Pressing by Cosine, Defending by Distance: When Football Learns Semantics

Halftime is where many analytics dashboards become strangely shy.

They can tell a coach which zones were overloaded, how many high-intensity runs dropped after minute 30, how pressing recoveries changed, and whether expected goals has decided to be emotionally cruel today. But when the actual question arrives—what should we do now?—the answer often slides back into expert intuition.

That is not because coaches dislike numbers. It is because most football analytics systems describe events better than they prescribe tactics. They know what happened. They are less comfortable translating a messy team state into a ranked tactical choice.

The paper “Can Semantic Methods Enhance Team Sports Tactics? A Methodology for Football with Broader Applications” tries to close that gap by treating football tactics as a semantic matching problem.¹ The idea sounds like an NLP metaphor at first: players are like words, teams are like sentences, and tactics are like meanings. Cute. Possibly dangerous. But the actual contribution is more concrete than the metaphor suggests.

The paper does not train a language model to “understand football.” It does not prove that an AI coach improves win rates. It builds an interpretable decision-support system where a team’s current state and a library of tactical strategies live in the same 14-dimensional space. Recommendation becomes geometry: choose the tactic whose ideal profile is closest to the team’s current capabilities, after adjusting for fatigue, time pressure, opponent fit, and other match conditions.

That distinction matters. This is not magic football intelligence. It is a disciplined way to turn expert tactical judgment into an auditable recommender. The useful question is not “does the system know football?” The useful question is: can it make tactical reasoning inspectable enough that a coach can agree, disagree, and know exactly why?

The paper turns tactical choice into a distance problem

The mechanism begins with a translation problem. A football team is not naturally a vector. It is a collection of players, roles, relationships, physical states, tactical habits, emotional conditions, and match constraints. So the authors build a context tree that aggregates raw observables upward into 14 macro-attributes.

At the leaf level, the system can ingest event data, tracking data, physiological data, and qualitative coach assessments. These inputs are then aggregated by role and function. At the root, they become the shared semantic space:

Each team state becomes a normalized vector in $[0,1]^{14}$. A value near 1 means strong capability or high availability on that dimension; a value near 0 means weakness, absence, or low readiness.

This first move is already the core business idea. The system creates a common accounting language for things that usually sit in different silos: xG, stamina, pressing quality, morale, cohesion, and clock pressure. It does not pretend that morale is measured as cleanly as pass completion. Instead, it gives the organization a place to put qualitative judgment without leaving the model.

That is valuable because many decision systems fail exactly here. They either use only what is easy to measure, or they preserve qualitative judgment as a loose comment beside the numbers. This paper tries a third path: formalize the judgment, keep it interpretable, and make the assumptions visible enough to argue with.

Strategy templates are expert artifacts, not discovered truths

The next step is to encode tactics as vectors in the same 14-dimensional space. The paper defines 20 canonical football strategies, including high pressing, gegenpressing, fast counterattack, build-up play, positional defense, compact zonal defense, cautious horizontal play, overlapping flanks, and others.

Each strategy is represented by an ideal requirement vector. For example, high pressing and gegenpressing demand strong pressing capability, physical base, tactical cohesion, and energy. Build-up play leans more toward technical base, midfield control, controlled progression, and cohesion. Positional defense puts more emphasis on defensive strength and time management while lowering the need for transition speed and high pressing.

This is not generated automatically from match reports. It is expert elicitation. Three domain experts independently rated 280 strategy–attribute pairs: 20 strategies times 14 attributes. Ratings used qualitative levels such as low, moderate, high, and critical, later converted into numerical values. Exact agreement across all three raters was 58.2%, and 89.6% of ratings were within one level. Disagreements were reconciled through structured discussion, with 42 of 280 pairs flagged for deliberation.

The paper then checks whether the resulting tactic vectors behave sensibly. Similar strategies should cluster; dissimilar ones should separate. High Press and Gegenpressing show very high cosine similarity. Build-up Play and Extended Possession also cluster. High Press and Positional Defense are farther apart. Two additional practitioners reviewed radar charts of the strategy profiles; 17 of 20 received full “yes” ratings, while three were adjusted or discussed.

This evidence does not prove that the templates are universally correct. It proves something narrower but useful: the strategy library is not arbitrary doodling. It is a structured, inspectable expert model.

For business use, that is the right standard at this stage. A club, academy, robotics team, or security operations unit would not adopt the authors’ exact vectors as sacred truth. It would localize them. “Our high press” is rarely identical to “your high press,” and anyone pretending otherwise should be made to watch 90 minutes of badly coordinated pressing as punishment.

The operational value is that the template structure is modular. Add a new strategy, change a vector, recalibrate weights, and the distance engine still works.

Cosine validates style; Euclidean chooses tactics

The title of this article mentions cosine because cosine similarity is part of the story. But the paper’s actual tactical selection relies on weighted Euclidean distance, not cosine similarity.

That choice is important.

Cosine similarity measures shape. If two vectors point in the same direction, cosine may say they are similar even if one is much smaller in magnitude. That is useful for style comparison. A weak team and a strong team may have similar profiles: both transition-oriented, both direct, both low-possession. Cosine can detect that resemblance.

But tactical recommendation is not only about resemblance. It is about feasibility.

A tired team may “look like” a pressing team in proportional terms. But if residual energy and physical base are too low, pressing is no longer a clever identity choice. It is a donation to the opponent.

The paper’s core distance logic is:

Here, $x_i$ is the team’s current score on attribute $i$, $v_{s,i}$ is the ideal requirement of strategy $s$ on that same attribute, and $w_i$ is the current contextual weight. The recommended tactic is the strategy with the smallest adapted distance.

The paper also runs a controlled Euclidean-versus-cosine comparison over 100 synthetic team profiles and 20 strategies. The two metrics agree on the top recommendation in 73% of cases and share at least two strategies in the top three in 91% of cases. The divergence is systematic: cosine becomes misleading when teams have uniformly low capabilities. In one example, a fatigued team receives high cosine similarity with High Press but Euclidean distance ranks High Press only 14th because the absolute energy and pressing gaps are too large.

That is the quiet lesson: style similarity is not operational readiness.

A business analogy is straightforward. A small company may have the “shape” of an enterprise AI program—data, workflows, dashboards, APIs—but not the absolute capability levels needed for autonomous deployment. Cosine says “similar profile.” Euclidean says “not yet.” In implementation decisions, Euclidean is usually the adult in the room.

Context weights make the same tactic age during the match

A tactic is not equally appropriate at minute 5 and minute 75. The paper handles this through dynamic attribute weighting.

The strategy vectors themselves do not change. High pressing remains high pressing. What changes is the penalty attached to mismatches under current conditions.

If residual energy is low, mismatches around pressing capability and physical load become more important. If time is nearly gone and the team needs a result, transition speed and offensive strength receive greater emphasis. If the team is technically or physically inferior, the system shifts attention toward defensive strength and tactical cohesion. The default parameter table includes an energy threshold of 0.50, a time-pressure threshold for the final quarter of the match, an opponent factor of 0.20, and clamping bounds to prevent any attribute from becoming meaningless or absurdly dominant.

This is the difference between a static recommender and a match-aware diagnostic tool. A static system says: “Your team is suited to build-up play.” A context-aware system says: “Right now, with energy falling and the clock changing, the cost of pretending to be a pressing side has increased.”

The paper also includes an optional opponent-aware adjustment. In simplified terms, the system can prefer strategies that the team can execute well and the opponent is poorly positioned to handle. That is sensible, but the paper treats it carefully. Opponent modeling is only useful when opponent data are reliable. When scouting data are thin, the authors recommend reducing the opponent factor rather than overfitting to guesswork wearing a tactical tracksuit.

Computationally, the model is cheap. With 20 strategies and 14 attributes, inference runs in milliseconds on standard hardware. The bottleneck is not computation. The bottleneck is measurement, calibration, and whether coaches trust the explanation at the moment they must act.

The experiments mostly prove coherence, not victory

The evaluation section is strongest when read as a behavioral audit of the system. The tests ask: does the recommender behave consistently when inputs change in tactically meaningful ways?

The answer is mostly yes.

In four simulated scenarios, the DSS behaves like a competent analyst would expect:

The authors then stress-test the system. Under independent input noise, top-1 consistency averages 89.3%, with top-3 stability at 94.1%. Under correlated perturbations across physical, psychological, and technical clusters, top-1 consistency drops but remains above 80% in the hardest tested case. Under missing data, the picture becomes more interesting: missing psychological inputs are relatively survivable, but sparse data—six random attributes missing—pushes top-1 match down to 67.3%, though qualitative category agreement remains 84%.

That is a useful operational signal. The system can degrade gracefully, but not magically. If data are thin, it should stop presenting one confident answer and instead show a ranked set with confidence flags. A tactical recommender that says “I am less sure because the tracking data failed” is not weaker. It is less likely to be embarrassing.

The distribution-shift tests are also important. The model performs best under the baseline context for which its assumptions are calibrated. Agreement falls under youth-football and style-shift simulations. In the style-shift case, expert agreement drops to 78%, with the paper noting that the model may recommend possession-based strategies where a more physical, direct style would fit better. Translation: tactical culture matters. A European professional calibration is not a universal football theology.

The ablation shows why attribute-wise weighting matters

One of the paper’s more useful tests compares three weighting approaches:

This is not just a technical footnote. It is the main evidence that the dynamic part of the model matters.

Uniform weighting ranks gegenpressing too highly in the fatigued-and-inferior scenario. Global scaling improves the fatigue case but cannot handle situations where the system must penalize one dimension while amplifying another. Under time pressure, the model needs to care more about transition speed without pretending every attribute became equally urgent. A single global “panic multiplier” is not strategy. It is a spreadsheet having a stressful afternoon.

Attribute-wise weighting also improves diagnostics. It can identify residual energy as the binding constraint in fatigue scenarios and transition speed as the critical dimension under late-game urgency. This matters because decision support is not only about the final recommendation. It is about the reason a human decision-maker can inspect.

The pilot case is a feasibility test with an awkward but useful ending

The paper’s real-data pilot uses a single C-Junioren Saarlandliga U14/U15 match: SSV Pachten versus JSG Stausee-Losheim in the 2023–24 season. The match ended 4–3 for the home team. The observational protocol recorded six tactical attributes per half on a three-level German scale: high, medium, low. These six observations map to five of the model’s 14 dimensions, because two transition-related observations are aggregated.

At halftime, using first-half observations and a projected fatigue adjustment, the DSS recommends Build-up Play. Its distance is slightly better than Fast Counterattack and substantially better than High Pressing, Gegenpressing, or Positional Defense in the reduced observed space.

The recommendation is not “stop attacking.” It is more specific: preserve control, manage tempo, avoid making a low-energy youth team defend its own chaos.

The team did not appear to follow that path. Second-half observations show continued transition-heavy play, declining defensive compactness, and residual energy falling to a low level. The team still won 4–3.

This is exactly where a lazy article would say: “The AI was wrong.” It would also be missing the point.

The pilot is not designed to prove that the DSS produces winning tactical decisions. The authors explicitly frame it as a feasibility demonstration. The system processed real observational data, generated non-degenerate rankings, produced diagnostic output, and received partial-to-positive expert agreement. Both expert reviewers considered the top recommendation appropriate or partially appropriate, and both endorsed at least one strategy in the top three.

But the default baseline also recommended Build-up Play and received the same expert ratings. That is inconvenient in the best possible way. It prevents overclaiming. In this specific match, the DSS did not outperform a safe default recommendation. Its value was diagnostic: it explained why Build-up Play made sense and why the actual high-risk continuation carried defensive and energy costs.

The team’s gamble worked. The system still correctly identified the risk structure: two second-half goals conceded, collapsing defensive compactness, and energy depletion. A recommender can be useful even when reality rewards a gamble, because not every good outcome was a good decision. Football is impolite that way.

What the paper directly shows, and what Cognaptus infers

The paper directly shows that a semantic-distance DSS can be built, implemented, stress-tested, and applied to a real observational pilot without collapsing into nonsense. It also shows that the mechanism is inspectable: recommendations can be decomposed into tactical attribute gaps rather than hidden inside a black-box policy.

Cognaptus infers a broader business pattern: this is a useful architecture for domains where teams must choose among strategy templates under incomplete information. Football is only the demonstration case. The deeper product idea is capability-template matching under context pressure.

That pattern appears in several business settings:

The ROI case is not “AI knows better than experts.” That would be the usual brochure perfume. The better case is cheaper diagnosis: faster comparison of candidate strategies, clearer articulation of binding constraints, reusable templates, and more disciplined post-match or post-project review.

In business terms, the paper is a template for building decision-support systems that do three things well:

1. Represent capability honestly. Do not recommend a strategy merely because it fits the desired identity.
2. Separate style from feasibility. Cosine-style resemblance is not the same as execution readiness.
3. Expose the reason for recommendation. A decision that cannot be challenged cannot be governed.

The main boundary: this is not yet operational validation

The paper is unusually clear about its own boundary. The strongest evidence is internal coherence under controlled scenarios and feasibility in one retrospective pilot. That is meaningful, but it is not the same as prospective validation.

The limitations fall into five practical groups.

First, some attributes are hard to measure. Residual energy can be supported by tracking and physiological data. Psychological resilience, morale, and relational cohesion are weaker unless the organization has disciplined observation protocols. If these become casual subjective ratings, the model will become a formal wrapper around informal bias. Very elegant. Still bias.

Second, the strategy vectors are expert-elicited. That is acceptable for an interpretable DSS, but the vectors require local calibration. Youth football, lower divisions, professional European football, and physically dominant tactical cultures may need different templates.

Third, the distance metric is linear and additive. Football interactions are not always linear. A small stamina drop can wreck pressing disproportionately. Morale and technical execution may interact in pressure phases. Euclidean distance is explainable, but it may smooth over tactical cliff edges.

Fourth, opponent modeling is static. Real opponents substitute players, change formation, alter pressing triggers, and adapt to your adaptation. The paper’s opponent adjustment is a starting point, not a live game-theoretic model.

Fifth, the pilot is retrospective and small. One match, partial attribute coverage, no opponent data, and no real-time coach interaction cannot prove performance improvement. The paper’s future-work path—multi-match datasets, expanded attribute protocols, opponent observation, and prospective deployment—is not decorative. It is the work required before anyone should claim competitive advantage.

The real contribution is auditability under pressure

The most interesting part of this paper is not that it borrows “semantic distance” from NLP. The metaphor is useful, but metaphors do not win matches. The contribution is that it converts tactical recommendation into a transparent chain:

1. collect heterogeneous observations;
2. aggregate them into named macro-attributes;
3. encode candidate strategies as expert-reviewed requirement vectors;
4. compare current state and tactical requirements using weighted Euclidean distance;
5. adjust attribute importance based on match context;
6. optionally include opponent mismatch;
7. report not only the recommendation but the diagnostic gaps behind it.

That chain is inspectable. A coach can challenge the energy estimate, alter the high-press vector, reduce opponent weighting, or disagree with the recommended strategy while still learning what the model saw.

This is what many AI decision tools miss. The goal is not to remove judgment. The goal is to make judgment less foggy, less memory-dependent, and less dependent on whoever speaks most confidently in the room.

Football does not become solved because tactics become vectors. It becomes more legible. And in any domain where coordinated teams act under time pressure, legibility is not a small thing.

It is the difference between saying “trust the model” and saying “here is the constraint you are about to ignore.”

The second one is much more useful. Also harder to sell in a glossy demo, which is usually a good sign.

Cognaptus: Automate the Present, Incubate the Future.