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Cold-Start Exposure Gate

This study separates two questions that were previously conflated in the draft-informed cold-start prior: what rate should a player have if he earns rotation exposure, and how likely is a first-NBA-season player to earn enough exposure to avoid the pooled replacement group?

The pooled replacement-token study answers the first question for the low-exposure pool. This page addresses the second question for first-NBA-season players only. Returning players keep their lagged RAPM prior; a low minute count in a returning season never activates this gate.

Model Contract

For historical first-NBA-season player \(i\), define realized regular-season team-opportunity share as

\[ s_i = \sum_{j \in \mathrm{teams}(i)} \frac{\mathrm{on\ court\ possessions}_{ij}} {\mathrm{team\ possession\ opportunities}_j}. \]

The binary label is \(r_i = \mathbb{1}[s_i < 0.05]\), so a positive label means the player fell in the low-exposure population used by the shared replacement token. The logistic gate estimates

\[ \Pr(r_i=1\mid x_i) = \sigma\left(\beta_0 + x_i^\top\beta\right), \]

where \(x_i\) contains centered linear and quadratic draft pick, draft-status indicators (undrafted, pick above 60, or unknown), draft age, listed height, listed body-mass index, and the draft-pick-by-draft-age interaction. Features are standardized and the model uses L2-regularized logistic regression.

Draft age is reported season age adjusted back to the draft year. As with the draft RAPM prior, this is conditional on recording a first NBA season: drafted players with no NBA appearance are absent. The gate is a conditional rotation/exposure model, not a general draft-prospect model.

2025-26 Diagnostic

The current immutable run is artifacts/models/cold_start_exposure/2025-26/cold-start-exposure-2025-26-20260806T013228Z-6072bdd3/. It trains on 2,299 first-NBA-season players from 1996-97 through 2024-25 and produces 100 preseason-only 2025-26 profiles. The target profile artifact excludes target RAPM, possessions, realized exposure share, and the replacement-candidate label.

The selected inverse L2 penalty was C = 10.0, based on six expanding validation seasons from 2019-20 through 2024-25. The profile features are meaningfully predictive:

Model Out-of-fold players Log loss Brier score ROC AUC
Draft-profile gate 611 0.5415 0.1850 0.7889
Constant historical candidate rate 611 0.6930 0.2499 0.5000

Draft-profile exposure gate

The left panel gives the partial draft-pick relationship at the historical reference draft age and body profile; the right panel is calibration over the six forward folds. The fitted probability rises from 2.8% for pick 1 to 60.3% for pick 60 at that reference profile. Rocco Zikarsky's low-exposure probability is 71.7%, correcting the earlier draft RAPM-rate artifact where the pick-age interaction made him appear unusually favorable.

The gate does not make a hard 5% probability decision. That would throw away useful uncertainty. The exposure-gated cold-start prior uses the probability continuously:

\[ \widehat R^{cold}_i = p_i^{replacement}\,\widehat R^{replacement} +(1-p_i^{replacement})\,\widehat R_i^{profile}, \]

It is evaluated with the full 2025-26 regular-season and playoff holdouts, while this study remains independently inspectable for calibration.

2025-26 Cold-Start Rankings

These sortable rankings are predicted rotation probability, not player quality or retrospective RAPM. A lower low-exposure probability means the player is less likely to receive the replacement component in a future blended prior. The complete 100-player table is target_exposure_predictions.parquet in the immutable run.

Top 25 Predicted Rotation Rankings

Rank Player Pos. Draft status Pick Draft age P(low exposure) P(rotation)
1 Dylan Harper G Drafted 1-60 2 20 2.2% 97.8%
2 Cooper Flagg F Drafted 1-60 1 19 2.4% 97.6%
3 VJ Edgecombe G Drafted 1-60 3 20 2.5% 97.5%
4 Kon Knueppel G-F Drafted 1-60 4 20 3.0% 97.0%
5 Jeremiah Fears G Drafted 1-60 7 19 3.5% 96.5%
6 Tre Johnson G Drafted 1-60 6 20 3.8% 96.2%
7 Ace Bailey F Drafted 1-60 5 19 3.9% 96.1%
8 Collin Murray-Boyles F Drafted 1-60 9 21 5.6% 94.4%
9 Egor Demin G Drafted 1-60 8 20 5.6% 94.4%
10 Cedric Coward G Drafted 1-60 11 22 6.9% 93.1%
11 Khaman Maluach C Drafted 1-60 10 19 8.1% 91.9%
12 Noa Essengue F Drafted 1-60 12 19 8.3% 91.7%
13 Carter Bryant F Drafted 1-60 14 20 8.8% 91.2%
14 Derik Queen C Drafted 1-60 13 21 9.3% 90.7%
15 Walter Clayton Jr. G Drafted 1-60 18 23 12.0% 88.0%
16 Nolan Traore G Drafted 1-60 19 20 12.5% 87.5%
17 Yang Hansen C Drafted 1-60 16 21 14.8% 85.2%
18 Kasparas Jakucionis G Drafted 1-60 20 20 14.8% 85.2%
19 Joan Beringer F Drafted 1-60 17 19 15.2% 84.8%
20 Drake Powell G-F Drafted 1-60 22 20 17.5% 82.5%
21 Jase Richardson G Drafted 1-60 25 20 18.1% 81.9%
22 Nique Clifford G Drafted 1-60 24 24 19.2% 80.8%
23 Will Riley F Drafted 1-60 21 20 20.9% 79.1%
24 Asa Newell F Drafted 1-60 23 20 23.6% 76.4%
25 Ben Saraf G Drafted 1-60 26 20 24.4% 75.6%

Artifacts

File Contents
training_first_nba_season_exposure.parquet Historical first-year labels, exposure shares, and preseason features
target_first_nba_season_profiles.parquet Outcome-free target-season player profiles
cross_validation.parquet Six expanding-fold candidates and scores
cross_validated_predictions.parquet One forward prediction per validation player
calibration_deciles.parquet Out-of-fold calibration bins
target_exposure_predictions.parquet 2025-26 cold-start probabilities and ranks
model.joblib Final logistic gate fit through 2024-25
metadata.json / manifest.json Scope, temporal boundary, source hashes, and integrity records