32_usage_bias.md

F32 — The usage / empty-stats bias in PPTF and the value board

F32 — The usage / empty-stats bias in PPTF and the value board

Date: 2026-05-30. Question (from David): PPTF = toss_points / tossups_faced, and tossups_faced (heard) is shared by all teammates who play a given game — within a game, every present player divides their points by the same denominator. So a lone competent player on a WEAK team vacuums all the buzzes their team wins (inflated PPTF / win-share); the same player on a STACKED team shares the buzzes (deflated). This is the basketball "usage rate / empty stats" confound. Does it threaten the PLAYER value board and the draft?

TL;DR — the bias is REAL but SMALL at the board level, and concentrated in a few names. The shared-denominator mechanic is confirmed. But once you control for a player's own combine ability, the teammate-quality penalty on PPTF is modest (≈ −0.04 PPTF per +1 SD of teammate strength, pooled p=0.027, not robust across seasons). Teammate-adjusting the whole board moves it almost nothing (Spearman obs↔adjusted 0.97–0.98; 24 of the top-25 stay, even under an aggressive upper-bound adjustment). The danger is not the aggregate ranking — it is a handful of specific top-10 names who are textbook lone-stars-on-weak- teams. Use this as a per-name flag, not a board-wide re-weighting.

Confidence: Med on the direction and the "small at board level" conclusion (multiple methods agree); Low on any magnitude (n=41 team-seasons, 159–207 player-seasons, the clean teammate coefficient is borderline and season-unstable).

0. The premise checks out: TUF is a shared per-game denominator

tossups_faced (TUF) is identical among teammates per game played, differing across a roster only because players miss games. On mount ellis (nsba1), the three players who played all 11 games each have TUF=242; players who played fewer games have proportionally fewer. TUF-per-game within a team-season has median std 0.34 (≈0, i.e. shared); raw TUF varies (37/40 team-seasons) only via games_played. So within any single game, all present teammates split a fixed pool of heard toss-ups — exactly David's empty-stats setup.

A direct accounting check confirms the mechanic: own_pptf + n_teammates · mean_teammate_pptf reconstructs team_pptf to within ±0.22 (residual only from differing games-played). PPTF is a share-of-a-fixed-pie statistic. This is why teammate PPTF and own PPTF are mechanically anti-correlated and must be interpreted with care.

(a) WITHIN-PLAYER: does a player's PPTF move inversely with teammate strength?

25 players appear in ≥2 team-seasons. Player fixed-effects (within-player demeaned) slope of own PPTF on teammate quality:

Read carefully. The big −1.03 slope on teammate PPTF is largely the shared-denominator identity, not behavior — teammate PPTF and own PPTF mechanically trade off within a fixed toss-up pool (see §0), so a strong negative is partly guaranteed by arithmetic. The clean, non-mechanical test uses teammate combine θ (independent of PPTF's denominator): slope −0.08, CI straddles 0 (n=20 players is thin). The within-player evidence is therefore suggestive of inflation in the right direction but underpowered once the mechanical channel is stripped out.

(b) CROSS-SECTIONAL: own PPTF on own θ + mean-teammate ability + SOS

SOS = mean Bradley-Terry strength of opponents faced (clean games only). Predictors standardized.

The teammate coefficient is negative only in the cleanest spec (M1) and in the uncontrolled spec (M3). Interpretation: - M1 (teammate θ, controlling own θ): a genuine, modest empty-stats signal — −0.039 PPTF per +1 SD of teammate ability, CI excludes 0 but barely (p=0.027). - M3 (no own-ability control): −0.062 is mostly confound — weak teams have weak teammates and the focal player is often also weak; not a clean estimate. - M2/M4 (teammate PPTF, controlling own θ): null. Once own ability is in, teammate production adds nothing — the shared-pie subtraction is already absorbed. - SOS is null everywhere — opponent strength does not drive individual PPTF (consistent with F2's SOS-robustness).

Season robustness (the load-bearing caveat): the M1 teammate-θ coefficient is −0.18 (p=0.17) nsba1, −0.03 (p=0.62) nsba2, −0.06 (p=0.41) nsba3 — not individually significant in any single season. The pooled p=0.027 leans on pooling. Treat the effect as real-ish but fragile.

(c) Are top value-board players disproportionately lone stars on weak teams?

Career value board (player_value_table.csv, n=181) merged to most-recent-season teammate quality:

The two signs look contradictory but tell a coherent story: top players are on WINNING teams (+0.16) but have WEAKER teammates (−0.19). That is the carry/empty-stats profile — the star is why the team wins, and they vacuum the buzzes. Top-25 board: mean team win% 0.57 vs 0.48 field, but mean teammate θ −0.15 vs +0.05 field. Part of the negative teammate-θ corr is a mechanical regression artifact (the best player is by construction stronger than their teammates), which inflates the apparent confound.

Direct lone-star cases. Defining a lone star as high own-PPTF, low-teammate-PPTF, team win% < 0.45 yields 11 players, and they are NOT buried — median board rank 38 of 181, with ne (rank 7) and dan.k.memes (rank 8) both inside the top-10. These two are the clearest empty-stats risks on the board. Their reliability is normal (median 0.83), so they are not small-sample flukes — they genuinely scored a lot on bad teams.

NSBA2 "steals" check. The nsba2 top-steal names (Yufei Chen, Geo, Joshua Wang, Dan Ni, Aditya, Stephen Chen, Rohan Garg) do skew toward weak teammates (negative tm‑θ for most) — but their team win% averages 0.56 (vs 0.48 field), i.e. they are mostly carries on decent teams, not pure tankers. Two genuine weak-team-vacuum steals stand out: Joshua Wang (win% 0.45, tm‑θ −0.41) and Dan Ni (win% 0.36, tm‑θ −0.26). Cross-reference: Rohan Garg is already an F12 game-backed BUY (tape beats combine) and Vishnu M (a §c lone-star, board rank 41) is already an F12 confirmed FADE (combine-inflated) — so the existing board partly handles these via reliability/combine anchoring.

(d) MAGNITUDE: how much does the board re-rank if PPTF is teammate-adjusted?

Teammate-adjusted PPTF = obs_pptf − β·(tm_θ − mean_tm_θ), β from M1 (clean spec, −0.087):

• Spearman(obs, adjusted) = 0.977; mean |rank shift| = 6.4 spots (driven by the tail); top-25: 24 of 25 stay, 1 swaps.
• Upper bound (fully de-trend teammate θ out of PPTF, effective slope −0.10): Spearman 0.971, top-25 still 24/25, mean |shift| 7.3.
• Among the obs-top-40, the maximum possible adjustment swing is ±0.14 PPTF against a top-40 PPTF spread of 0.80 — i.e. the teammate correction is ≈18% of the spread only for the most extreme-teammate cases, and near-zero for typical ones.

Notably, the biggest upward movers under the adjustment (Praneel Avula, Arjun D, Euna Kim) are players with strong teammates whose modest PPTF gets credited up — the adjustment does NOT simply demote everyone on a weak team; it is a two-sided correction and at the board level it nets out. Artifact: data/processed/usage_bias_32.csv (per-player obs vs teammate-adjusted PPTF and rank shift).

Verdict and draft action

Is this a big problem or a small one? Small at the board level, sharp for a few names.

1. Do NOT board-wide re-weight PPTF for teammate quality. The clean coefficient is small, season-unstable, and re-ranking moves the top-25 by ~1 name. PPTF survives as the value currency (consistent with F2). A blanket usage adjustment would add noise, not signal.

2. DO apply a per-name "carry flag" to the handful of true lone-stars-on-weak-teams — especially ne (#7) and dan.k.memes (#8), the two top-10 empty-stats archetypes, plus weak-team nsba2 steals Joshua Wang and Dan Ni. For these, discount toward their combine θ (own ability) when projecting onto a stronger future roster — this is exactly the "draft the empty-stats guy, he regresses on a better team" trap. The board's existing reliability/combine anchoring already catches some (e.g. Vishnu M is an F12 fade).

3. The direction confirms the basketball analogy (carries on weak teams over-credited, stars on stacked teams under-credited), but the magnitude is bounded small — the worst plausible single-player correction is ≈0.14 PPTF, ~0.5–0.6 SD, and only for extreme cases.

Caveats (load-bearing). n=41 team-seasons / 159–207 player-seasons; the clean teammate-θ coefficient is borderline (p=0.027) and not significant in any single season. The −1.03 within-player PPTF slope is largely a shared-denominator identity, not behavior. Teammate θ covers only 180/207 player-seasons (combine-linked). The negative VORP↔teammate-θ correlation is partly a mechanical "best-player-has-weaker-teammates" artifact, which overstates the confound — the true behavioral inflation is at the small end of the range. Read directions and the specific flagged names; distrust the point magnitudes.

Artifacts: data/processed/usage_bias_32.csv (teammate-adjusted board + rank shifts).

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