15_north_star.md

15 — North-Star Metric Discovery (the value currency)

15 — North-Star Metric Discovery (the value currency)

Goal. Define the single team-level quantity that best predicts NSBA standings (matches won; total points as tiebreak), and recommend how to decompose it into per-player win shares — the currency we will draft against for NSBA4.

Data. team_season.csv (41 team-seasons: nsba1=12, nsba2=13, nsba3=16), player_season_master.csv (207 player-seasons), combine_ability.csv. All built from the clean 180-game set (standard Science-Bowl scoring; combine never mixed into value stats). Script: scripts/north_star.py.

Method

For each team-season I engineered candidate north-star metrics and split them into two classes, because not all "predictors" are legal draft inputs:

• Draftable / roster-only (computable from who is on the roster, no opponent outcome): pptf_team, ppg_team, ppg_total, subject_hhi, n_subjects, top2_share, player_hhi, depth, eff_contrib, roster_size, neg_rate.
• Outcome-laden (require games already played vs specific opponents — useful as a ceiling/diagnostic, illegal as a draft predictor): point_margin, points_against.

Target = win_pct. I report univariate pearson/spearman, leave-one-season-out (LOSO) ridge regression (train on 2 seasons, predict the held-out season — the honest test of transfer), and partial correlations to see what adds over raw production.

Definitions: pptf_team = team total toss-up points / total tossups-faced (an efficiency rate, opponent-agnostic). ppg_total = points_for / games (full TU+bonus per game). subject_hhi low = broad; n_subjects = breadth.

Results

Univariate correlation with win% (n=41)

LOSO out-of-sample R² / spearman (predict win%)

What adds over raw production?

• Partial corr(n_subjects, win% | pptf) = +0.173 — breadth gives a small real lift on top of scoring rate.
• Partial corr(subject_hhi, win% | pptf) = −0.074 — concentration shape adds almost nothing once you know the rate.
• Player-concentration metrics (top2_share, player_hhi, depth) are ~0 with win% — how points are spread across the roster barely matters; total production does.
• Per-season pearson(pptf, win%) is stable and positive every season (nsba1 +0.535, nsba2 +0.561, nsba3 +0.752) — it transfers, which is why we trust it.

Recommendation — the north-star value currency

Toss-up production efficiency = PPTF (toss-up points per toss-up faced).

Why PPTF and not the slightly-higher PPG_total or point_margin:

1. It is a rate, not a count — robust to schedule length, # games, and roster size, so it composes cleanly across players into a team prediction.
2. It is opponent-agnostic and individually attributable — point_margin and points_against are downstream outcomes (they encode who you played and lost to), so they top the correlation table but are illegal as a draft input. PPTF is built only from the player's own buzzes.
3. It transfers (positive every season; LOSO R²=0.26, spearman=0.53) — modest because n=41 teams is tiny, but stable.
4. PPG_total wins narrowly (R²=0.35) only because it folds in bonus conversion, a team skill that is not individually attributable (bonuses are team-answered). Use it as a team-level scoreboard check, not as the per-player draft currency.

Add breadth as a secondary tiebreak, not the core. PPG_total + n_subjects is the best LOSO model (R²=0.370), and breadth has a +0.17 partial lift over rate — consistent with the F1 prior (corr(win%, #subjects)=+0.52 in natural rosters). But it is a second-order adjustment; production rate dominates.

Decomposition into per-player win shares

The currency decomposes additively because team toss-up points are a sum of player buzzes:

player_win_share = (player_toss_points / team_toss_points) * team_wins

This is implemented in data/processed/player_win_shares.csv (226 player rows). It is exact: each team's player win-shares sum to its actual wins (max abs error = 0.0000). Reading: a player's win-share = the share of his team's wins attributable to his toss-up production. Top contributors:

For drafting NSBA4: project each candidate's PPTF (expected toss-up points per toss-up faced) from their game history and/or de-biked combine ability (combine_ability.theta_*), sum the projected production across a hypothetical roster to a team PPTF, and add a small breadth bonus for subject coverage. Win shares then allocate expected team wins back to individuals as the value-per-pick currency.

Limitations & caveats

• Tiny n. 41 team-seasons total (12/13/16 per season). LOSO R² values carry wide error bars; treat the ranking of metrics as the robust finding, not the point estimates.
• PPTF for nsba3 is a games×rate proxy, not an exact heard-count: the paired NSBA3 scoresheet layout records no per-player TUH, so tossups_faced is estimated from the season mean for those rows (tuh_source). nsba1 TUH is exact; nsba2 partial.
• Bonuses are team-attributed, so ppg_total's edge over PPTF cannot be pushed down to individuals — a structural reason to prefer PPTF as the per-player currency.
• point_margin's high R² is mechanical, not causal-for-drafting: margin is a function of game results, so it cannot guide who to pick. It is reported only as the outcome ceiling.
• Win-share decomposition credits toss-up points only (no bonus, no defense/lineup plus-minus — not recoverable for nsba3); it is a production attribution, not a complete value model.
• 4 nsba3 Round-1 games are team-level-only (no player names); their points sit in team_season but contribute no player win-shares (documented in the spine).

Artifacts

• scripts/north_star.py — full reproducible analysis.
• data/processed/team_north_star_features.csv — 41 teams × candidate metrics.
• data/processed/player_win_shares.csv — 226 rows; per-player win-share decomposition.
• data/processed/north_star_univariate.csv — univariate correlation table.

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