch of competitors.

In a single-elimination competition, even with seeding, it is possible that the best team will eliminate the second-best team in the first round. Also, in a single-elimination competition, half of your competitors will play only one game because they have been eliminated in the first round, and another quarter will play only two games because they have been eliminated in the second round. To deal with these problems the Swiss system adds a “consolante” competition (in addition to the main “concours” competition) for teams that lose their first game. This creates a double-elimination format, but it requires a LOT more games than a single-elimination format.

The bottom line, as far as I can tell, is that unless your competition is a round robin, your competition MUST actually consist of TWO competitions. The purpose of the first competition is to take the motley crew of competitors as input, and to produce a set of seeded competitors as output. The purpose of the second competition is to take the set of seeded competitors as input, and to produce a small number of “winners” as the output. (This is a retired computer programmer speaking.) In our case, the challenge is to shoehorn both competitions into a single day of play, and to produce a result that has at least a chance of being close to fair. That’s what I tried to create in the format for this competition. It is the best design that I could come up with, given our goals and constraints.

You’re overthinking it. You need only a 3-round snake with predrawn fixtures, to find 2 finalists.
According to the EPA Competition Organizers Manual, a snake is simply a competition in which teams play a predetermined number of games against randomly-selected opponents. The distinctive feature of a snake is the procedure by which teams are ranked. Teams are ranked by number of games won, then by winning margin, then by total points scored.

The games played in a snake are a randomly-selected subset of the games that would be played in a full round robin competition, which means that the bigger the randomly-selected subset is (i.e. the more games that each team plays), the more likely it is that the team rankings produced by the snake will be correct (i.e. the same as the team rankings produced by a full round robin competition).

This design is similar to a snake in being a randomly-selected subset of the games that would be played in a full round robin. It is better than a 3-round snake, I think, for the following reasons.
(1) 5 rounds rather than 3 gives us a larger random sample, and so a better chance of ranking teams correctly.
(2) Ranking teams by average margin rather than number of games won also gives us a better chance of ranking teams correctly. A team that (on average) scored 6 points more than its opponents will be ranked higher than a team that (on average) scored 3 points more than its opponents, even if both teams won the same number of games.
(3) Ranking teams by average margin rather than number of games won avoids one of the problems with a snake— the necessity to have all teams play the same number of games, and to make special arrangements when there is an odd number of teams.


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