Aydın Tiryaki (2025)

Subject: Managing leagues with an odd number of teams in a higher-level even-numbered (n+1) model using the Dummy Pivot layout.

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INTRODUCTION

In this phase of the Dynamic Fixture Model (DFM), we resolve the symmetry issues inherent in odd-numbered league organizations through the “Two-Block Model.” The core principle of this strategy is to pair each odd-numbered league with its immediate even-numbered “neighboring model” (n+1) and balance the mathematical discrepancy using a strategic “Dummy Pivot” (an imaginary team placeholder).

APPLICATION GUIDELINES AND ADJACENT MODEL MATCHING

The model begins by dividing the league into two operational blocks (A and B) based on team performance. Each odd-numbered league then adopts the even-numbered algorithm appropriate to its next-level scale:

• 7-Team League: Operates using the 8-Team Model framework.
• 9-Team League: Operates using the 10-Team Model framework.
• 13-Team League: Operates using the 14-Team Model framework.
• 21-Team League: Operates using the 22-Team Model framework.

DUMMY (BYE) PIVOT PLACEMENT LIST

For the system to function flawlessly as a higher-level even-numbered model, the “Dummy” (D) pivot must be placed at specific strategic points within Block B (the Lower Block) to ensure equilibrium:

• 21-Team League (11+10 Structure):
  • Based on the 22-team model.
  • Dummy (D) is assigned to the 6th position (B6) in Block B.
  • This creates a perfect 5+D+5 symmetry in the lower group.
• 13-Team League (7+6 Structure):
  • Based on the 14-team model.
  • Dummy (D) is assigned to the 4th position (B4) in Block B.
  • This establishes a 3+D+3 equilibrium in the lower group.
• 9-Team League (5+4 Structure):
  • Based on the 10-team model.
  • Dummy (D) is positioned at the 3rd row (B3) of Block B.
• 7-Team League (4+3 Structure):
  • Based on the 8-team model.
  • Dummy (D) is positioned at the 3rd row (B3) of Block B.

OPERATIONAL PROCEDURES OF THE TWO-BLOCK MODEL (21-TEAM EXAMPLE)

The implementation of the model for a 21-team league (the most complex version) follows these steps:

1. Block Assignment: At the end of the first half of the season, teams are divided into two groups: Group A (Ranks 1-11) and Group B (Ranks 12-21).
2. First Stage and Reserved Week: In Group A (11 teams), a scheduling gap exists. One team’s match slot per week is held in a “Reserved Week” pool.
3. Performance Update (y series): After Week 10, teams are re-ranked internally within their groups based on current performance without transferring between blocks (creating the Ay1-Ay11 and By1-By10 series).
4. Neighboring Model Integration: From Week 11 onwards, the league transitions into the mathematical algorithm of the 22-team model.
5. Dummy Function: In Group B, the team paired with the Dummy (D) effectively receives its BYE week. The reserved match gap from Group A is then integrated into the schedule, mathematically equalizing the number of rest weeks across the entire league.

CONCLUSION

The “Two-Block Model” liberates odd-numbered leagues from administrative and mathematical complexity, providing them with the structural stability of even-numbered leagues. The strategic placement of the dummy pivot within Block B prevents algorithmic bottlenecks, while performance-based updates (Ay and By series) ensure that competitive tension remains at its peak in both blocks until the end of the season.

Aydın Tiryaki
Ankara, December 22, 2025