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5. For division II and below, after 7 Swiss-system-like matches, teams will be divided into 16 groups by ranking, with the top 1/16 in the first group, the next 1/16 in the second group, and so on.
Within each group, 6 more Swiss-system-like matches will be played to determine the final rankings within the group.
- Keep record.
- The cash prize is the same as in the first stage. (open to discussion)
- If the number of teams in a group is odd, then add the next highest-ranked team.
For example, 4072/16*1=254.5 , the first group is round(254.5)+1=256 teams, the second group is round(4072/16*2)-256+1 = 254 teams.
- After 7 matches and being divided into 16 groups, you can know roughly where your team stands in terms of strength within the same division globally.
It improves (1), too.
- As the number of teams increases, the issue in (2) might worsen, but at least in the second stage, we divide them into 16 groups based on their performance.

6. For division I, after 7 Swiss-system matches, top 64 teams advance to 64 Team Seeded Single Elimination and Placement Matches instead of just 64 Team Seeded Single Elimination.
The remaining teams will be divided into 13 groups by ranking, with the top 1/13 in the second group, the next 1/13 in the third group, and so on.
Within each group, 6 more Swiss-system matches will be played to determine the final rankings within the group.
- For top 64, the cash prize after one loss is open to discussion.
- Keep record and match history for the remaining teams.
- For the remaining teams, the cash prize is the same as in the first stage. (open to discussion)
- If the number of teams in a group is odd, then add the next highest-ranked team.
- Set a minimum number of teams per group, such as 26. If the number of teams is too few, reduce the number of groups.
- The part where teams are divided into 13 groups is the same as Division II and below; it improves (1).

7. For division II and below, use the Random2 from the paper below and allow for repeated matches against the same opponents, instead of using the Swiss system.
Führlich, Pascal, Ágnes Cseh, and Pascal Lenzner. "Improving ranking quality and fairness in Swiss-system chess tournaments." Proceedings of the 23rd ACM Conference on Economics and Computation. 2022.
https://arxiv.org/html/2112.10522v2
- Random2: Every player from the top half of her score group is paired against a random player from the bottom half of her score group.
- To avoid high computational workload, repeated matches are allowed.
- The algorithm roughly looks like this: (323515.4)

8. In the first round, opponents are determined using Random2 based on world rankings or points.
- The current first round doesn't seem to be determined by world rankings using the Dutch system; it looks more like it's random.

9. After 13 rounds, for sorting teams with the same number of wins, consider whether to continue using the point differential or to use a separate Glicko-2 rating that only considers B3 and BBM.
- If using separate Glicko-2 rating, set the rating period to one season of 13 matches.
(The document says, "The Glicko-2 system works best when the number of games in a rating period is moderate to large, say an average of at least 10-15 games per player in a rating period.")
- If using a separate Glicko-2 rating, then within BBM, replace the world ranking with the separate Glicko-2 rating.
- This will determine the order for the extra promotion spot when teams in the same group have the same number of wins.

10. Whether to allow newly signed-up teams to join BBM midway can be discussed.
- If allowed, it would also involve the need to remove certain computer teams.


p.s. I'm not sure if BB uses maximum weight matching to implement the Swiss system.
I personally prefer using Random2. This is because the current Dutch system might make people not want to win by too much to avoid having a strong opponent in the next match.

Last edited by little Guest at 5/22/2024 7:53:56 AM

For 7. in (323515.3), the algorithm roughly looks like this:

There are a total of n teams (suppose n is even) that have played r rounds, and now we need to determine the pairings for the r+1 round.
Clear MDPs (moved-down players) and let # of MDPs = 0.
For the number of wins k = r to 0,
MDPs are placed at the front, followed by those with k wins.
If (# of MDPs + # of k wins) is even,
then, based on the order, the first half and the second half are paired randomly for matches, and clear MDPs, let # of MDPs = 0.
Else, based on the order, divide into the first half and the second half, with one extra team in the second half. Select one MDP randomly from the second half, and the rest pair randomly with the first half for matches. Let # of MDPs = 1.

p.s. Today (2024/6/25), I found that B3 in this season is not using the Dutch system.
I might have misunderstood before and thought that BB was using the Dutch system.
Anyway, BB, good job.

Last edited by little Guest at 6/25/2024 7:41:39 AM

Someone told me they don't approve of mixing BBM results into the league because it would make arranging the lineup not relaxed and with concerns.
I agree with this viewpoint. Mixing BBM results into the league might go away from the original design of BBM: to satisfy those who want more matches while not troubling those who prefer a slower pace.

Therefore, I continued to think of the meaning of BBM, and eventually, I found an answer.
The meaning related to "main objectives" is to gain experience: the players' experience and the manager's game experience (though some may disagree with the latter).

Compared to knowing roughly where your team stands in terms of strength within the same division globally, I believe that playing against teams with similar strength is more important, and cross-division matches should be more beneficial for the rating system.
As a substitute, add a record showing the ranking and number of teams in the same division within the tier to evaluate one's results.

Besides, due to the restriction of division difference within the same tier, many newly sign-up teams in small countries are forced to stay in an unsuitable tier.
This should be improved.

The following is the new solution:

Plan C

For B3:
1. For top 64 teams, use 64 Team Seeded Single Elimination and Placement Matches instead of just 64 Team Seeded Single Elimination,
and allow the bottom 64 teams to continue with 6 Swiss-system matches to determine a ranking.

- Bracket for top 64 teams: https://imgur.com/JwQT4K0
- The part with zero losses is exactly the same as the original single elimination format.
- The cash prize after one loss is zero. (open to discussion)

- For bottom 64 teams, keep record and match history. (The number of wins is too different.)
- The cash prize is zero. (open to discussion)

- The page can be modified like this:
Add a drop-down menu to the left of the Season, with the following items: Group 1 - Advancing, Group 1 - Ranking, Group 2 - Ranking.
- BuzzerBeater's Best Knockout Stage Draw remains the same (only reveal the part with zero losses) in Group 1 - Advancing.
- In Group 1 - Ranking, the standings are sorted by number of wins, whether loss in last round, point difference, and so on.

For BBM:
2. For top 64 teams, use 64 Team Seeded Single Elimination and Placement Matches instead of just 64 Team Seeded Single Elimination,
and allow the remaining teams to be divided into 15 groups based on their rankings and to continue with 6 Swiss-system matches to determine their rankings.

- For top 64 teams, it is similar to the case in B3.

- For the remaining teams, there's no need to keep records and match history.
- The cash prize is zero. (to avoid match-fixing)(open to discussion)

- The page can be modified like this:
Add a drop-down menu between Tier and Season, with the following items: Group 1 - Advancing, Group 1 - Ranking, Group 2 - Ranking, ..., Group 16 - Ranking.

3. If a team's world ranking is lower than the median world ranking of the next lower division, then the team is not subject to the restriction of division difference.

4. Add a record showing the ranking and number of teams in the same division within the tier to evaluate one's results,
and change the color of the world ranking box to be divided by division, similar to the national tournament.
- In team history, it can be changed to this:
XXX were one of the final 16 teams in the B3, 10th of 64.
XXX played in the Group 2 of B3, 10th of 64.
XXX were one of the final 16 teams in the BBM Tier 1, 10th in Div I of 623.
XXX played in the Group 3 of BBM Tier 1 with 5 wins, 86th in Div II of 401.


Last edited by little Guest at 6/4/2024 10:30:35 AM