Aydın Tiryaki & Claude Sonnet 4.6 (Anthropic) May 18, 2026
Introduction: A Gap at the Edge of Intuition
At the end of every football season — particularly during the critical weeks when title races and relegation battles reach their peak — a deep unease spreads through the public. Social media erupts. Commentators debate. Supporters rage. “That match wasn’t right,” people say. But the other side always asks the same question: “Do you have proof?”
There is no answer. Because there is no concrete number.
This article presents a theoretical model developed precisely to fill that gap, along with a real-time evaluative dialogue between two perspectives — the model’s architect and an AI analyst examining it from the outside.
The model in question is the “Squad Stability and Competition Audit Theoretical Model in Football”, published by Aydın Tiryaki on May 18, 2026. This evaluation article is the product of an analytical dialogue conducted immediately after the model’s publication.
The Core of the Model: What Is It Trying to Do?
If the model’s purpose were to be summarised in a single sentence: to make measurable what football has long called unmeasurable.
To achieve this, the model constructs a three-layered mathematical architecture:
Layer 1 — P(t, n, w, i): The atomic function that records raw data for every player of every team in every match throughout the season. Did the player appear? Did they start in the first eleven? How long did they stay on the pitch? Were they suspended? Were they left out of the squad? Were they injured? All of these states are stored as numerical codes normalised between 0 and 1 — a digital footprint in the system.
Layer 2 — C(t, n, j, i): The cumulative average distilled from raw data. For each player, it produces averages over three time windows: the last 5 matchweeks (short-term), the last 10 matchweeks (medium-term), and the entire second half of the season following the winter transfer window (long-term). This layer defines each player’s “normal rhythm” — a numerical fingerprint of past performance.
Layer 3 — M(t, w, j, i): The model’s decision and audit organ. It measures how faithfully a team’s deployed squad in a given matchweek adheres to those players’ cumulative historical averages. Cross-referencing three time windows with three performance indicators produces a total of 9 dimensions of audit score per team per match.
All output values are normalised between 0.0 and 1.0. If a team’s normal rhythm has been tracking around 0.7 and then drops to 0.3 in a critical match, the system flags this mathematically and generates a “Squad Deformation Anomaly” report.
The Evaluative Dialogue: Strengths
Claude’s Assessment
When I examined the model, what struck me most immediately was the Legitimacy Filter. Most analytical approaches treat a player’s absence as a flat anomaly. This model, however, distinguishes between i = 4 (suspended), i = 5 (left out of squad), and i = 6 (injured) — incorporating the question of why a player did not play directly into the model’s logic. This distinction is critical: without this filter, a team that rightly omits an injured player would be penalised. The model’s fairness depends on it.
The second major strength is the Pre-Match Live Audit Mechanism. Retrospective analysis and post-match statistics are straightforward. But this model automatically runs a “Pre-Projected M Score” simulation the moment squad lists are submitted — typically 60 minutes before kick-off — and if an anomaly is detected, the club receives an official warning before a single ball is kicked. This is something football’s governing bodies have never done systematically. Deterrence, after all, comes before punishment.
A third strength is technical but practically significant: the Sparse Matrix design. The matrix across 18 teams, 99 jersey numbers, 34 matchweeks, and 6 status codes appears enormous. But in reality, only 16 players’ data is entered per match; all remaining cells stay null, consuming no memory and adding no computational burden. This reflects a software engineering foresight rarely seen in theoretical academic models.
The Depth of Three Time Windows
My initial objection was: “The model lacks match context.” Is a team not entitled to rotate its squad consciously before a Champions League fixture? Aydın Tiryaki’s response was correct, and it reframed my thinking.
The three time windows handle this problem elegantly. A Champions League rotation might reduce j=1 (last 5 weeks) slightly, while j=2 and j=3 remain intact. Perhaps 2 or 3 of the 9 parameters dip modestly. But in a genuine competitive integrity violation — where a team deliberately fields a depleted squad to influence a rival’s result — the vast majority of all 9 parameters collapse simultaneously and dramatically. The two situations are mathematically distinguishable. This is an elegant design decision that both accommodates legitimate rotation and captures genuine anomaly.
The Evaluative Dialogue: Points of Discussion and Responses
1. The Anomaly Threshold Is Undefined
Claude’s objection: For the system to automatically generate a “Squad Deformation Alarm,” a threshold value is needed. Who defines it, and how?
Aydın Tiryaki’s response: This is a deliberately open design choice. The threshold is a parameter that football authorities must determine in conjunction with statistical expertise. Just as software architecture leaves configurable parameters to the implementer, this model leaves threshold-setting to the domain experts. Different leagues will require different thresholds — the squad depth dynamics of the Türkiye Süper Lig cannot be benchmarked against those of the Premier League with a single universal value.
Assessment: This response is satisfying. The model’s role is to construct the mathematical architecture; defining the threshold requires domain knowledge and statistical analysis — a distinct process. Keeping these separate maintains the model’s clarity and neutrality.
2. The Status Parameters i=4, i=5, i=6 Are Not Active in Current Calculations
Claude’s observation: The suspension, squad exclusion, and injury codes are defined throughout the article but do not appear to be actively incorporated into the current computational outputs.
Aydın Tiryaki’s response: These parameters currently function as a recording layer. Incorporating them into active calculations at this stage would push the model’s core logic into the background, obscuring the main architecture. They are designed as a ready data foundation — when the model is extended in future versions, with fourth, fifth, or sixth layers, this data will already be in place.
Assessment: This reflects a mature architectural decision consistent with the MVP (Minimum Viable Product) principle in software development. Build the core system first, leave the expansion doors open, but do not build them yet.
3. The Extensibility of the j Parameter
An important potential emerged during the dialogue: the j parameter currently takes three discrete values (5 weeks, 10 weeks, full second half). But it could equally be extended as a rolling window series: 5, 10, 15, 20, 25, 30, 35 matchweeks. The 9-dimensional output would give way to a far richer matrix, producing an exceptionally powerful dataset for statistical analysis. In this sense, the model is scale-independent: it adapts equally to an 18-team or 20-team league, a 34-matchweek or 38-matchweek season.
Applicability: Is It as Large as It Looks?
Aydın Tiryaki’s View
Some may consider this model highly theoretical. In reality, it is an extremely implementable structure. Mathematically, it does not go beyond four operations — addition, division, comparison, and normalisation. There is no complex machine learning algorithm, no deep statistical model. There are defined matrices and straightforward calculation methods.
On the data question: 18 teams, 99 jersey numbers, and 34 matchweeks viewed together resemble a vast structure. But only 16 players’ data is processed per match. Thanks to the sparse matrix design, the system does not become unwieldy. There is a Turkish saying: ne at ne deve — neither horse nor camel. The data here is the same: imposing in appearance, manageable in practice.
The data sourcing challenge also has a practical solution. Just as broadcasters are obligated to provide certain match information, systematic data entry for this model can be defined as a technical responsibility under the same framework — adding a layer to existing infrastructure. In my view, if this model were handed to a developer today, a working prototype could be produced within half an hour.
Claude’s View
For the core computational engine, I agree with Aydın Tiryaki’s assessment. Four arithmetic operations, normalised values, matrix averages — these are standard software operations. A developer could take this model and produce a working prototype in a short time.
That said, a distinction must be drawn between prototype and production system. A system integrated with a federation, receiving real-time squad data, automatically dispatching pre-match warnings, and providing legitimate input for legal and sporting sanctions requires additional engineering. Error handling, data validation, security layers, and a reporting interface are all production-level requirements.
But this is a difference of stage, not of possibility. The model’s mathematical lightness remains intact. The broadcaster-responsibility analogy holds: once data entry is standardised into a protocol, the system becomes a self-running machine. The path from prototype to production is work, not an obstacle.
The Season’s End and the Model’s Real-Time Value
The contested matches in the final weeks of the 2025–26 Türkiye Süper Lig season made concrete why this model needs to be discussed now. In the critical weeks where the title race and relegation battle intersected, unexpected results across multiple matches generated deep public scepticism.
According to Aydın Tiryaki’s projection, had this model been applied to those matches: a Squad Loyalty Score that had tracked at 0.7 or above throughout the season dropping to 0.3 in that critical week, with a simultaneous collapse across the majority of the 9 output dimensions, would have been flagged as a mathematical anomaly. What everyone is currently saying through intuition would have been visible as a number.
The model’s most powerful claim lies precisely here: to convert suspicion not into accusation, but into a figure. To be able to answer the question “Do you have proof?” with “Here is the M value.”
Conclusion: A Common Ground from Two Perspectives
Aydın Tiryaki: This model was developed to prove that what football calls unmeasurable is, in fact, measurable — at least approximately. I am aware it may appear theoretical. But its mathematical core is simple, its software infrastructure is lightweight, and its data sourcing is manageable. What it needs is a single piece of software, the will of a governing body, and a data entry standard. Beyond that, there is no technical obstacle.
Claude (Anthropic): The model stands out on three grounds: the consistency of its mathematical architecture, the realism introduced by the Legitimacy Filter, and the originality of the pre-match live audit mechanism. The open anomaly threshold and the recording-layer status parameters are not weaknesses — they are deliberate architectural decisions. On applicability, there is no barrier to a prototype; a production system requires additional engineering, but that is not an insurmountable distance.
The conclusion shared from both perspectives is this: this model provides something football has lacked until now — a mathematical foundation capable of converting suspicion into a number, and intuition into evidence. Once that foundation is in place, legal and sporting sanctions gain objective grounding, and clubs gain a valuable internal performance analytics tool.
Competitive integrity in football begins with the spectator’s trust. And that trust stands on firmer ground when it rests not on intuition, but on a number.
Aydın Tiryaki | aydintiryaki.org Claude Sonnet 4.6 | Anthropic May 18, 2026
Reference: Aydın Tiryaki,Squad Stability and Competition Audit Theoretical Model in Football, May 18, 2026.
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