METHODOLOGY

Offensive Estimated Plus/Minus from Dunks & Threes (off column). The offensive-side component of EPM — a RAPM-family estimator isolating individual offensive win-probability contribution from teammates and opponents. V3.0 uses the offensive component only to avoid encoding defensive signal in the Offensive Impact pillar. Deshpande & Jensen (2016) identify RAPM-family metrics as more predictive than box-score alternatives at equivalent sample sizes.

Full methodology is unpublished — no external peer review. Single-season estimates carry wider confidence intervals for players in system transitions or limited high-leverage minutes. The regression-to-prior can suppress historically extreme peaks. Combined with O-LEBRON and OBPM to reduce dependence on any single unpublished methodology.

Offensive component of LEBRON (BBall-Index). Measures offensive win-probability contribution with explicit luck adjustment for single-season shooting variance. V3.0 uses the offensive-side component only — prior versions used full two-way LEBRON, which encodes defensive signal and caused double-counting against the Defensive Impact pillar. Franks et al. (2016) establish the theoretical basis for luck-adjusted on/off estimation.

Despite luck adjustment, partially team-contaminated for primary offensive options in elite systems. The RAPM component depends on lineup frequency; infrequent lineup combinations produce estimates with higher uncertainty. Replacing full LEBRON with O-LEBRON removes the defensive channel but also narrows the signal to offensive contexts only.

Offensive Box Plus/Minus (Basketball-Reference). Offensive-side estimate of individual contribution per 100 possessions using box score inputs only. The most historically available offensive metric, with data from 1973-74 onward — essential for the 40-season backtest. V3.0 uses OBPM rather than full BPM to keep the Offensive Impact pillar free of defensive signal. Jewell et al. (JQAS) identify BPM as the box-score metric most robustly significant at high minutes loads; OBPM inherits this reproducibility advantage.

Box-score construction misses off-ball offensive contributions: spacing, screening, and movement without the ball. Does not adjust for teammate or opponent quality. Switching from full BPM to OBPM removes the defensive-side signal but reduces the pillar's ability to capture two-way contributors through this metric alone — the design intent, since Defensive Impact carries that channel separately.

Relative True Shooting Plus (BBall-Index). TS% relative to league average, adjusted for shot quality — location, contest level, and shot type — relative to the player's own shot distribution. A Rel TS+ of +5 means the player scores 5 points per 100 attempts above what an average player would score on the same shot diet. Raw TS% was dropped in v3.0 because it is already encoded inside O-EPM, O-LEBRON, and OBPM; Rel TS+ is retained at 60% because its difficulty-adjustment provides signal not captured in those composite inputs.

Proprietary adjustment methodology using discrete location and contest categories rather than continuous tracking data; within-category variance is treated as noise. Cannot fully resolve the creativity trade-off: a player who manufactures a high-quality contested mid-range off a screen and one who catches and shoots from the same spot receive similar credit, despite different generative difficulty.

Usage Rate interaction modifier (v1.6). Applied as a within-pillar multiplier: penalizes Shot Quality scores for high-volume seasons with below-average efficiency, and rewards efficient high-usage seasons. Addresses volume-scorer inflation — a player using 35%+ of possessions at below-average efficiency should not receive the same Shot Quality score as an equally efficient player at lower volume. Computed via linear regression of TS% on USG% within each K-means offensive archetype group. Raised from 10% to 40% pillar weight in v3.0 as TS% was dropped and USG interaction now serves as the second primary signal.

Modifier thresholds derived from backtest optimization, not external peer review. Does not distinguish forced high usage (team's sole offensive option) from self-selected volume — both receive equivalent adjustments at the same efficiency level. Edge cases near the penalty threshold may introduce minor discontinuities in scoring.

Defensive component of LEBRON (BBall-Index). Regression-adjusted and luck-adjusted — explicitly accounts for single-season opponent shooting variance that inflates raw on/off defensive metrics. Primary metric at 47% within the Defense pillar: its luck-adjustment framework handles team-context noise more reliably than raw RAPM components in high-minute, single-season samples (Franks et al., 2016). Normalized within BBall-Index Defensive Role peer groups to compare defenders against players in structurally similar assignments.

Partially team-contaminated despite luck adjustment — anchor bigs in strong defensive schemes can record inflated D-LEBRON through the team-defense halo effect. Does not capture deterrence: altered shots, off-ball positioning, and perimeter disruption are invisible to on/off methods. Byman (2023) demonstrates off-ball movement features dominate predictive defensive RAPM models (R²=0.848) — a dimension no current on/off estimator can access.

Defensive component of EPM (Dunks & Threes). RAPM-family estimator using regularized adjusted plus/minus to isolate individual defensive contribution from team context. Ranked as the most-trusted public defensive metric by EPM/RPM co-creator Steve Ilardi and first in a HoopsHype survey of approximately 30 NBA front-office executives (2024). Correlated with D-LEBRON (Pearson r ≈ 0.65) but captures independent variance — each metric identifies defenders the other systematically misses (Terner & Franks, 2021). Raised to 43% pillar weight in v2.6 to reflect growing external validation.

RAPM estimates require large samples to stabilize; single-season figures carry meaningful uncertainty for players in role or system transitions. Does not capture deterrence or off-ball positioning — the same structural gap as D-LEBRON. Full methodology is unpublished, the same transparency limitation as EPM in the Impact pillar. Correlation with D-LEBRON creates partial redundancy, though the independent variance each captures justifies retaining both.

Defensive Box Plus/Minus (Basketball-Reference). Box-score estimate of individual defensive impact per 100 possessions. Retained at minimal weight (10% within Defense pillar) solely as a Bayesian stabilizer — prevents D-LEBRON and D-EPM from overreacting to single-season lineup outliers in small samples. Franks, D'Amour, Cervone & Bornn (JQAS, 2016) establish that box-score inputs fail to predict individual defensive RAPM at population level, which is why it is excluded from higher weighting.

Systematically biased against players assigned the hardest defensive matchups — guarding elite scorers produces worse DBPM through proximity effects, not worse defense. Jewell, Page & Reese (JQAS) confirm box-score defensive counting stats show null predictive significance at the high minutes loads that characterize the APEX qualified pool. Used only as a stabilizer; never a meaningful signal in isolation at this player tier.

Assist Percentage — estimated percentage of teammate field goals a player assisted while on the floor. The most direct box-score proxy for primary creation volume. Retained in v1.7 after backtest confirmed net contribution: removing AST% over 40 seasons produced a net loss of 1 correct MVP prediction. Per Deshpande & Jensen (2016), AST% provides complementary signal to RAPM-based estimates in separating playmaking impact from scoring impact — a distinction the offensive composites partially conflate.

Does not distinguish creation quality — a simple two-man game dump-off and a contested skip pass for a corner three count identically. Structurally rewards players in ball-movement systems over equally skilled creators in isolation-heavy offenses, where fewer touch opportunities reduce assist volume. Within-archetype normalization partially corrects for system context but does not resolve stylistic asymmetries in assist accumulation.

Assist-to-Turnover ratio — assists generated per turnover committed. Captures decision-making efficiency alongside creation volume: a player with 8 assists and 4 turnovers (2.0) is scored below one with 6 assists and 1.5 turnovers (4.0) despite higher raw volume. Separates efficient creators from high-volume ball-handlers who inflate AST% at the cost of ball security. Combined with invTOV, provides a two-dimensional view of playmaking discipline within the pillar.

Structurally favors non-primary handlers and conservative passers over high-volume creators in fast-paced offensive systems. A lead point guard with full-possession responsibility faces inherently more turnover pressure per touch than a secondary playmaker with limited ball-handling duties — the ratio format amplifies this asymmetry. Within-archetype normalization mitigates but does not fully resolve this structural difference.

Inverted Turnover Percentage — TOV% inverted so that higher values indicate better ball security. Applied as a penalty signal: players with disproportionate turnover rates relative to their archetype peer group receive a lower pillar contribution. Complements AST/TOV by penalizing absolute turnover rate, preventing high-AST% players with heavy turnover loads from being fully rewarded on volume alone. Weight reduced from 20% (v2.x) to 15% in v3.0.

Highly correlated with usage rate by construction — primary ball-handlers face the most turnover exposure per possession as a structural feature of their role, not purely a decision-making signal. High-USG playmakers are penalized more steeply than spot-up shooters even at equal decision-making skill levels. Within-archetype normalization is the primary mitigation.

Free throw attempt rate — free throw attempts per field goal attempt. Moved to Creation & Playmaking in v3.0: foul-drawing is a shot-creation and aggression proxy, not a shooting-efficiency metric (which is how it was classified in v2.x). A stable, repeatable individual skill tied to driving aggression and body control. Kubatko et al. (2007) confirm FTA rate as a persistent offensive differentiator across seasons — players who draw fouls at a high rate are generating offensive creation opportunities independent of field goal results.

Partially reflects playing style rather than pure creation quality. Free throws drawn on three-point foul-baiting attempts inflate FTA/FGA without representing genuine drive-based creation. High FTA/FGA combined with below-average FT% reduces net scoring value from those possessions; this interaction is captured upstream by the O-EPM and O-LEBRON composites but not within this pillar directly.

Total Rebound Percentage — estimated percentage of available rebounds (offensive + defensive) secured while on the floor. The sole Physical Contribution metric following the v1.7 audit that removed STL% and BLK% on Jewell et al. (JQAS) null-significance grounds. Pillar weight raised from 8% to 10% in v3.0. Per Franks et al. (2016), total rebounding is among the most position-independent predictors of possession gain at the individual level. Above-average REB% at guard and wing positions represents genuine physical versatility — contested board capacity that translates across positional assignments.

Structurally advantages centers and power forwards with greater rebound proximity by design. K-means archetype normalization significantly mitigates this by grouping rim-dominant bigs together, measuring their elite REB% against each other rather than against perimeter players. Within-cluster position variance means the bias is reduced, not eliminated. True positional versatility — switchability, transition contributions, multi-assignment defensive coverage — is not captured by REB% alone and remains a V3 scope item.

Defensive Win Shares (Basketball-Reference). Distributed team defensive efficiency to individual players based on playing time and box-score inputs — blocks, steals, defensive rebounds — using the Dean Oliver win-shares framework.

Jewell, Page & Reese (JQAS) demonstrate null predictive significance for box-score defensive counting stats at high minutes loads. DWS inherits this limitation — it distributes team defensive credit via the same null-signal metrics, meaning it primarily reflects assignment opportunity and team quality rather than individual defensive impact. D-LEBRON's luck-adjusted on/off framework is a more direct individual signal.

Steal Percentage — percentage of opponent possessions ending in a player steal while on the floor. Intended to proxy for perimeter defensive activity and anticipation.

Jewell et al. (JQAS) find null significance at the high minutes threshold where APEX operates. Steals are strongly influenced by defensive scheme, opponent ball-handling quality, and assignment — a help-side defender positioned in passing lanes records more steals than an equal-quality on-ball defender assigned to the screener. The metric primarily tracks opportunity and scheme, not individual defensive skill. Additionally, steals carry a non-trivial luck component (tempo, opponent decision-making) that cannot be adjusted at the box-score level.

Block Percentage — percentage of opponent two-point field goal attempts blocked while on the floor. Intended to capture rim protection and deterrence contribution.

Jewell et al. (JQAS) — same null-significance finding. More critically, blocks are a proxy for shot alteration, not a measure of it. Byman (2023) demonstrates that off-ball movement features dominate predictive individual defensive RAPM models at R²=0.848, while block counts have negligible marginal contribution. Retaining BLK% created a partial double-count with D-LEBRON for elite rim protectors while failing to capture the actual deterrence effect (altered-but-not-blocked shots) that represents the primary defensive value of elite rim protectors.

Defensive On/Off differential — team defensive rating when the player is on the floor minus when off. Used at 85–90% of the Defense pillar weight in v1.6–v1.7 before being superseded by D-LEBRON.

Severely team-contaminated without adjustment: a dominant defender on a team with strong second-unit defenders records a flat or negative DefOnOff; a mediocre defender surrounded by weak backups records a strong positive. Franks et al. (2016) identify this as the fundamental problem with raw on/off metrics. D-LEBRON's luck adjustment was specifically designed to address this; once D-LEBRON was integrated and validated, raw DefOnOff was removed from scoring and retained only as player-card context.

Dynamic and Regressed Kentucky Outcomes (Sill, 2010 framework). A Bayesian Kalman-filter metric designed to stabilize player estimates rapidly and project future performance while accounting for lineup context.

The DARKO creator explicitly notes the metric "cannot meaningfully be used in backwards-looking MVP debates" — its Kalman filter pulls outlier peaks toward the long-run prior, compressing the very multi-sigma seasons that APEX is designed to identify. A dominant 2021-22 Jokić season or a 2024-25 SGA peak is exactly the kind of outlier DARKO suppresses by design. The metric's primary purpose is projection and rapid stabilization for in-season use, not retrospective season assessment. EPM (RAPM-family, no Kalman suppression) serves the Impact pillar's retrospective evaluation goal more accurately.