Initial Summary
The Top 7.2 system, which requires winning the last two rounds in addition to finishing first to earn a bye, is the most effective of those studied for promoting competitiveness in both final rounds. This format encourages undefeated players after the third-to-last round round to compete, preventing strategic draws and significantly improving upon the traditional top 8 system, without extending the tournament’s duration.
Introduction
A year ago, we presented the Spanish tournament system. This system, like what’s been done in Magic tournaments for the last 30 years, has a Swiss phase and a knockout phase. However, we proposed awarding byes in the elimination phase to those meeting certain conditions in the Swiss phase.
Adding byes has two objectives:
- To encourage playing rounds that would otherwise be strategically drawn if a top 8 were in place. This is especially evident at the top table in the final round, where both players are already qualified even if they lose, and there’s no relevant advantage to finishing first in the Swiss. Thus, it’s better for them to draw.
- To reduce the role of luck. By giving byes to those who perform very well in the Swiss, you reward that strong performance, ensuring they advance to a later knockout round. This prevents the scenario where a top-seeded, undefeated player could be eliminated early by someone who barely made it into the knockout rounds with a worse Swiss record.
The Spanish tournament system includes various structures that grant byes, but the most commonly used is typically called “Top 7”, which achieves the above objectives without lengthening the tournament.
This system has been used throughout the Liga Mensual de Premodern Valencia, as well as in other tournaments such as the 2023 and 2024 Old Frame Vintage World Championships, and some Premodern events in Alicante.
| SWISS + TOP 8 | SWISS + TOP 7 | |||
| Players | Swiss Rounds | KO Rounds | Swiss Rounds | KO Rounds |
| 9-16 | 5 | 2 | 5 | 2 (Top 3) |
| 17-32 | 5 | 3 | 5 | 3 (Top 7) |
| 33-64 | 6 | 3 | 6 | 3 (Top 7) |
| 65-112 | 7 | 3 | 7 | 3 (Top 7) |
| 113-128 | 7 | 3 (Top 8) or 4 (Top 15) | ||
| 129-204 | 8 | 3 | 8 | 3 (Top 7) |
| 205-226 | 8 | 3 (Top 8) or 4 (Top 15) | ||
| 227-372 | 9 | 3 | 9 | 3 (Top 7) |
| 373-408 | 9 | 3 (Top 8) or 4 (Top 15) | ||
As more tournaments have been organized, we’ve observed fewer intentional draws than would occur in tournaments with a top 8. However, situations still arise in which drawing is neutral or even optimal. This happens especially in two cases:
- At the lower end of a player range (e.g., around 17 players in a 5-round tournament), the final round at the top table often pairs an undefeated player against a player who has lost only once. In this scenario, it’s often optimal for both to draw: the undefeated player secures the bye, and the 3-1 player secures qualification. Only if the 3-1 player can also qualify if losing and possibly earn the bye by winning would we see that round being fought out.
- At the upper end of a player range, it’s possible to have four undefeated players after the third-to-last round round. In that case, those players might agree to draw the penultimate round and then play the last round.
How can we improve the Top 7 system even further, reducing scenarios where drawing is optimal? One possibility is to add extra requirements to earn the bye so that simply finishing first in the Swiss is not enough.
What if we require that the first-place player must also have won the last round? This would discourage draws in scenarios that currently favour them, such as in a 5-round tournament close to the lower limit of its player range (like 17 players).
However, for tournaments at the upper end of the range, it might be even better to require winning the last two rounds, to prevent the typical scenario where four undefeated players agree to consecutive draws.
In this article, we will analyze which of the three systems best incentivizes competitiveness in Swiss tournaments. We focus on a 64-player case, where undefeated players after the penultimate round face critical strategic decisions. Will the standard Top 7 system suffice, or is it better to require that the first-place Swiss finisher won the last round (“Top 7.1”) or even both of the last two rounds (“Top 7.2”)?
Our analysis starts from the point after four rounds have been completed:
- 4 players at 4-0
- 16 players at 3-1
- 24 players at 2-2
General Scenario Analysis
Below is a summary of the results, which we will explain in detail in the sections dedicated to each of the three systems.
| Average Probability of Reaching the Semifinals | |||
| Scenario | Top 7 | Top 7.1 | Top 7.2 |
| 1: Play 5th, draw 6th (5-0 & 4-1) | 50% | <50% | <50% |
| 2: Play 5th, 5-0s draw 6th, 4-1s play 6th | 50% | <50% | <50% |
| 3: Play 5th, 5-0s play 6th, 4-1s draw 6th | 50% | 50% | 50% |
| 4: Play 5th, everyone plays 6th | 50% | 50% | 50% |
| 5: Draw 5th, everyone draws 6th | 37.5% | <50% | <50% |
| 6: Draw 5th, some draw 6th and others play | 50% | <50% | <50% |
| 7: Draw 5th, everyone plays 6th | 50% | 50% | <50% |
The Top 7.2 system discourages draws and encourages competitiveness in the final rounds, while “Top 7” only discourages the double draw of the four undefeated players in the last two rounds.
Top 7 System
Scenario 1: Play the 5th round, draw the 6th (5-0 and 4-1)
Standings:
- 2 players with 16 points (2)
- 4 players with 15 points
- 2 players with 13 points (2)
- 14 players with 12 points
Probabilities:
- 25% gets the bye (100% semifinals)
- 25% second (50% in quarters)
- 25% seventh (50%)
- 25% eighth (0%)
Average semifinals: 50%.
Players with 12 points often prefer to play here, because the one with worse tiebreakers might be eliminated by drawing.
Scenario 2: Play 5th, 5-0s draw 6th, 4-1s play 6th
Standings:
- 2 with 16 points (2)
- 5 with 15 points (1)
- 15 with 12 points (1)
Probabilities:
- 25% first (100% semifinals)
- 25% second (50%)
- 25% 3rd-7th (50%)
- 25% 8th-22nd (0%)
Average semifinals: 50%.
This situation is more likely than the previous one for the reasons discussed.
Scenario 3: Play 5th, 5-0s play 6th, 4-1s draw 6th
Standings:
- 1 with 18 points (1)
- 5 with 15 points (1)
- 2 with 13 points (2)
- 14 with 12 points
Probabilities:
- 25% gets the bye (100%)
- 25% 2nd-6th (50%)
- 25% seventh (50%)
- 25% eighth (0%)
Average semifinals: 50%.
As in scenario 1, the 4-1 players often choose to play for a better shot at qualification, especially if one has worse tiebreakers.
Scenario 4: Play 5th, everyone plays 6th
Standings:
- 1 with 18 points (1)
- 6 with 15 points (2)
- 15 with 12 points (1)
Probabilities:
- 25% first (100%)
- 50% 2nd-7th (50%)
- 25% eighth or lower (0%)
Average semifinals: 50%.
Additional Analysis
From the first four scenarios:
- 4-1 players should play the last round if tiebreakers differ, to secure a spot.
- 5-0 players should also play the last round if they have different tiebreakers, to secure the bye and improve their position.
Thus, after playing the fifth round, it’s likely they will also play the sixth.
Scenario 5: Draw 5th, everyone draws 6th
Standings:
- 4 players with 15 points
- 4 players with 14 points (4)
- 14 players with 12 points
Probabilities:
- 75% 5th-7th (50%)
- 25% eighth (0%)
Average semifinals: 37.5%.
Scenario 6: Draw 5th, some draw 6th and others play
Standings:
- 1 with 16 points (1)
- 4 with 15 points
- 2 with 14 points (2)
- 1 with 13 points (1)
- 14 with 12 points
Probabilities:
- 25% first (100%)
- 50% sixth or seventh (50%)
- 25% eighth (0%)
Average semifinals: 50%.
Scenario 7: Draw 5th, everyone plays 6th
Standings:
- 2 with 16 points (2)
- 4 with 15 points
- 2 with 13 points (2)
- 14 with 12 points
Probabilities:
- 25% first (100%)
- 25% second (50%)
- 25% seventh (50%)
- 25% eighth (0%)
Average semifinals: 50%.
Additional Analysis
If you don’t know what the other 13-point table will do, playing is superior. If you do know, it’s still correct to play if tiebreakers differ. Thus, it’s expected that all four would play in the last round.
Conclusion for the Top 7 System
In the Top 7 system, the average chance of reaching the semifinals is 50%, regardless of the 5th round decision. However, playing the last round is optimal.
Top 7.1 System (Bye if the first place also won the last round)
Now we apply the same scenarios if the bye requires the first-place Swiss finisher to have also won the last round.
Scenario 1: Play 5th, draw 6th (5-0 and 4-1)
Standings:
- 2 with 16 points (2)
- 4 with 15 points
- 2 with 13 points (2)
- 14 with 12 points
Probabilities:
- 25% first (50% semifinals, no bye)
- 25% second (50%)
- 25% seventh (50%)
- 25% eighth (50%)
Average semifinals: Less than 50%.
It’s less than 50% because additional 13-point tables reduce the guaranteed spots.
Scenario 2: Play 5th, 5-0s draw 6th, 4-1s play 6th
Standings:
- 2 with 16 points (2)
- 5 with 15 points (1)
- 15 with 12 points (1)
Probabilities:
- 25% first (50%, no bye)
- 25% second (50%)
- 25% 3rd-7th (50%)
- 25% 8th-22nd (~3.33%, maybe slightly higher due to good tiebreakers)
Average semifinals: at least 38.33%.
Scenario 3: Play 5th, 5-0s play 6th, 4-1s draw 6th
Standings:
- 1 with 18 points (1)
- 5 with 15 points (1)
- 2 with 13 points (2)
- 14 with 12 points
Probabilities:
- 25% first (100%)
- 25% 2nd-6th (50%)
- 25% seventh (50%)
- 25% eighth (0%)
Average semifinals: 50%.
Scenario 4: Play 5th, everyone plays 6th
Standings:
- 1 with 18 points (1)
- 6 with 15 points (2)
- 15 with 12 points (1)
Probabilities:
- 25% first (100%)
- 50% 2nd-7th (50%)
- 25% eighth or lower (0%)
Average semifinals: 50%.
Additional Analysis
Considering the first four scenarios:
- If the 4-1 players don’t know what Table 1 will do, drawing might be preferred since it could be neutral or better if Table 1 also draws.
- For the 5-0 players, if they have different tiebreakers, it’s better to play.
Thus, after playing the fifth round, it’s still likely that they will play the sixth.
Scenario 5: Draw 5th, everyone draws 6th
Standings:
- 4 with 15 points
- 4 with 14 points (4)
- 14 with 12 points
Probabilities:
- 75% 5th-7th (50%)
- 25% eighth (0%)
Average semifinals: 37.5%.
Scenario 6: Draw 5th, some draw 6th and others play
Standings:
- 1 with 16 points (1)
- 4 with 15 points
- 2 with 14 points (2)
- 1 with 13 points (1)
- 14 with 12 points
Probabilities:
- 25% first (100%)
- 50% 6th-7th (50%)
- 25% eighth (0%)
Average semifinals: 50%.
Scenario 7: Draw 5th, everyone plays 6th
Standings:
- 2 with 16 points (2)
- 4 with 15 points
- 2 with 13 points (2)
- 14 with 12 points
Probabilities:
- 25% first (100%)
- 25% second (50%)
- 25% seventh (50%)
- 25% eighth (0%)
Average semifinals: 50%.
Additional Analysis
If it’s unknown what the other 13-point table does, playing is superior. If known, it’s also correct to play if tiebreakers differ. Thus, all four would likely play the last round.
Conclusion for the Top 7.1 System
After examining the 7 scenarios, the optimal strategy is to play the last round, as it maximizes success probabilities. However, the final probability of reaching the semifinals remains 50% regardless of whether the fifth round was played or drawn, so many draws in the penultimate round are still expected.
Top 7.2 System (Bye if first place won the last two rounds)
Now we consider the scenarios if the bye requires the first-place player to have won both of the last two rounds.
Scenario 1: Play 5th, draw 6th (5-0 and 4-1)
Standings:
- 2 with 16 points (2)
- 4 with 15 points
- 2 with 13 points (2)
- 14 with 12 points
Probabilities:
- 50% to be first or second (50%)
- 50% to be seventh or eighth (50%)
Average semifinals: less than 50%.
Scenario 2: Play 5th, 5-0s draw 6th, 4-1s play 6th
Standings:
- 2 with 16 points (2)
- 5 with 15 points (1)
- 15 with 12 points (1)
Probabilities:
- 50% first or second (50%)
- 25% 3rd-7th (50%)
- 25% 8th-22nd (~3.33%)
Average semifinals: at least 38.33%.
Scenario 3: Play 5th, 5-0s play 6th, 4-1s draw 6th
Standings:
- 1 with 18 points (1)
- 5 with 15 points (1)
- 2 with 13 points (2)
- 14 with 12 points
Probabilities:
- 25% first (100%)
- 25% 2nd-6th (50%)
- 25% seventh (50%)
- 25% eighth (0%)
Average semifinals: 50%.
Scenario 4: Play 5th, everyone plays 6th
Standings:
- 1 with 18 points (1)
- 6 with 15 points (2)
- 15 with 12 points (1)
Probabilities:
- 25% first (100%)
- 50% 2nd-7th (50%)
- 25% eighth or lower (0%)
Average semifinals: 50%.
Additional Analysis
Considering these four scenarios:
- If the 4-1 players don’t know what Table 1 does, drawing might seem better if others also draw.
- For the 5-0 players, if they have different tiebreakers, it’s better to play.
Scenario 5: Draw 5th, everyone draws 6th
Standings:
- 4 with 15 points
- 4 with 14 points (4)
- 14 with 12 points
Probabilities:
- 75% 5th-7th (50%)
- 25% eighth (0%)
Average semifinals: 37.5%.
Scenario 6: Draw 5th, some draw 6th and others play
Standings:
- 1 with 16 points (1)
- 4 with 15 points
- 2 with 14 points (2)
- 1 with 13 points (1)
- 14 with 12 points
Probabilities:
- 25% first (50%)
- 50% 6th-7th (50%)
- 25% eighth (~5%)
Average semifinals: less than 50%.
Scenario 7: Draw 5th, everyone plays 6th
Standings:
- 2 with 16 points (2)
- 4 with 15 points
- 2 with 13 points (2)
- 14 with 12 points
Probabilities:
- 50% first or second (50%)
- 50% seventh or eighth (50%)
Average semifinals: less than 50%.
Additional Analysis
After drawing the fifth round, playing is optimal if you don’t know what the other table will do. If you do know, playing still makes sense if one has better tiebreakers. Thus, it’s often correct to play the last round.
Conclusion for the Top 7.2 System
Considering the 7 cases, what should they do in the fifth round? The Top 7.2 system incentivizes playing both final rounds, offering the highest overall probability (50%) of reaching the semifinals when both rounds are played. This makes Top 7.2 the best of the three systems, as it truly incentivizes playing both final rounds.
If the bye can only be earned by someone who ends up undefeated, why not simply say this system gives a bye to the undefeated player, instead of “to the player who finished first after winning the last two rounds”?
This is to prevent the four 4-0 players from agreeing to draw the last two rounds, ensuring that no one ends undefeated and defaulting to a top 8 situation, granting all four of them quarterfinal spots. With the Top 7.2 system, if they do that, a player with 15 points (not one of the drawn-out undefeated players) would get the bye, leaving one of the pact-makers out of the elimination phase, as shown in scenario 5. Thus, the double draw is not beneficial, and it encourages everyone to play both rounds.