Replacement-Level Exposure Study

This study documents a rejected attempt to estimate replacement level by averaging individual low-exposure RAPM coefficients.

It is a descriptive report, not a predictive model and not a Leaderboard entry. In particular, it must not be read as a value estimate for a player who never appears in NBA play-by-play data.

Exposure Contract

For player \(i\), team \(j\), and season \(t\), let \(P_{ijt}\) be the player's on-court RAPM possessions with that team and let \(T_{jt}\) be that team's total regular-season RAPM possession opportunities. The study defines the season share as

This matches the possession definition used by the RAPM target. A player who is traded is credited with the fraction of each team's full-season opportunity set during which he was on court. The construction is validated against the player-season panel's rapm_possessions column for every row.

The cohort contains every regular-season player-season with a RAPM outcome, not only rookies. This better represents the pool of low-minute players that rookies compete with for an NBA rotation spot, including likely two-way, 10-day, and fringe-roster seasons. Contract type is not yet available in the panel, so the pool can also contain established players returning from injury or otherwise playing little; the report publishes experience bands to make that contamination visible.

Players who never record an NBA possession are still absent. The exposure analysis is therefore conditional on reaching the NBA play-by-play data set.

Rejected Estimate

The current immutable run is artifacts/models/replacement_level/2025-26/replacement-level-2025-26-20260806T005038Z-5393fb5c/. It covers 14,550 regular-season player-seasons across 1996-97 through 2025-26.

The original low-exposure reference was the season-balanced equal-player mean across all player-seasons with \(s_{it}<5\%\):

Its season-block bootstrap interval is [-0.275, -0.220]. Each season gets equal influence in that estimate, rather than allowing the larger modern player pools to dominate it.

Interpretation

The low-exposure estimate is rejected as a replacement-level measure. The 0-5% cohort is less negative than the higher-exposure groups because small-sample individual RAPM coefficients are regularized toward zero. The three experience bands are similarly near zero for the same reason; they do not identify contract status or separate injuries from fringe roles.

It therefore does not establish a usable fallback value or a hard "below 5% means replacement level" rule. It does not alter the draft-informed prior or the frozen preseason evaluation. The Pooled Replacement-Token RAPM applies the correct group-token design.

Next Model

The next slice can build a preseason-only exposure gate and mix a validated replacement token with a profile-rate prior:

That gate must be evaluated strictly out of season. A complete candidate population, including drafted players with zero NBA possessions, is required before it can estimate the probability of appearing at all rather than merely rotation share conditional on appearance.

Artifacts