28_archetypes.md

28 — Player Subject-Ability Profiles + Archetypes

28 — Player Subject-Ability Profiles + Archetypes

Date: 2026-05-30. Status: exploratory (Task A). Lead with the caveats.

TL;DR

• Built a 6-dim subject-ability vector per player-season by fusing within-season-z combine theta (predictor) with within-season-z game per-subject PPTF (outcome), game evidence weighted by √(games_played, capped at 4), combine weight 1.0. Where only one source exists (e.g. nsba4 = combine-only, nsba1 = no CS anywhere), the available source is used alone. Output: data/processed/player_archetypes.csv (344 player-seasons).
• k=5 wins silhouette (0.234) and is reasonably stable (seed ARI 0.99, bootstrap ARI 0.84). k=4 is comparably stable; k≥6 degrades (bootstrap ~0.75). Five archetypes emerge: 1. bio specialist (n=47) 2. ESS specialist (n=59) — the "ESS-soph" role 3. elite multi-science, chem+phys core (n=33) — the captain/star tier 4. math+phys specialist (n=65) — the physics/math role 5. low-output / replacement (n=140)
• CS does NOT form its own archetype. A CS-aware re-clustering (ARI 0.72 vs main) shows high-CS players cluster with the broad elites, not in a standalone CS pod. There is no "pure CS specialist" type in this pool — consistent with F5 (CS is table-stakes the field already covers) and intel that credible CS is scarce.

HARD CAVEATS (read first)

1. n is tiny and clusters are only moderately stable. 344 player-seasons, but the silhouette is 0.23 (weak separation — these are soft, overlapping blobs, not crisp types). Seed-stability is high but bootstrap ARI 0.84 means ~1 in 6 resamples reshuffles a meaningful chunk. Treat archetypes as descriptive tendencies, not hard labels. A player near a boundary could flip on a different sample.
2. The fusion mixes two scoring worlds on purpose, but they don't fully agree. Combine↔ game per-subject r is only 0.38–0.54 (F3). The fused vector is a deliberate compromise: it lets us place nsba4 combine-only entrants (137 rows, no games) into the same space as proven players. For those 137 rows the profile is 100% combine — i.e. as gameable / noisy as the combine itself.
3. "low-output / replacement" (n=140) is partly an artifact of thin reads. 55 of 140 are combine-only nsba4 rows pulled toward 0; the rest are genuinely low-PPTF game players. Do not read this cluster as "these players are bad" for the combine-only members — read it as "no evidence of a hot subject."
4. CS absent for all of nsba1. CS is imputed to season-mean (z=0) for distance only; has_cs_profile flags the 215/344 rows with a real CS reading.
5. Grade/role mapping is qualitative only. grade_or_age is sparse free-text; I do NOT claim a quantitative grade-by-archetype effect.

Method

scripts/A28_archetypes.py. - Crosswalk: combine theta_{bio,chem,cs,ess,math,phys} ↔ game pptf_{b,ch,cs,ess,m,p}. - Standardize: z-score each subject within season separately for combine and game, so cross-season difficulty drift (F7) and the two scales don't contaminate the vector. - Fuse per subject: fused = (w_g·game_z + w_c·combine_z)/(w_g+w_c), w_g=√min(games,4), w_c=1. Single-source rows use that source. This down-weights 1-game flukes and lets combine carry unproven players. - Cluster: k-means on the 6-dim fused matrix (CS→0 where absent). k chosen by silhouette over k=4..7, cross-checked for interpretability; stability via 50 seeds + 50 bootstraps (ARI). CS-aware re-cluster on the 215 rows with real CS as a robustness check.

Archetype profiles (mean fused z; outputs/archetype_profiles.csv)

Among players with ≥1 game (drops combine-only noise), the value ordering is preserved: elite multi-science PPTF 0.71 / WS 2.5 >> math+phys 0.40 / 1.39 > bio 0.33 / 0.92 ≈ ESS 0.31 / 0.95 >> replacement 0.075 / 0.19.

Characterization

• A2 — elite multi-science (chem+phys core). The star/captain tier. Hot on chem, phys, math (and CS), broadly above average everywhere — these are not narrow specialists, they are broad-and-deep. Carries ~4× the WS of the next tier and essentially all the VORP. Members: Anurag Sodhi, Rohan G, sanj, yufei, Vish. This is where wins come from.
• A3 — math+phys specialist. The "captain deep in physics+math" role from Gideon's theory, in its specialist (non-elite) form. Solid contributors, modest CS lean.
• A0 — bio specialist. Bio-dominant, weak physics — the "bio main." Note bio+astro complementarity (Gideon's bio-junior-with-astro) is not separable here: ESS (which holds astro) is neutral/negative in this cluster, so the data does NOT confirm a distinct bio+astro hybrid type; bio specialists are bio-first, ESS-neutral.
• A1 — ESS specialist. Earth/space/trivia-dominant, science-neutral. Matches the "ESS-soph" role. Modest output; a coverage-filler, not a carry.
• A4 — low-output / replacement. No hot subject. Mostly bench/unproven (incl. 55 combine-only nsba4 rows).

Mapping to Gideon's role theory (docs/INTEL.md)

So Gideon's roles exist as tendencies, but the data does not support the finer complementarity pairings (bio+astro, chem-as-its-own-main) as distinct player types — those collapse into either the broad-elite cluster or a single-subject specialist.

Stability (honest)

k=5 is the sweet spot. The low absolute silhouette (~0.23) is the real story: subject profiles overlap heavily; these are soft regions of a continuum, not discrete species.

Artifacts

• data/processed/player_archetypes.csv — per (canonical_id, season): theta_ (z), pptf_ (z), fused_* (6-dim), archetype_id, archetype_label, overall_value (PPTF), win_shares, vorp, has_cs_profile.
• outputs/archetype_profiles.csv — cluster-mean profile + value table.
• scripts/A28_archetypes.py — reproducible pipeline (seed 42/0).

Draft implication (tentative, do not over-weight)

The only archetype that reliably wins is the broad-and-deep elite (A2). Pure specialists (bio, ESS, math/phys) are coverage pieces of similar middling value (~0.3–0.4 PPTF). This echoes the spine: draft for production rate / the broad-elite tier; treat single-subject specialists incl. CS as roughly interchangeable coverage, not differentiators.

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