With the introduction of the new Initial Swiss Matchups rule added for the 2024 Copenhagen Major cycle, a flaw with assigning round 3 matchups was created.
There's a 0.6% chance that 1-1 record teams in round 3 cannot find valid matchups. It can cause the round 3 matchups selection to force a rematch, which is not allowed by the current ruleset.
In round 2 and 3, the highest seeded team faces the lowest seeded team available that does not result in a rematch within the stage.
Here's an example round 3 1-1 matchup pool. First we seed based on the mid-stage seed calculation rules;
After the initial matches, seed is determined (in order) by:
- Current W-L record in the stage
- Difficulty Score in the current stage
- Initial seeding of the current stage
| Team | Difficulty | Seed | Previous Opponents |
|---|---|---|---|
| 1 | 2 | 1 | 1>9, 16>1 |
| 5 | 2 | 5 | 5>13, 12>5 |
| 7 | 2 | 7 | 7>15, 10>7 |
| 11 | 2 | 11 | 11>3, 6>11 |
| 3 | -2 | 3 | 11>3, 3>14 |
| 9 | -2 | 9 | 1>9, 9>8 |
| 13 | -2 | 13 | 5>13, 13>4 |
| 15 | -2 | 15 | 7>15, 15>2 |
Then we follow the rule for round 3 matchup assignment:
In round 2 and 3, the highest seeded team faces the lowest seeded team available that does not result in a rematch within the stage.
The matchups are created from highest seed first, picking the lowest seed that doesn't result in a rematch:
- 1 is top seed, so they pair with the bottom seed 15 first
- 5 is next highest seed, but already played 13, so they pair with the next lowest seed, which is 9
- 7 is next highest seed, and pair with the lowest seed available, which is 13
- 11 and 3 remain, but they already played each other in round 1.
| Team A | Team B |
|---|---|
| 1 | 15 |
| 5 | 9 |
| 7 | 13 |
| 11 | 3 |
This conflicting matchup is not present when using the old seeding rules (1v16, 2v15, etc). There is no explanation in the rules how to resolve this scenario.
To fix this, the rules should be updated to either:
- Add a rule to resolve the scenario where rematch conflicts appear (e.g. swap opponents for the last two matchups when a conflict occurs)
- Revert the Initial Swiss Matchups rule
- Seed the teams using the Initial Swiss Matchups rule throughout the entire Swiss event
This project has code based on the cs-buchholz-simulator, but modified to get better insight as to what match outcomes are most likely to cause the round 3 matchup rematch conflict.
To run on Node 20, just run:
npm i
npm startIt will simulate 600,000 Swiss Buchholz, which is usually enough to generate all 400 unique conflicting scenarios.
It then does some analysis on what scenarios are most likely to trigger the conflict. The results of that analysis can be found in output.
top-subsets shows the top 10 combinations of results by subset length that are most likely to cause a conflict. For example, 16>1,9>8 with the count 120, means that 120 of the 400 conflicting scenarios contain 16 beating 1 and 9 beating 8.
Ultimately, the conditions that cause conflicting scenarios are very varied, so it's hard to make a definite rule describing what causes a round 3 conflict.
In initial-matchups.ts, you can comment/uncomment the generateInitialMatchups definition to test out the original initial matchups rules, and see that it generates no conflicting scenarios.
In mid-matchups.ts, you can comment/uncomment the generateMidMatchups definition to test out a proposed new fix for generating round 3 matchups that walks back matchups until a rematchless solution is found