RPG EUROLEAGUE PLAYER ARCHETYPES

1. Purpose and Research Question

RPG EuroLeague Player Archetypes v1.0 discovers repeatable EuroLeague player roles from observed on-court behaviour without using traditional position or any other external player label as a clustering input. The system separates role from performance, quantifies uncertainty and hybridity, remains stable over time when behaviour remains stable, and reacts when the same player's behaviour changes. Version 1.3 retains the post-clustering Guard/Forward/Center descriptive layer introduced in v1.2, locks the publication-standard canonical role names and analytical definitions, expands the three-season descriptive interpretation by season, and formalizes the forward application roadmap for team role structures and longitudinal player role profiles. Position remains excluded from feature engineering, clustering, model selection, fit, certainty and performance calculations.

• Primary question: What does the player actually do on the court?
• Defensive question: What tracked defensive actions and assignments characterize the player?
• Performance question: How effectively does the player execute the role identified from behaviour?
• Applied question: Which Player×Season observations are behaviourally similar or substitutable?

2. Closed-Data Experimental Protocol

2.1 Authorized empirical universe

2.2 What 'file-only' means

• Training/discovery uses only variables contained in the five authorized files.
• Feature engineering uses only numerators, denominators and identifiers contained in those files.
• Eligibility and reliability thresholds are selected only from distributions and stability tests inside those files.
• Cluster count, algorithm, preprocessing and feature selection are selected only from internal statistical tests on those files.
• Temporal validation uses only the season separation already contained in those files.
• Archetype names are derived only from the statistical behavioural profiles of the clusters, never from public reputation or prior scouting knowledge.
• Player similarity and replacement outputs use only the locked transformed feature space produced from those files.

2.3 Explicitly forbidden empirical inputs for v1.0

2.4 What external literature may do

Statistical and academic literature may be used only to justify or explain generic methods such as compositional analysis, consensus clustering, bootstrap stability or gap statistics. It contributes no basketball observations, priors, player labels, role definitions, thresholds or validation outcomes. The empirical test remains completely closed.

3. Preliminary Data Audit and Scope

The five authorized workbooks provide a consistent 130-column Player×Season schema across all five seasons. A preliminary audit was used only to confirm feasibility and set the methodological scope; the formal Data Dictionary and Schema Audit remain Actions 2–3.

4. Model Architecture

Offense and defense are discovered separately before any integration, preventing one feature family from overwhelming the other and preserving distinct role information.

5. Observation Unit and Eligibility

5.1 Canonical observation

The canonical observation is Player×Season. Team and Season remain internal contextual fields because both exist in the files.

5.2 Eligibility

These eligibility thresholds are now locked for the v1.0 discovery framework. Their adequacy was tested against the closed dataset through stability and population-sensitivity analysis; no external league convention was used to justify them.

6. Data Semantics and Reconstruction

Displayed percentages are recomputed from their supplied numerators and denominators wherever possible. Count fields and rate fields are never treated identically when the source displays a dash.

• Observed count dash may become zero only where schema and paired fields establish that the statistic is tracked.
• Percentages are recomputed from counts; zero attempts produce undefined efficiency, not 0%.
• Zero makes on positive attempts produce a genuine 0% efficiency.
• Identifiers and descriptive fields are never zero-filled mechanically.

On-court offensive and opponent possession fields contained in the files are the preferred exposure denominators for secondary per-possession behaviour rates. Their internal coherence will be verified in Action 2/3 using only the supplied data.

7. Behaviour / Performance Firewall

8. Offensive Behaviour Feature Architecture

8.1 Primary tracked-action allocation

These tracked-action counts form an internally normalized allocation vector. They are not forced to reconcile exactly to official FGA because the source taxonomy may overlap or omit tracked actions.

8.2 Secondary offensive behaviour candidates

9. Defensive Behaviour Feature Architecture

9.1 Primary defensive exposure profile

Opponent Drives remain a secondary overlapping behaviour rather than an additional mutually exclusive primary category.

9.2 Secondary defensive behaviour candidates

Opponent FG%, play-type defensive FG% and DRtg are defensive outcomes and remain outside defensive role discovery.

10. Compositional Treatment and Zero Handling

Counts are regularized through an empirical-Bayes Dirichlet prior estimated exclusively from the discovery subset of the supplied files. The posterior expected shares remove computational zeros without importing any external prior.

11. Reliability and Shrinkage

• Play-type compositions: empirical-Bayes Dirichlet shrinkage fitted on the closed discovery sample.
• Rare count rates: shrink only when instability is demonstrated internally.
• Efficiency measures: retain numerator/denominator and shrink using internal season/archetype priors where necessary.
• Every performance output retains a reliability/sample indicator.
• No hand-tuned coefficient based on external conventions or player knowledge.

12. Preprocessing, Redundancy and Feature-Family Balance

Pearson, Spearman, exact mathematical dependency and basketball-semantic redundancy are assessed using only the five-file feature matrix.

• Z-score and robust scaling are benchmarked on the discovery data.
• Rank/percentile transforms remain a heavy-tail sensitivity test.
• Feature-family balance uses an internally specified 1/sqrt(p_f) baseline and an unweighted sensitivity comparison.
• All transformers are fitted only on the discovery seasons and carried forward unchanged to validation seasons.

13. Dimensionality Reduction

PCA is mandatory for closed-data diagnostics of latent structure and redundancy. UMAP may be used for visualization only. Full-space clustering and PCA-space clustering are compared without using any external player labels to decide which is 'more correct'.

14. Candidate Clustering Algorithms

15. Number of Archetypes and Hierarchy

Candidate flat solutions are evaluated primarily across k=4–12, plus multiple hierarchical cuts. No target number is imported from NBA studies or prior basketball taxonomies.

16. Consensus, Bootstrap and Null Testing

Each candidate solution receives 500 resampling replications at approximately 80% of eligible discovery observations; preprocessing is refitted inside each resample.

• Pairwise co-clustering probabilities form a consensus matrix.
• ARI/NMI assess partition stability after label matching.
• Centroid/medoid drift and cluster population drift are tracked.
• Leave-one-discovery-season-out sensitivity is mandatory.
• Feature-family and scaling perturbation tests are mandatory.

Null/reference datasets are generated from the supplied feature matrix by destroying multivariate player structure while preserving relevant marginal distributions. The real solution must outperform this closed-data null structure.

17. Soft Membership and Uncertainty

No player is manually moved because the result conflicts with prior basketball expectations.

18. Archetype Interpretation and Naming

Statistical IDs O1, O2… and D1, D2… are assigned before names and remain the stable model identifiers. Public-facing names are created only from locked cluster feature profiles, medoids and repeated examples contained in the closed discovery files. Version 1.3 locks the publication-standard canonical English public names and analytical definitions reported in Section 31; future editorial wording changes must not alter the statistical IDs or cluster semantics.

• No position label may be imported to create, split, merge or override a cluster. Position may be examined only after taxonomy lock as an external descriptive cross-tab.
• No player reputation may justify a cluster name.
• No video or scouting description may be used to resolve ambiguous clusters.
• If a cluster is statistically stable but difficult to name, the statistical ID remains acceptable until its behavioural description is clear.

19. Internal Context Tests Available From the Files

19.1 Team concentration

Because Team exists in the supplied files, cluster-team concentration is measured after discovery. This is a contamination diagnostic, not an input. A cluster dominated by one team is investigated to determine whether the feature vector is representing a player role or merely a team-specific statistical environment.

19.2 Context-Adjusted Style — conditional secondary layer

A Context-Adjusted Style layer may be built only if team-level behavioural baselines can be reconstructed consistently from the same player files. The reconstruction must pass internal reconciliation tests. If it fails, this layer is excluded from v1.0 without replacement by external team data.

19.3 Season drift

Cluster/season association and season-relative normalization are tested using only the Season field and player data in the five files.

20. Closed-Data Validation Framework

20.1 Temporal split

No information from 2025–26 may tune thresholds, features, cluster count, algorithm choice or names before the final test.

20.2 Internal predictive-utility benchmark

Traditional position remains excluded from model selection and from the closed-data predictive-utility benchmark because it is not contained in the five authorized files. Version 1.2 introduced, and v1.3 retains, a separate post-clustering broad-position (Guard/Forward/Center) descriptive layer. This extension is interpretive only and cannot alter any archetype assignment, cluster definition or validation outcome.

This does not require the archetype prototype to beat an individual's immediately previous behaviour in every case. Its purpose is to quantify how much information the role representation preserves and whether soft membership improves transport.

20.3 Structural validation without external labels

• Cluster stability under resampling.
• Transport of centroids/prototypes to 2024–25 and 2025–26.
• Season representation and absence of purely era-defined clusters unless behaviour genuinely changes.
• Team concentration diagnostics.
• Player-level silhouette / membership certainty.
• Recurrent-player consistency conditional on behavioural-vector stability.
• Null-model superiority.

21. Longitudinal Role Persistence and Change

The repeated-player history within the five files provides the longitudinal validation set; 76 players appear in all five seasons.

• Role persistence when transformed behavioural distance is low.
• Continuous Role Change distance between consecutive seasons.
• Migration matrix between archetypes.
• Membership-probability changes for hybrids/boundary players.
• Potential future RPG Role Evolution Index derived solely from these histories.

22. Performance Overlay

Performance is calculated only from performance fields present in the files and only after role assignment.

23. Player Similarity and Replacement Distance

Similarity is computed only in the locked transformed space derived from these files.

• Role Similarity: behavioural distance.
• Performance Delta: difference in within-role execution.
• Replacement Distance: transparent role distance plus separately reported performance difference.
• Nearest neighbours retain Season and Team context from the files.

24. Production Assignment for Future File Drops

Production assignment assumes future season files preserve compatible fields. New observations are passed through the stored file-only transformations and model objects. Archetypes are not rediscovered whenever a new file arrives.

Apply the locked data dictionary and cleaning rules.

Construct the same behavioural features.

Apply stored reliability/shrinkage parameters or the formally governed update rule.

Apply stored transformation/scaling pipeline.

Assign offensive and defensive memberships.

Generate two-way, uncertainty and performance outputs.

Mark provisional observations until the locked sample threshold is reached.

25. Deferred Beyond v1.0 Because the Fields Are Not in the Five Files

26. Quality Assurance and Governance

27. Gate Criteria

28. Definition of Success

• The real data exhibit stronger and more stable structure than the closed-data null models.
• Archetypes are driven by behaviour rather than efficiency or reputation.
• The solution survives reasonable preprocessing and feature-family perturbations.
• It transports from discovery seasons to 2024–25 and then untouched 2025–26.
• Repeated players remain stable when their file-based behavioural vectors remain stable.
• Meaningful behavioural changes produce measurable role movement.
• Hybrids and unique cases are represented without forced certainty.
• The model improves closed-data player similarity, replacement analysis and roster role mapping.

29. Known Limitations

• Player×Season granularity cannot isolate intra-season team stints.
• Defensive tracked exposure cannot fully isolate scheme or matchup quality.
• Tracked offensive/defensive action counts are not assumed to equal official FGA exactly.
• No external age, height, coach, market or scouting context is permitted in the v1.0 clustering core. Traditional position remains prohibited as a modelling input; the post-clustering broad G/F/C descriptive annotation introduced in v1.2 and retained in v1.3 cannot affect the model.
• Unsupervised models may partition continuous structure; null and stability tests therefore remain mandatory.
• Archetype names describe the statistical behaviour observed in these files, not an external 'true' basketball ontology.

30. Locked Methodological Decisions — v1.3 Revision

31. Locked Discovery Taxonomy and Canonical Role Definitions

The discovery taxonomy is now locked at eight offensive and four defensive operational archetypes. Statistical IDs remain permanent model identifiers; the English names below are the canonical public-facing role names for v1.0. The definitions describe behavioural function, not quality. A player may fit a role strongly while performing poorly within it, or fit it weakly while producing strong outcomes.

31.1 Offensive archetypes

31.2 Defensive archetypes

31.3 Locked distinctions between adjacent roles

32. Discovery-Sample Results and Cluster Selection

The role solution is based on the three discovery seasons 2021–22, 2022–23 and 2023–24. After the locked eligibility thresholds, the discovery population contains 550 certified offensive Player×Season observations and 555 certified defensive Player×Season observations. Of these, 549 observations are certified on both sides of the ball.

32.1 Offensive resolution

Offensive candidate solutions were tested across multiple algorithms and cluster counts. KMeans produced the most reliable operational structure. The k=8 solution recorded median ARI 0.853 across 500 discovery-only 80% resamples with the full preprocessing pipeline refitted inside every resample. Its median leave-one-discovery-season-out ARI was 0.905, stronger than the k=4 macro solution (0.650) and k=10 control (0.762). The k=8 solution is therefore the locked operational resolution, with k=4 retained as a higher-level macro hierarchy.

32.2 Defensive resolution

Defensive stability testing selected k=4 as the primary operational resolution. Across 500 discovery-only 80% resamples, k=4 produced median ARI 0.934, compared with 0.761 for k=5 and 0.754 for k=7. A separate Team×Season contamination test found no evidence that the four defensive clusters were simply team-system artifacts: observed Team×Season Cramér’s V was 0.281 versus a permutation-null mean of 0.315, while no single Team×Season accounted for more than 4.3% of a k=4 cluster.

32.3 Absolute role population by discovery season

Offensive certified Player×Season counts:

Defensive certified Player×Season counts:

33. Post-Clustering Broad-Position Descriptive Layer

Traditional position was not available in the five-file closed-data universe and was not used in any stage of discovery, feature engineering, clustering, cluster-number selection, stability testing, membership assignment, Archetype Fit, Role Certainty, Hybrid Index or performance evaluation. The broad-position layer was introduced in v1.2 and is retained unchanged in v1.3 only after taxonomy lock as a descriptive Guard/Forward/Center cross-tab. Its purpose is to ask where each already-discovered behavioural role is most often found in conventional roster language; it does not use position to define the role.

The following tables reproduce the frozen article-level G/F/C descriptive cross-tabs. N refers only to certified Player×Season observations in the discovery sample. Percentages are within role-season.

33.1 Offensive roles by broad position and season

Overall offensive certified-sample position mix: 2021–22: 77 Guards (45.0%), 65 Forwards (38.0%), 29 Centers (17.0%); 2022–23: 82 Guards (42.9%), 68 Forwards (35.6%), 41 Centers (21.5%); 2023–24: 82 Guards (43.6%), 70 Forwards (37.2%), 36 Centers (19.1%).

33.2 Defensive roles by broad position and season

Overall defensive certified-sample position mix: 2021–22: 77 Guards (44.5%), 66 Forwards (38.2%), 30 Centers (17.3%); 2022–23: 82 Guards (42.7%), 69 Forwards (35.9%), 41 Centers (21.4%); 2023–24: 82 Guards (43.2%), 72 Forwards (37.9%), 36 Centers (18.9%).

34. Three-Season Descriptive Findings

34.1 Position remains informative, but is not a role

The strongest concentrations confirm that conventional position still contains substantial information. Lead Creator is 95.5%, 88.9% and 96.3% Guard across the three seasons; PnR Maestro becomes 100% Guard in both 2022–23 and 2023–24; Rim Diver remains predominantly Center; Off-Ball Scorer remains overwhelmingly Forward. These concentrations do not invalidate the archetype model. They show that position is a useful prior, while the role provides the functional description that position alone cannot supply.

The clearest evidence is within the same broad position. Guards are distributed across Lead Creator, PnR Maestro, Flex Secondary Creator and Movement Spacer. Frontcourt players split into materially different functions such as Rim Diver, Post Hammer and Pop & Roll Big. Therefore “Guard”, “Forward” and “Center” describe roster location more than they describe the exact basketball job.

34.2 2021–22: Position remains informative, but functional differentiation is already visible

The 2021–22 season provides the clearest starting point for understanding why broad position remains useful but insufficient. Lead Creator is 95.5% Guard and PnR Maestro is 93.8% Guard, while Rim Diver is 94.1% Center and Off-Ball Scorer is 90.0% Forward. These concentrations show that traditional position retains substantial information. However, players inside the same broad position divide into materially different functions: Guards distribute across Lead Creator, PnR Maestro, Flex Secondary Creator and Movement Spacer, while frontcourt players split into Rim Diver, Post Hammer and Pop & Roll Big.

The frontcourt split is especially instructive. Rim Diver is almost exclusively a Center role, Post Hammer is evenly divided between Forwards and Centers (50.0% / 50.0%), and Pop & Roll Big is distributed across Forwards (53.8%) and Centers (46.2%). The broad label “big” therefore conceals distinct offensive jobs: rimward finishing, post-based pressure creation and dual roll/pop screen functionality. Defensively, Paint Anchor is predominantly Center (71.0%), Screen Chaser and POA Hound are predominantly Guard, while Utility Defender is 73.2% Forward. The season already demonstrates that role provides the functional description that position alone cannot supply.

34.3 2022–23: Frontcourt role separation becomes more pronounced

The 2022–23 offensive certified sample increases from 171 to 191 Player×Season observations, so absolute count changes must be interpreted together with the changing denominator. Within that constraint, frontcourt role differentiation becomes more pronounced. Rim Diver remains predominantly Center but Forward representation rises from 5.9% to 16.7%. Post Hammer becomes more Center-heavy at 66.7%, while Pop & Roll Big shifts sharply toward Centers, from 46.2% Center in 2021–22 to 77.8% in 2022–23. These patterns reinforce the distinction between three separate frontcourt functions rather than variants of a single positional class.

Creation roles remain strongly perimeter-based. PnR Maestro becomes 100% Guard, Lead Creator is 88.9% Guard and Flex Secondary Creator is 76.9% Guard. On defense, POA Hound increases from 31 to 49 observations while Utility Defender declines from 56 to 42. Screen Chaser becomes less Guard-dominated: the Guard share falls from 80.0% to 66.7% while Forward representation rises from 20.0% to 30.2%. This is a descriptive shift in where defensive functions appear within the certified sample; it is not, by itself, evidence of a causal league-wide tactical change.

34.4 2023–24: Point-of-Attack responsibility becomes the most visible defensive signal

By 2023–24, several offensive roles remain strikingly stable. Off-Ball Scorer records 32 observations and remains 93.8% Forward. Movement Spacer rises from 24 observations in 2021–22 to 31 and becomes moderately more Forward-oriented (58.1% Forward, 41.9% Guard). High-responsibility creation is almost completely concentrated in Guards: Lead Creator is 96.3% Guard and PnR Maestro is 100% Guard for the second consecutive season. Frontcourt differentiation persists: Rim Diver is 87.5% Center, Post Hammer is 60.0% Center / 40.0% Forward, and Pop & Roll Big is 72.2% Center / 27.8% Forward.

The largest defensive movement across the discovery period is POA Hound: 31 → 49 → 59 observations, an increase of approximately 90% from 2021–22 to 2023–24. In the final discovery season it becomes the most populous defensive archetype and remains 83.1% Guard. Screen Chaser falls to 50 observations and becomes more position-diverse, with 60.0% Guards and 38.0% Forwards. Utility Defender declines to 41 observations but becomes increasingly Forward-dominated at 85.4%. Paint Anchor remains primarily a Center role at 77.5%, while still retaining a meaningful Forward minority. These changes are research signals that require confirmation in held-out seasons before any claim of league-wide defensive evolution.

34.5 Three-season synthesis: Offensive architecture is comparatively stable

Across the three discovery seasons, offensive role populations move without any core archetype disappearing: Off-Ball Scorer 30→32→32, Lead Creator 22→27→27, Pop & Roll Big 13→18→18 and Movement Spacer 24→27→31. This descriptive persistence is consistent with the strong k=8 leave-one-discovery-season-out ARI (0.905) and supports the interpretation that the eight-role solution captures recurring offensive functions rather than one-season artifacts.

The defensive mix changes more visibly: Paint Anchor 31→38→40, Screen Chaser 55→63→50, POA Hound 31→49→59 and Utility Defender 56→42→41. The combination of rising POA Hound prevalence, declining Utility Defender counts and broader Forward representation inside Screen Chaser is sufficiently coherent to justify monitoring as a longitudinal signal, but not yet sufficient to establish causality. The locked 2024–25 and 2025–26 transport tests are required before stronger temporal conclusions are permitted.

34.6 Role, position and performance remain separate analytical layers

The v1.3 framework therefore preserves three distinct concepts. Conventional position is a descriptive roster label. Archetype is a data-discovered functional identity. Performance is evaluated afterward within and across roles. The position layer can describe where a role is commonly found, but cannot create or modify the role; the performance layer can measure execution quality, but cannot redefine role membership. This separation is necessary to preserve interpretability and to prevent the reintroduction of assumptions the closed-data experiment was designed to avoid.

35. Forward Application and Publication Roadmap

The next application phase moves from taxonomy discovery to EuroLeague mapping. Future RPG publications will present the offensive and defensive role structure of every EuroLeague team for which the locked data pipeline supports certified assignments, showing how the archetypes are distributed inside each roster and what those combinations reveal about team construction beyond conventional positions.

At player level, future RPG publications will present role profiles for every player for whom the database contains a sufficient and comparable sample from the previous three seasons. These profiles will allow the analysis to move beyond the current label and examine persistence, migration and functional change across seasons on both offense and defense.

The resulting framework will support team role maps, player similarity and replacement analysis, roster-complementarity studies, longitudinal role evolution and, once the validation gates are completed, downstream inputs to RPG team and coach assessment products. These applications must consume the locked archetype IDs and definitions; they may not redefine the taxonomy ad hoc.

36. Version 1.3 Revision Scope

Version 1.3 is an article-aligned methodological revision. It does not alter the locked statistical partitions, cluster IDs, discovery medoids, eligibility rules, preprocessing, algorithm choice, cluster counts or validation governance. It updates the canonical public-facing names and definitions to the approved RPG vocabulary, expands the descriptive interpretation of the three discovery seasons, and formalizes the next publication applications. Any future change to O1–O8 or D1–D4 semantics requires explicit model-version governance rather than editorial renaming.

37. Statistical Method References

The references below are methodological anchors only. They do not contribute EuroLeague observations, player labels, basketball priors, archetype names or validation data.

Mateus N, Esteves P, Gonçalves B, et al. (2020). Clustering performance in the European Basketball according to players’ characteristics and contextual variables. International Journal of Sports Science & Coaching, 15(3), 405–411.

Egozcue JJ, Pawlowsky-Glahn V, Mateu-Figueras G, Barceló-Vidal C. (2003). Isometric Logratio Transformations for Compositional Data Analysis. Mathematical Geology, 35(3), 279–300.

Monti S, Tamayo P, Mesirov JP, Golub TR. (2003). Consensus Clustering: A Resampling-Based Method for Class Discovery and Visualization of Gene Expression Microarray Data. Machine Learning, 52, 91–118.

Tibshirani R, Walther G, Hastie T. (2001). Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society: Series B, 63(2), 411–423.

John CR, Watson D, Barnes MR, Pitzalis C, Lewis MJ. (2020). M3C: Monte Carlo reference-based consensus clustering. Scientific Reports, 10, 1816.

37.1 External references for post-clustering position annotation

Eurohoops (2021). The full rosters of all 18 EuroLeague teams, 29 September 2021. Used only as an external roster-position reference for the post-clustering descriptive layer.

EuroLeague / Eurohoops Gamecenter season-coded team roster pages (2022–23). Used only as an external roster-position reference; never as a clustering or model-selection input.

Eurohoops (2023). EuroLeague 2023–24 roster preview, 7 September 2023. Used only as an external roster-position reference for the post-clustering descriptive layer.