29_duo_synergy.md

29 — Duo / Pair Synergy: does coverage work as DUOS?

29 — Duo / Pair Synergy: does coverage work as DUOS?

Date: 2026-05-30. Status: exploratory (Task B). LEAD WITH THE CAVEAT.

TL;DR (the honest answer)

No duo synergy survives skeptical correction. Across 474 co-rostered pairs in 38 team-seasons, teammate pairs' joint production is statistically indistinguishable from the additive sum of the two members' individual baselines. Neither archetype-complementarity nor subject-disjointness predicts super-additive production once you (a) test at the clean team level (38 independent units, not 474 pseudo-replicated pairs) and (b) control the family of tests with FDR. Every candidate effect dies at q>0.05. The one nominally-significant raw result points against the coverage-duo hypothesis (disjoint-subject pairs slightly under-perform additivity, a talent-density artifact), and it too dies under FDR.

This is the duo-level confirmation of the aggregate null (F4): coverage does not become a winning lever when you look at it as pairs instead of as a roster total.

HARD CAVEATS (read first)

1. Pseudo-replication is the central trap and it nearly fooled the first pass. 474 pairs sit inside only 38 team-seasons; pairs in the same team share ONE outcome. The naive pair-level table flagged elite+repl (q=0.037). That is pure additive inheritance, not synergy: elite players are systematically under-predicted by the talent model, so any pair containing one inherits a positive residual additively. The genuine spillover test (does a non-elite player's own residual rise when he has an elite teammate?) is +0.135 win-shares, p=0.155, ns. All clean inference is reported at the team level (n=38) or with team-season cluster bootstrap.
2. "Solo baseline" is not directly observable. Every game a player plays shares all his teammates, so there is no within-data solo. "Synergy" is therefore defined as a residual above an additive talent baseline (member win-shares predicted from a team-independent ability score; team residual = wins − Σ predicted). This is the best available definition, not a clean A/B.
3. The talent baseline leans on combine theta (team-independent) and falls back to game pptf_z (endogenous) for combine-less players. The fallback can muddy individual credit. Subject vectors come from the fused archetype profiles (finding 28), which are soft (silhouette 0.23).
4. n bounds everything. 38 team-seasons; 3 game seasons; many of the breadth-relevant cases are nsba3-only (per F4). Treat magnitudes as ±a lot; trust the direction (flat null) and the fact that nothing survives FDR.

Method (scripts/A29_duo_synergy.py)

• Units & spine: co-rostered pairs built from team_season.roster_canonical_ids, restricted to players with ≥1 game. Per-player ability = mean combine theta (team- independent), within-season z-scored; fallback to pptf_z. Win-shares from player_win_shares.csv (exactly additive, sum to team wins).
• Additive baseline: OLS win_shares ~ ability_z (r=0.71, n=207). Player residual = actual − predicted win-shares. resid_sum of a pair is additive by construction — it contains NO interaction term, which is exactly why a real synergy must show up as something beyond it (partner-archetype dependence, or team-level super-additivity).
• Subject complementarity: each player's "strong set" = subjects with fused z > 0.5 (checked at 0.3 / 0.5 / 0.75). Pair complementarity = 1 − Jaccard(strong_i, strong_j); disjoint = no shared strong subject.
• Inference: team-season cluster bootstrap (5000×) for pair-level stats; iid team bootstrap for the 38-team tests; Benjamini-Hochberg FDR across the whole test family; empirical-Bayes shrinkage of archetype-pair cell means toward the grand mean.

Results

Subject-complementarity (the direct coverage-duo test) — NULL

At the clean team level, complementarity ↔ synergy is +0.025 (p=0.88) — a flat zero. The two nominally-significant raws (disjoint pairs under-perform: −0.35, p=0.007; frac-disjoint negative: p=0.049) (i) point the wrong way for the "cover disjoint subjects" thesis and (ii) both fail FDR (q=0.054, q=0.198). Threshold sensitivity: the disjoint-underperformance is stable (~−0.3) at z>0.3/0.5/0.75, which marks it as a real but small talent-density confound — overlapping-strong pairs tend to be two strong (often elite) players — not a coverage signal.

Archetype-pair synergy — additive inheritance, not interaction

The pair-level archetype table (outputs/duo_archetype_pairs.csv) ranks elite+repl (+0.87, q=0.037) and elite+mathphys (+0.83) on top — but resid_sum is additive, so this is just "contains an elite player" (corr(resid_sum, has_elite)=+0.23; mean resid_sum 0.60 with an elite vs −0.11 without). The decisive interaction test:

Non-elite player's own win-share residual WITH an elite teammate: +0.031 vs WITHOUT −0.104. Welch t=1.43, p=0.155 (ns), q=0.41.

So elite players do not measurably lift their partners beyond their own additive contribution. The "elite-pair" effect is an accounting echo of the single-player elite premium (finding 28's A2 tier), not a duo interaction.

Team-level super-additivity exists but is unattributable

Total team synergy (wins − additive talent prediction) ranges −5.7 to +5.9 (sd 2.26 over 38 teams) — teams do over/under-perform their summed talent. But none of that spread is explained by archetype-complementarity or subject-disjointness (corrs +0.025 / −0.32, neither surviving FDR). Whatever drives team super-additivity (schedule, chemistry, captaincy, availability, noise at n=38) is not the coverage-duo structure tested here.

FDR across the full synergy family (8 tests)

Sorted by raw p, BH at α=0.05: 0 of 8 survive. Smallest q = 0.054 (disjoint pairs under-perform — wrong-signed for the hypothesis anyway).

Verdict

• Does coverage work as duos? No — not detectably at this n. Complementary archetype combinations and disjoint-subject pairs do not over-perform additivity; if anything disjoint pairs slightly under-perform (a talent-density confound, not a coverage benefit), and that too is non-significant after correction.
• Is duo synergy distinguishable from additive at this n? No. Pair joint production = sum of solo baselines, within the resolution we can measure (38 team- seasons). The honest claim is a bounded null, not "proven zero" — a true synergy smaller than ~±0.3 win-shares per pair would be invisible here.
• Consistency with the spine: This extends F4 (aggregate coverage null) to the finer duo/archetype-pair structure the task asked about. The thesis stands: draft for production rate / the broad-and-deep elite tier (finding 28's A2); treat coverage and subject-complementarity as cheap table-stakes, not a duo-synergy lever. There is no recoverable "build complementary pairs" edge in this data.

Artifacts

• scripts/A29_duo_synergy.py — reproducible pipeline (seeds 42/7/1).
• data/processed/duo_pairs.csv — all 474 co-rostered pairs with complementarity, disjointness, archetype-pair, and additive residual-sum.
• outputs/duo_archetype_pairs.csv — archetype-pair cells with shrunk means, cluster- bootstrap CIs, and FDR q-values.
• outputs/duo_team_residuals.csv, outputs/duo_team_synergy.csv — team-level additive- talent residuals and total super-additivity per team-season.

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