Draft-Informed Cold Starts

This is an interpretable diagnostic for the cold-start problem: what can draft information alone say about a player's first NBA season before any NBA possession data exist? It is deliberately separate from the Frozen Preseason Leaderboard until it proves incremental lineup-level value.

Model Contract

For historical first-NBA-season player \(i\), let \(R_i\) be that season's regular-only canonical RAPM. The fitted prior is

where \(q_i=(p_i-30.5)/29.5\) for overall draft pick \(p_i\in[1,60]\), \(U_i,L_i,M_i\) flag undrafted, pick-above-60, and unknown-draft-record statuses, \(A_i\) is estimated draft age, and \(\widetilde A\) is the historical training-median draft age. \(H_i\) is listed height and \(B_i\) is listed body-mass index. Features are standardized and the model is ridge regression. The ridge alpha is regularization * training_row_count; training weights are reconstructed on-court possessions normalized to mean 1.

Estimated draft age is the reported season age adjusted back to the draft year. It is a draft-profile variable, not an assertion that every player entered the NBA in the year he was drafted.

The rows are players whose first NBA season is marked is_rookie in the player-season panel. This is a conditional sample: players drafted but never recording an NBA season are absent. That survivor conditioning matters when interpreting draft position and prevents this chart from being treated as a general draft-value curve.

2025-26 Diagnostic

The current immutable run is artifacts/models/draft_prior/2025-26/draft-prior-2025-26-20260806T001505Z-0c6a670a/. It trains on 2,299 historical first-NBA-season players from 1996-97 through 2024-25 and scores 100 2025-26 first-NBA-season players. The target profile artifact excludes both target RAPM and target possession count. The selected regularization was 0.30, based on six expanding validation seasons (2019-20 through 2024-25).

Regularization Stability

The final 0.30 choice comes from the six most recent available validation seasons, not a claim that one alpha is stable across NBA history. The following pre-target snapshots each select alpha with their own six expanding folds. The first snapshot needs 12 historical label seasons so that its inner validation window still has a meaningful preceding training history.

The shift is material in older snapshots but the recent selections mostly concentrate at 0.30, with one 1.00 exception. This supports the current recent-window choice while making it clear that a future recursive model must select regularization separately at every historical cutoff.

The result does not display the naive expectation that an earlier pick monotonically implies stronger first-season RAPM. In the observed, possession-weighted sample, picks 1-3 average -0.67, picks 21-30 average -0.41, and picks 46-60 average -0.37. The adjusted pick-only partial curve has the same direction, moving from -0.53 at pick 1 to -0.28 at pick 60 for a fixed reference profile.

This is a substantive diagnostic result, not a charting error. The analysis is conditioned on players who reached the NBA data set, so later picks are a selected group of successful survivors while every high pick is observed. Older entry paths and static profile differences also matter. The model should therefore not be added to a cold-start prior or frozen evaluation yet. The next useful experiment is a proper out-of-season cohort evaluation against the forward training mean and the current lagged-RAPM prior, with an explicit playing-time/roster-selection treatment.

The shaded adjusted-curve band is a 90% season-block bootstrap interval. For undrafted or draft-record categories, ranking bands use the historical weighted residual spread instead, so those two uncertainty displays are not directly comparable.

Frozen Cold-Start Ablation

The first downstream test replaces the neutral 0.0 prior for only the 100 first-NBA-season 2025-26 players. It retains completed 2024-25 lagged RAPM for 462 returning players and zero for the other 20 no-immediate-prior players. The draft model is the immutable study above, fit through 2024-25; neither the historical RAPM sequence nor any 2025-26 player coefficient is refit.

The regular-season improvement is small but consistent across the listed regular-season metrics. Playoff results worsen, so the ablation is recorded as promising rather than promoted. The complete comparison is in the Frozen Preseason Leaderboard.

2025-26 First-NBA-Season Rankings

The following sortable table is a profile-only ranking, not a retrospective 2025-26 RAPM ranking. It begins in predicted order; select Pick to inspect the class in draft order. The full-fidelity table, including uncertainty bands, is rookie_rankings.parquet in the immutable run above.

Top 100 Draft-Prior Rankings