Rest, load and outcomes

1 Question

This note asks how an NBA team's schedule exposure and roster availability relate to observed outcomes. The published Schedule Fatigue Tax claimed a team-season offensive-rating penalty, but that unit is under review; the supported schedule facts are back-to-back counts and frequencies plus a separate raw per-36 box comparison. The Load-Bearing Index uses two different one-season estimators of player dependence and records where they disagree.

The public correction receipt is /data/audits/nba-schedule-fatigue-units.json, reviewed 2026-09-29. That is the audit date, not the observation date of the rest comparison; the source receipt does not publish an as_of timestamp.

Both measures are pre-tip-off conditioning variables. Rest days are fixed once the league schedule is released; which player is or is not available is known, with injury reports, before a game starts. Neither measure is presented here as a forecast, and neither is tested here as a live input to a probability model.

2 Data and definitions

The historical Schedule Fatigue Tax source (novel_schedule_fatigue_tax.json) reports 90 team-seasons from 2023-24 through 2025-26, including back-to-back game count and frequency. Its points-per-100 offensive-rating variant is under review because the cited mechanism receipt measures scoring margin. The source manifest has no as_of date; these seasons are the published observation scope, not a verified computation date.

That module's source_artifacts field points to schedule_density.json, which supplies the underlying per-36 box-composite means by schedule-density state: 12000 back-to-back player-games, 17531 in a 3-in-4 window, 20120 in a 4-in-6 window, and 40157 rested player-games (2 or more days rest, no compression), pooled from 77744 total rows and 7222 team-games across the same three seasons. schedule_density.json's manifest as_of is also not published. Its own methodology states the three density classes overlap -- a back-to-back that closes a cluster is also a 3-in-4 -- so their player-game counts are not additive.

The public mechanism ledger records two b2b_rest_penalty runs on the same corpus tag. The n=4732 run reports average scoring margin -1.41 on zero rest (n=856) versus +0.32 after at least one rest day (n=3876), giving zero-rest-minus-rested -1.73 (p=0.005645490426098632). The n=7192 run reports -1.61 versus +0.35, giving approximately -1.955 (p=0.0001174325580081608). These are scoring-margin associations, not offensive ratings or points per 100 possessions. Neither ledger row has an as_of timestamp, and the overlap of their two samples is unrecorded.

The Load-Bearing Index module (novel_load_bearing_index.json) reports 30 teams, each with two independently sourced estimators: estimator_a is an Elo on/off win-probability comparison for the 2024-25 season, and estimator_b is a raw win-rate comparison between games a player was active and games that player was missed, for the 2025-26 regular season through 2026-04-12. These two as_of windows (as_of.estimator_a, as_of.estimator_b) are printed inside the module itself and are not the same population; that distinction is kept separate throughout this note.

nba_form_curves.json carries no back-to-back, rest, or schedule field in either its insights or showcase build, so it contributes nothing here. nba_consistency_profiles.json (as_of 2026-04-12) does not condition its coefficient-of-variation numbers on rest either, but its own caveat and not_this fields explicitly flag rest as an uncontrolled variable in that module, consistent with the treatment below.

3 Method

The historical SFT source multiplied each team-season's back-to-back frequency by -1.73 and labeled that product a credible points-per-100 offensive-rating tax. That interpretation is unsupported because the anchor came from average scoring margin, not offensive rating. Its team ordering is only a rescaling of back-to-back frequency. Separately, schedule_density.json reports a raw -0.315 box-composite-per-36 difference for back-to-back versus its own rested baseline. That baseline requires at least two rest days and no compression, while the mechanism ledger compares zero rest with at least one day; these are different cohorts and should not be fused into one tested effect.

The rest-state margin test behind the -1.73 anchor compares average scoring margin on zero rest days (a back-to-back) against average margin on one or more rest days, within one corpus of player boxscores. It is not a controlled experiment: the schedule-maker chooses which games fall on a back-to-back, and travel, opponent quality and home-away patterns are not held fixed between the two rest states.

LBI is defined as LBI_a = the largest, over a team's roster, of win probability with a given player minus win probability without that player (Elo on/off), and LBI_b = the largest, over a team's roster, of win rate while a given player was active minus win rate while that player was missed (raw record). Agreement is flagged true only when the two estimators name the same player for a team. Because estimator_a draws on 2024-25 and estimator_b draws on 2025-26, a match or mismatch between them is a directional cross-check across two different one-season samples, not a paired measurement of the same games.

4 Results

The first two tables show the published scoring-margin and raw per-36 rest comparisons. The third lists team-season back-to-back exposure and the separate per-36 descriptive rescaling; it withholds the unsupported offensive-rating tax. The remaining tables show LBI's two estimators.

The two public rest comparisons both point toward lower recorded outcomes with less rest, but they measure different outcomes and use different rested baselines. The scoring-margin receipt does not validate an offensive-rating tax. Team-season back-to-back frequencies can still be compared directly.

The Load-Bearing Index results below rank the same 30 teams under each estimator separately. Only 1 of 30 teams is named by both estimators (IND, Pascal Siakam), an agreement rate of 0.0333 (agreement_summary.n_agree over agreement_summary.n_teams_both_estimators).

CHA, LAC, MIL and DET each appear in the estimator B top five while sitting outside the estimator A top five for the same team, which illustrates that the two estimators frequently disagree on magnitude as well as on which player is named.

5 Robustness and what would falsify this

The validation ledger records two negative zero-rest-minus-rested average scoring-margin differences, -1.73 (n=4732, p=0.005645490426098632) and -1.955 (n=7192, p=0.0001174325580081608). Both share one corpus tag, and their row overlap is unrecorded, so the second is not an independent out-of-sample replication. They do not measure offensive rating. The published SFT offensive-rating variant is under review; a fresh possession-based receipt would be needed to support that unit.

A team-by-schedule interaction analysis would test whether the observed margin association differs by team. No such test is published. The historical SFT ranking simply rescales each team's back-to-back frequency, so it cannot establish which team is more fatigue-prone.

For LBI, a robustness check would run both estimators on the same season for the same 30 teams; the agreement rate would be expected to rise if the underlying signal were estimator-independent. At 1 of 30 (3.33 percent) across two different seasons, the current data does not support treating either estimator's top-named player as validated. Running estimator B on the 2024-25 season, matching estimator A's window, would be the natural next check.

6 Limitations

This note does not establish a team-specific or causal fatigue effect. The source rest receipt measures scoring margin, while the published SFT variant mislabeled its derived values as offensive rating; that variant is under review. The separate per-36 box composite uses another rested baseline and is unadjusted for roster, opponent, minutes, and venue. The two LBI estimators remain associational and cover different NBA seasons.

• The historical SFT numerical ranking is a constant times back-to-back frequency. It is not a validated points-per-100 offensive-rating ranking; compare the supported back-to-back frequencies directly.
• The two b2b_rest_penalty runs (n=4732 and n=7192) share one corpus tag and the overlap between their rows is not recorded, so they are not two independent samples; rest days are chosen by the schedule-maker rather than assigned at random, so either run is an association, not a randomized comparison.
• The two LBI estimators cover different seasons (2024-25 versus 2025-26 through 2026-04-12), so their 1-of-30 agreement is cross-season corroboration, not a paired estimate.
• Both measures aggregate to the team level and do not adjust for roster changes, opponent strength, minutes distribution, or blowout-driven lineup substitutions.
• Estimator A publishes no game-count denominator, so its ranking cannot be weighted by sample support the way estimator B's active and missed game counts allow.

7 How to read this on the site

Read the source rest-margin receipt and raw schedule-density rows alongside this paper. The historical SFT module and chart retain under-review offensive-rating values for audit, not as current performance claims; use its back-to-back counts and frequencies for descriptive schedule comparison. The nba-schedule-compression-profile analysis is a different summary of schedule shape. The LBI estimators should be read with their separate season windows and player support counts.