BuzzerBeater Forums

After seeing JoeMaverick's proposed 10-week season schedule (304302.65)(304302.70)(304302.80),
it made me think that even though we have BBM now, about 15/16 of the teams will have no matches after Week 7.
Even if they make it to the knockout stage, only 1/16 of the teams will have matches during the postseason.
And before the offseason, 1/8 of the teams have a two-week break in the playoffs, 1/4 of the teams have a 1.5-week break, and 1/8~5/16 of the teams have a one-week break.
Only 1/8 of the teams do not have a break during the postseason.

In this thread, I will focus on the postseason.
The issue is that teams may feel bored when they don't have matches (excluding scrimmages) during the playoffs.
(In reality, I guess the NBA might be the same.)

The following is my solution.

Plan
Improve BBM/B3: 1+2

1. Allowing the teams that did not enter the top 64 to enter another 64-team seeded tournament.
- No fortune, no trophies, (to avoid match-fixing)(open to discussion)
but we can still regard it as our own participation in B3, leaving a mark in the team's history.
- 16 groups in a full tier.
- If the tier has fewer than 1024 teams, except for the group of top 64, the other groups can adjust the number of teams, with the remaining slots left empty.
- Teams in the same group will be closer in strength compared to the Swiss system stage.
This will enhance the enjoyment of international competitions.

2. Use 64 Team Seeded Single Elimination and Placement Matches instead of just 64 Team Seeded Single Elimination.
Bracket: https://imgur.com/JwQT4K0
Example: https://imgur.com/uwM5HP8
- The part with zero losses is exactly the same as the original single elimination format.
- Same as before, there are no fixed cash prizes after one loss.
- Each team can play a total of 13 matches (including Swiss system stage).
- Each team does not play the same opponent more than once (in this 6 matches).
- The principle is to let strong teams meet each other as late as possible.
- Participating in such international tournaments (without worrying about weekly minutes and training) is a great experience, and it would be a pity not to play all 13 matches.


If BBM switches to a 13-match format, the scheduling of matches on different days of the week can be reviewed.
However, there doesn't seem to be a perfect solution.
The current system, while feeling a bit dense with matches on Tuesday through Thursday, may be satisfactory or acceptable for those who prioritize only two league matches, two league matches and cup/scrimmages, or two league matches and BBM.

If I understand correctly, some people feel that
(1) the matches in BBM lack meaning, and that
(2) the opponents in matches are still too random, with significant differences in strength. (323509.9)

Regarding (1), upon closer consideration, BBM has no connection to "main objectives" such as B3 champions and league champions, except that Tier 1 champions can participate in B3.
Though BBM doesn't require managing training minutes and game shape, not everyone finds the experience of this type of match against opponents of similar strength helpful for themself.
The prize money is also very little, which isn't very helpful.
It seems that BBM itself cannot be considered a "main objective" either, since it is simply impossible for a team staying in the same division to defeat most of the teams in higher-level divisions.

For (2), I'm not sure what the reason is. I can only come up with two possibilities:
(2a) Teams with medium strength have a significantly larger number of teams in their score group than the strongest or weakest score groups.
If the distribution of strength is uniform, then this situation may occur.
(2b) The ranking at the same number of wins is not ideal.
But it's hard to find a better one.

The following is my new solution.

Plan B: Using the ranking in BBM to determine the extra promotion spot in the league.

For B3:
1. Use 64 Team Seeded Single Elimination and Placement Matches instead of just 64 Team Seeded Single Elimination.
Bracket: 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 open to discussion.

2. Allowing the bottom 64 teams to continue with 6 Swiss-system matches to determine a ranking.
- Keep record and match history.
- The cash prize is the same as in the first stage. (open to discussion)

For BBM:
3. Each division forms a group.
- If the number of teams in the division is odd, then add a computer team.
- The current number of teams in each division is approximately:
Division I: 9xx, Division II: 4xxx, Division III: 8xxx, Division IV: 9xxx.

- If the number of teams in division I, after deducting those participating in B3, still exceeds 1024 teams,
for scheduling matches, the first two rounds are considered as split into two groups: one group of 1024 teams, and the other group consisting of the remaining teams (unable to compete for the championship), playing within their groups.
In the third round, the two groups merge, but the remaining group starts with a record of 0 wins and 2 losses, while retaining their point differentials.
- If, after deducting those participating in B3, there are 1025 to 1027 teams, then computer teams are added to reach 1028 teams.
- The composition of the group of 1024 teams is as follows: teams that participated in B3 last season, teams from the top 512 of BBM in division I last season, and the remaining teams determined by their world ranking.

- For division II and below, set a minimum number of teams, such as 256.
If the number of teams is below this threshold, they will be merged into the division above.

4. Division I competes for the championship to get a B3 ticket, while division II and below compete for extra promotion spot.
- For the extra promotion spot, the priority order is as follows:
teams that qualified for the league playoffs are ranked by the ranking in BBM,
teams that did not qualify for the league playoffs are ranked by the ranking in BBM,
and teams that did not participate in BBM are ranked by original criteria.
- Improve the issue of teams with notably low salaries and exempt from paying the minimum total salary promoting to higher division. (319749.2)
- Improve (1).

Last edited by little Guest at 05/21/2024 12:57:26

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 05/22/2024 07:53:56

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.