Aydın Tiryaki (2025)
Category: Sports Management, League Engineering, Operational Algorithms
I. INTRODUCTION: The Odd-Numbered Team Paradox and the N to N+1 Transformation
The presence of an odd number of teams in professional leagues (e.g., 7, 11, 15, 17, 19, 23) necessitates that one team remains idle (a “bye”) each week. In traditional scheduling, this often triggers a crisis of competitive integrity and engagement, particularly in the final weeks. For instance, a team battling for the championship or fighting against relegation may be forced to have a “bye” during the most critical juncture of the season, losing competitive rhythm while their rivals continue to play.
The Dynamic Fixture Model (DFM) resolves this systemic flaw by utilizing a mathematical surrogate known as the “Dummy Slot.” This approach upgrades the scheduling structure from N to N+1, allowing the model to operate based on an ideal even-numbered framework.
By applying the N to N+1 methodology, leagues with 7, 11, 15, 17, 19, and 23 teams are modeled as if they consist of 8, 12, 16, 18, 20, and 24 participants, respectively. By integrating a Dummy Slot, the DFM ensures a mathematically consistent and predictable “BYE” sequence throughout the season.
II. THE “DUMMY PIVOT” (C1 / D1) STRATEGY
In the DFM, the Dummy Slot is not assigned randomly. Instead, it is strategically positioned at “Pivot Points” – the equilibrium centers of the league’s structural balance. The primary objective of this strategy is to sequester the calendar’s inherent asymmetry (the free week) away from the most sensitive regions: the “Top” and “Bottom” classification groups.
Pivot Placement Rules:
- In 4-Group Models (20, 16, 12, 8 teams): The Dummy position is fixed at point C1.
- In 6-Group Models (24, 18 teams): The Dummy position is fixed at point D1.
III. OPERATIONAL PROCESS AND THE FAIRNESS FILTER
1. Neutralizing Extremities During the Marathon Phase
During the Classification Marathon (the league’s initial stage), groups are paired in predetermined periods. The groups situated at the extremities of the league blocks complete their scheduled encounters with the “Dummy” during this phase. Consequently, by the time the marathon concludes, the “BYE” burden for the league’s “showcase” teams (those at the very top or bottom) has already been cleared.
2. Uninterrupted Competition in the Decider Stage
In the “Showdown” phase following reorganization, no team actively contending for the championship (e.g., A1, A2) is assigned a bye week. The asymmetry of the bye week is effectively mitigated by being confined only to the middle-tier blocks. This ensures that the battle for the title is determined at full intensity, with all contenders on the field until the final whistle.
IV. TERMINOLOGICAL DISTINCTION: RESERVED MATCH VS. STORED WEEK
Distinguishing between these two fundamental concepts is essential for the operational success of the DFM:
- Reserved Match: This is the high-stakes encounter between the group’s two premier teams (e.g., A1-A2), strategically postponed to the final week to ensure the title is decided in the season’s closing moments. It is a tool for competitive suspense and peak engagement.
- Stored Week: This refers to a full period of matches that is shifted as a single unit to preserve scheduling symmetry. It is strictly a planning and logistical tool.
V. RESULTS AND PRACTICAL APPLICATION (17-TEAM EXAMPLE)
Consider a league with 17 teams. The DFM plans this according to an 18-team (6×3) model, with the Dummy Slot placed at point D1.
- Outcome: By the conclusion of Week 12, all teams in the top 6 and bottom 6 tiers will have already completed their required bye weeks.
- Final Phase: In the final 5 weeks of the season, neither the championship contenders nor the teams in the relegation zone will have a bye week.
- Conclusion: The league concludes with 17 active participants but operates with the perfect mathematical symmetry of an 18-team system.
BIBLIOGRAPHY AND REFERENCES
For a comprehensive analysis of the mathematical foundations and core operational principles of this model, please consult the primary study:
- Tiryaki, A. (2025). DYNAMIC FIXTURE MODEL (DFM): Performance and Fairness Based League Management Algorithm (2006-2025). Aydın’s Repertoire. Access Address: https://aydintiryaki.org/2025/12/21/dinamik-fikstur-modeli-dfm-performans-ve-adalet-tabanli-lig-yonetim-algoritmasi/
Aydın Tiryaki
Ankara, December 21, 2025
Aydın Tiryaki 