Aydın Tiryaki (2025)

The Dynamic Fixture Model (DFM) is a framework specifically developed for the second half of double round-robin leagues. In this model, teams are grouped according to their standings after the first half of the season. The primary objective is to ensure that teams compete against opponents with progressively closer league positions as the season reaches its climax.

Core Philosophy: Strategic Sequencing

The fundamental principle of the model is to ensure that teams far apart in the standings face each other in the initial matches of the second half. As the weeks progress, the algorithm ensures that teams with similar rankings play against each other. This structure guarantees that in the final weeks, championship contenders face similarly strong opponents, while teams in the relegation zone compete directly against one another. This creates a high-integrity, fair competition for both the title race and the battle for survival.

In the final weeks of the season, this prevents competitive imbalances, such as a title contender facing a team that has already secured its position or has no remaining motivation. Similarly, it allows teams fighting against relegation to decide their fate on the pitch against their direct rivals. Mid-table teams also compete against one another to determine their final seasonal ranking.

Block Stability and Dynamic Transitions

In this model, teams are placed into groups determined by their standings, and neighboring groups form “blocks” to ensure operational efficiency.

• Block Integrity: Teams cannot move between blocks once the second half begins, as such movement would render the scheduling problem mathematically unsolvable.
• Intra-Block Mobility: However, movements between groups within the same block are possible. This allows for dynamic changes in the standings to be reflected in the schedule as the league progresses. Except for a few specialized cases, re-ranking within a block before teams have faced each other does not pose a structural problem for the model.

The DFM functions perfectly in leagues with common sizes, such as 16, 18, and 20 teams. Leagues with a high number of teams offer a particularly wide spectrum of performance data, which the model utilizes to maximize engagement.

Flexibility and Alternative Applications

While the model ideally divides teams into 4 or 6 groups forming two-group blocks, the algorithm can be simplified into a basic “two-block model” for any league size.

• Seasonal Adaptability: Group adjustments based on the first-half standings can remain fixed until the end of the season if preferred.
• First-Half Implementation: Although designed for the second half, the model can be applied to the first half of a season by using historical data, such as rankings from the last five years or the previous season’s final standings.

Dynamic Scheduling and Operational Phases

The scheduling is termed “dynamic” because league standings are updated in predetermined stages without violating core scheduling rules.

1. Classification Phase: Teams initially play “classification matches” against opponents outside their own blocks or groups. No team initially faces an opponent from within its own group.
2. Restructuring: Once the classification matches are complete, each block is restructured into two groups and updated internally based on the new points table.
3. Neighboring Group Phase: Teams then begin playing matches against neighboring groups but still do not face their own internal group rivals.
4. Intra-Group Showdown: Finally, each team faces its closest rivals within its own group.

During this process, teams in lower blocks or neighboring groups may gain points and overtake those above them. However, to maintain fixture integrity and ensure every team plays each other at least once in each half, the system does not allow for mid-stage intervention between blocks.

Constraints and Optimization Opportunities

A significant challenge for the DFM is that it does not allow for a perfectly alternating home-and-away sequence. This is the model’s primary limitation.

• Venue Balance: While ensuring an equal total of home and away matches over the full season is mandatory, the sequence may be uneven.
• Algorithmic Support: To mitigate this, each phase (classification, neighboring groups, intra-group) can be optimized to create the most balanced schedule possible.
• Performance-Based Acceptance: Since the scheduling is dictated entirely by performance rather than a committee’s decision, the slight imbalance in home-away sequences is often accepted as a “performance-driven” outcome. Regardless of the sequence, every team finishes the season with an equal number of home and away games.

UEFA Compliance and Modern Solutions

Current UEFA regulations state that a team can play a maximum of two consecutive matches either at home or away. Playing three consecutive matches at the same venue type is prohibited for logistical and fairness reasons. The DFM can be optimized using modern algorithms to ensure full compliance with these standards.

Match Postponements: The DFM requires high discipline regarding postponements. Since postponements can undermine the stage-based system, they should be rejected except in extreme circumstances. Any mandatory postponement must be resolved before the next scheduling stage begins.

Conclusion: The Role of AI

In some seasons, the champion may be decided weeks in advance. While the DFM cannot always influence the championship race in such cases, it significantly enhances the excitement of mid-table and relegation battles. Although the model may appear complex, modern software and Artificial Intelligence (AI) solutions can easily manage this complexity, optimizing home-away distributions to their near-full potential.

Aydın Tiryaki
Ankara, December 22, 2025