16_generalist_specialist.md

A16 — Generalist vs Specialist + Roster Coverage (HEADLINE)

A16 — Generalist vs Specialist + Roster Coverage (HEADLINE)

Question. Is a player who is strong across all subjects worth more win-share than a single-subject specialist, and what roster coverage profile wins? Regress team win% on coverage breadth (a credible answerer in each subject) vs concentration (HHI), controlling for total talent; compare to the natural-roster Science Bowl baseline (F1); find the optimal coverage profile and test complementary pairings.

TL;DR. 1. Coverage is a threshold good, not a gradient. The thing that wins is not having a hole: teams that leave any subject with no credible answerer ("punt") lose far more. Among teams with ≥5 games, 0 punts → 52% win, ≥1 punt → 28%. corr(win%, #punts) = −0.54 (p=0.001) and it survives controlling for star talent (partial r = −0.37, p=0.026). 2. Beyond filling all six slots, redundancy/depth adds almost nothing. Among fully-covered teams the # of subjects with a second credible answerer is uncorrelated with winning (r = 0.01). The strength of your weakest subject correlates with winning (+0.44) but is collinear with overall talent — it does not survive a talent control (partial r = −0.09, ns). 3. At the player level, generalists ARE more valuable — but mostly because breadth IS talent. corr(player toss_points, #subjects answered) = +0.76. The best players are broad; pure one-subject specialists are rarely high-volume. 4. NSBA replicates the natural-roster F1 finding in direction: breadth helps, concentration hurts (corr(win%, subject_HHI) = −0.46 in NSBA vs −0.57 in real Science Bowl). But the level differs: real Science Bowl rosters vary a lot in breadth and celerity dominates; NSBA drafted rosters are already so balanced that breadth only bites at the bottom (the few teams that punt a subject).

Data & method

• Backbone: team_season.csv (41 team-seasons; nsba1=12, nsba2=13, nsba3=16) and player_season_master.csv (207 player-seasons), both built only from game data (standard SB scoring, clean 180-game set). Robustness restricts to games ≥ 5 → 37 team-seasons (drops 4 tiny-sample nsba3 teams with 1–4 games).
• Talent controls: roster_toss_points (sum of roster net toss-up points, season-z) and top2_toss (sum of the two highest-scoring players, the "star" proxy, season-z). Win% z is not used; win% is the raw outcome.
• Coverage metric: for each team × subject, count roster players whose net toss-up points in that subject ≥ 8 (≈ ≥2 net correct over the season) = a "credible answerer." coverage = # subjects with ≥1; punts = # subjects with none; deep_subjects = # with ≥2 (redundancy). Active subject slate per season: nsba1 = {b,ch,ess,m,p,ene}; nsba2/nsba3 = {b,ch,cs,ess,m,p}. (nsba1 Energy is kept; CS exists only nsba2/3 — never mixed.)
• Concentration: team subject_hhi (Herfindahl of positive subject-point shares; ~0.17 = balanced, 1.0 = one subject).
• Baseline: scibowl_team_stats.csv (84 natural-roster teams) for the F1 reference (n_subjects_covered, breadth_hhi, avg_celerity).
• Regressions are plain OLS (numpy lstsq, analytic SEs); n is small so treat p-values as directional.
• Reproduce: /home/david/code/nsba/.venv/bin/python scripts/analysis_16_coverage.py → writes data/processed/team_coverage_16.csv.

1. Player level — are generalists worth more than specialists?

Among productive players (toss_points > 20, n = 124), median own-subject HHI = 0.38 (pure specialist = 1.0, perfectly broad over 6 = 0.17).

Read: the highest-value players are broad answerers; single-subject specialists are almost never high-volume scorers. Breadth and talent are entangled at the individual level — a generalist out-produces a specialist largely because being broad is how you rack up points in a format where every subject is in play. So the draft answer is prefer the generalist when raw output is comparable; you almost never get a high-output pure specialist anyway.

2. Team level — what coverage profile wins?

Univariate (games ≥ 5, n = 37):

Win% by coverage gap (games ≥ 5):

Regressions (win% outcome, n = 37):

• Each punted subject costs ≈ 7 percentage points of win% on top of talent (β = −0.075, p = 0.028 over star talent). Adding #punts to a star-talent model raises adj R² from 0.507 → 0.560.
• Redundancy beyond first coverage does not help. deep_subjects is flat once talent is in (β = +0.009, p = 0.59); among the 32 fully-covered teams, corr(win%, deep_subjects) = +0.01. A second expert in a subject you already cover is wasted roster value; talent there should go to your weakest slot or to raw star power.
• Partial correlations (control star talent): corr(win%, #punts | top2) = −0.37 (p = 0.026); corr(win%, coverage | top2) = +0.37. Coverage carries real, talent-independent signal.

Where the signal lives. At FLOOR = 8 the punt variation is entirely in nsba3 (every nsba1/nsba2 team with ≥5 games already covers all 6 subjects). Raising the bar makes punts appear in all seasons and strengthens the effect — a good robustness sign:

Continuous "weakest-link" caveat. Using the strength of the worst-covered subject's best answerer (continuous, defined every season): corr(win%) = +0.44, but it does NOT survive a talent control (partial r = −0.085, ns). So it is the binary gap (does a credible answerer exist at all) that matters beyond talent, not the marginal depth of your weakest subject. Coverage is a threshold good.

3. Optimal coverage profile

Cover all six subjects with at least one credible (≥2-net-correct) answerer, then spend every remaining pick on raw scoring talent / a star — not on a second answerer in a subject you already cover.

A fully-covered, top-heavy roster (high top2, 0 punts) is the modal winner: top2 + #punts is the best small model (adj R² = 0.560). Depth/redundancy and a balanced-but-mediocre spread (low HHI alone) do not beat star talent once the holes are filled.

4. How common is good coverage of each subject in NSBA drafts?

(games ≥ 5; "covered" = ≥1 credible answerer, "deep" = ≥2.)

• CS is the scarcest coverage (92% covered, only 40% have a second CS answerer) and the thinnest bench — consistent with the prior that CS is the rarer/"unbikable" skill. The subjects most often punted are CS and ESS depth. In a draft, a credible CS answerer is the most differentiating coverage pick because they're hardest to find on the board.
• Punting Biology or Math is rare but catastrophic (the lone teams that did went 0.000).

5. Complementary pairings

Subject pairs both covered vs not (games ≥ 5), win% difference:

These pairings are not evidence of a special synergy — they mostly re-express the single-punt penalty (a team that covers both members of any pair is a team without a hole). The honest reading: no specific two-subject combo beats simply "cover everything." ESS- and CS-involving pairs top the list only because ESS-depth and CS are the holes teams actually leave.

Comparison to the natural-roster baseline (F1)

Same direction, different regime. Breadth helps and concentration hurts in both. But natural school rosters span a wide coverage range (HHI 0.17→1.0, many genuinely narrow teams), so breadth is a first-order driver there. NSBA's snake draft already forces balance — drafted rosters cluster tightly near HHI ≈ 0.18 and 37/41 cover all six subjects — so in NSBA, coverage only separates the bottom (the handful of teams that fail to land a credible answerer in a subject, almost always CS or ESS), while talent/star power separates the top.

Limitations

• n is small (37–41 team-seasons) and coverage variation at FLOOR=8 is almost entirely nsba3; treat p-values as directional. The effect strengthens and spreads across seasons at higher thresholds, which is reassuring but not dispositive.
• Win% is a noisy outcome (4–12 games/team; several nsba3 teams ≤7 games). Schedule strength is not modeled.
• Talent and breadth are entangled at the player level by construction (a broad player scores more), so "generalist value" partly reflects that broad players are simply better, not a pure breadth premium.
• Coverage is buzz-attributed, not on-floor: nsba3 has no lineup/TUH data, so a player credited in a subject is whoever buzzed, which can understate quiet capable answerers. The credible-answerer floor (≥2 net correct) mitigates this.
• CS exists only in nsba2/nsba3; Energy only in nsba1 — the per-subject prevalence table mixes these eras (handled by per-season active slates, but CS/ESS numbers rest on ~28 team-seasons, not 41).
• Coverage here is a necessary-not-sufficient threshold result: it tells you not to leave a hole; it does not say depth is worthless in a longer/elimination format where a single off-night for your lone subject expert is riskier than these round-robin win%s reveal.

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