HoopQ

What it is. Regularized Adjusted Plus-Minus, the standard "all-in-one" basketball impact metric. Each player gets two coefficients: an offensive rating (points contributed per 100 possessions when they're on offense) and a defensive rating (points conceded per 100 possessions when they're on defense, where more negative is better). Total RAPM = ORAPM − DRAPM.

How it's computed. For every NBA possession from 2000-01 through 2025-26 (5.49M possessions across 30,815 games), we record the 5-on-5 lineup and the points scored. A sparse linear regression then solves for each player's marginal contribution while controlling for who they shared the floor with. We use a Bayesian prior built from each player's box-score profile (per-100 stats: points, assists, turnovers, rebounds, steals, blocks, etc.) so that low-minute players shrink toward what their box stats predict rather than toward zero. Ridge regularization strength (λ) was chosen by 3-fold cross-validation on held-out possessions.

Strengths. Captures impact you can't see in the box score: screens, spacing, defensive positioning. Multi-season pooling reduces single-season noise by ~10× (the GOAT-era list is dominated by Jokić, LeBron, Embiid, Chris Paul, Curry, Giannis, Kawhi, Garnett, Luka, Nash, consensus-correct).

Limitations. No causal claim, RAPM is correlational. Small-sample players (Wembanyama, Chet Holmgren: 2 seasons each) still appear in the top 25 with wide uncertainty. Doesn't separate role from talent (a great defender on a great defense gets partial credit for teammates' help).

What it is. A deep-RL player rating with two complementary flavors per side, both in points per 100 possessions (RAPM units):

• Off / Def (action), sum of per-action-bucket contributions. Each event is credited to its actor; tells you which buckets (3pt pullups, rim finishes, blocks, rebounds, etc.) drove the value.
• Off / Def (presence), neural ORAPM / DRAPM via a leave-one- out lineup swap on the trained Q model. Captures value not tied to any single event: spacing, screen-setting, rim deterrence, screen navigation. Closer analog to RAPM.

How it's computed. Each NBA possession is an RL episode; each event (shot, rebound, turnover, foul) is a step. A neural network learns Q(state, action, player), the expected remaining points in the possession given the game context, action, and actor. Player identity is a learned embedding; lineups are pooled by a 4-head self-attention layer. Action ratings = average advantage (Q with actual embedding − Q with league-average embedding) × usage per 100 possessions, summed per side. Presence ratings = average Q change at the start of each possession when the player is replaced with a neutral baseline (the mean of all real player embeddings), averaged across every possession they were in the off / def lineup, × 100.

Empirical-Bayes shrinkage. Per-100-poss rates have high variance for low-sample players, so every rating is shrunk by n / (n + κ) with κ = 8000 on-floor events (~1 season for a half-time player). Veterans keep ~90% of their raw rating; small-sample noise players collapse toward 0.

How to read it. Presence is the headline number; action shows where the value came from. For elite defenders the two diverge, Def (action) is mostly blocks/steals/rebounds, Def (presence) includes the value of just being out there. Player embeddings also cluster meaningfully (Curry near Lillard near Trae; Jokić near Sabonis), so the model isn't just memorizing role.

What it is. A DARKO-style Kalman filter over per-game Q-Rating, producing a smoothed skill trajectory across every game a player has played. The observation is per-game Q-Rating in points per 100 team possessions, not a Game Score composite: it's the neural action-bucket decomposition redistributed per event, so the trajectory tracks actual skill rather than box-score production.

How it's computed. Each season's per-player action-bucket coefficients are decomposed into per-event credits, aggregated per (player, game) as a per-100 rate, and fed one at a time into a Kalman filter. Aging drift comes from a smoothed age curve fit on all observations pooled by age. The rookie prior is seeded from a draft-slot prior (median career-year-1 Q-Rating by pick). Career-average presence is folded in as a season-constant so elite defenders and off-ball creators surface at their real magnitudes.

How to read it. The bold line is the posterior mean; the shaded band is a ±1.96σ 95% confidence interval; small dots are per-game observations. For players drafted since 2000-01 the x-axis is career game number so trajectories are apples-to-apples across eras; for earlier careers the axis falls back to date since our data window starts mid-career. The Compare-With input overlays a second player.

Limitations. Career-average presence gives the trajectory its right magnitude but is constant within a career, so within-season presence changes (injury, role shift) don't move the line beyond what action-bucket noise contributes. Rookies have wide bands until they've played enough games.

What it is. A heterogeneous graph neural network over each 5-vs-5 possession, treated as a 10-node graph with three edge types: within-offense (chemistry among the offensive 5), within-defense (chemistry among the defensive 5), and cross (offense-vs-defense matchup edges). Two hops of message passing let signal like "my teammate has a favorable matchup, which frees me up" propagate through the graph.

How it's computed. Node features are learned player embeddings plus a role token (offense or defense). Each layer aggregates three separate messages (within side, within side, cross) into an update. Two layers are applied, node representations are pooled by side, and a standard Q head predicts expected reward on the possession. Downstream artifacts: per-player GNN presence via leave-one-out lineup swaps, a per-player synthetic matchup sweep (X vs candidate defender in an isolated 5-vs-5 context), and team-vs-team predictions aggregated over each team's most-used 5-man lineups.

Where it shows up. The Matchup Influence table on every player profile (defenders whose presence lowers or raises the player's expected Q per possession), the vs-team preview widget on team profiles, and the GNN presence stat card on the Lineup Sim page.

Limitations. Play-by-play has no per-shot defender attribution, so the matchup signal is on-court concurrence not literal 1-on-1 assignment. Same-era filtering restricts candidate defenders to seasons a player actually played in so anachronistic pairings don't populate the table.

What it is. Extra points per 100 possessions a specific pair generates (offense) or prevents (defense) when they're on the floor together, beyond what their individual RAPMs predict. A measure of two-player chemistry / fit / synergy.

How it's computed. Same ridge regression as RAPM but with an extra binary feature for every player pair that played enough possessions together. The pair coefficient is what's left after the individual player effects are accounted for: the "team-up bonus." Positive on offense = synergy. Negative on defense = synergy (less points allowed).

Limitations. Identifiable pairs need a meaningful number of possessions together; one-game cameos shrink to zero. Pair coefficients are still correlational, not causal, and can't separate "lineup synergy" from "shared strategy" or "shared coach.")

What it is. A distributional-RL companion to the Q-Rating model. For every offensive event, we predict the per-event reward distribution above a no-actor baseline Q(s, a, teammates, defenders, context). The per-player skill advantage is the mean of that residual, points per event the actor adds beyond what a league-average player would have produced in the same situation. The 95% CI shown in the Player Profile is a proper SE-of-the-mean confidence interval, not the spread of individual outcomes.

How it's computed. Two-stage: first a baseline mean-Q model is trained with the actor masked out of the offensive lineup; then a Quantile-Regression DQN with 51 quantile heads is fit (pinball Huber loss) on advantage = actual return − baseline prediction. Per-player aggregation averages the distributional mean across each player's events.

Strengths. Interpretable units (pts/event) and clean residualization that removes the action-outcome variance dominating a raw RTG estimate. Top players by mean advantage are consistently the league's high-usage per-event creators.

Limitations. Per-event efficiency systematically undersells cumulative creators (Jokić, Giannis show small positives) because action-by-action credit can't capture possession-spanning value the way RAPM does. Best read alongside RAPM, not as a replacement.

What it is. A LightGBM classifier that estimates expected FG% for each shot given the shot location, action type, and shot-clock state. Per-player it aggregates to two axes: Shot Making (actual points minus expected points, how much the player beats their location-baseline) and Shot Selection (mean xFG per attempt, how high-quality the shots they take are on average).

How it's computed. Gradient-boosted trees trained on every field-goal attempt with the shot's location coordinates, primary action bucket, and clock features. Per-shot xFG is used to compute per-player pts and selection aggregates, then compared against actual pts scored on those shots.

How to read it. Shot Making of +150 pts means the player scored 150 more points on their attempts than xFG expected. Shot Selection of 0.55 means the average shot they attempted had a 55% baseline FG probability. Two axes let a low-volume rim finisher (high selection, modest making) and a high-volume creator taking hard shots (lower selection, positive making) end up on different quadrants.

Limitations. The model doesn't see defender proximity or contested-vs-open state (no tracking data). That context lives in the Possession Value transformer instead.

What it is. A prefix-only transformer over possession event sequences that predicts the expected reward of the possession-ending event given every event that preceded it (dribbles, screens, passes, off-ball actions). Publishes per-player Shot Luck as actual reward minus predicted reward.

How it's computed. The transformer reads the sequence of events in a possession, produces an expected reward for the final event conditioned on the prefix. Actor attribution walks back from the possession end to find the shot-taker, so rebounds pass credit through to the missed shot's shooter and and-one free throws roll into the generating shot. A calibration constant is applied at scoring time to keep the metric zero-centered on possession totals since the training target was last-event reward.

How to read it. Positive Shot Luck = player hit shots or avoided turnovers better than the model predicted given the possession context. Distinct from xFG because the model sees the full sequence of dribbles/screens/passes, not just where the shot went up. A contested pull-up after 22 seconds of dribbling and a wide-open catch-and-shoot get different difficulty estimates.

Limitations. Currently trained on 2024-25 only; multi-year retrain queued. The metric captures per-possession-context beat over baseline but doesn't distinguish shot-making from decision-making the way OPE does.

What it is. Per-player distribution over 12 offensive "options" inferred heuristically from the action stream: pnr_handler, pnr_finisher, isolation, post_up, cut, putback, spot_up, off_screen, transition, free_throw, rebound, other. Tells you what a player does, not how well they do it. Click a player for offensive distribution + per-option success (pts/action) + defensive rates per 100 def-poss (steals, blocks, fouls).

How it's computed. Each event is labeled by a rule combining action bucket, is_assisted, possession step, and seconds-into-possession. Isolation vs PnR handler split uses the assisted flag (assisted pullup/drive → PnR; unassisted → isolation). Defensive credits are computed separately: stealer/blocker via player3_id from steal/block events, normalized by the player's defensive possessions on the floor.

Limitations. Heuristic, not learned. Without tracking data, "iso vs PnR" is an imperfect proxy; missed shots default to isolation since assist credits only attach to makes. Transition uses a clock-only proxy (no start_type available in the possessions parquet). Use it for shape/role inference, not for skill grading.

What it is. Win Probability is a gradient-boosted classifier that predicts the home team's chance of winning from (period, clock, score margin, possession side, off/def lineups). Win Probability Added (WPA) is the per-event change in WP attributable to the actor, split into offensive and defensive halves and broken down by action bucket. Powers the Clutch / WPA page.

What it is. 1-, 2-, and 3-year-ahead forecasts of each per-100 metric (points, assists, rebounds, etc.) using DARKO-style aging curves and a Kalman-flavored update that blends a player's own trajectory with a prior built from comparable players at the same age. Surfaced on the Projections page and in the Player Profile career trajectory chart.

What it is. Each player's action-frequency vector projected into a low-dim space, then used to find their nearest neighbors in style (not in impact). Useful for "who plays like X?" comparisons. Distinct from the Play Types view: that one shows the raw distribution, this one shows similarity.

What it is. For each (player, action, game-context) triple, the log-ratio of the player's frequency against the league baseline, what actions a player chooses reveals their inferred reward weights. Reveals e.g. DeMar DeRozan's strong midrange preference, Curry's elevated clutch-3 preference. State contexts: clutch, blowout, early-clock, late-clock, transition, normal.

What it is. For each team, exhaustively scores every 5-man lineup over its rotation players and returns the best by predicted net rating.

How it's computed. Lineup score = sum of the 5 players' Q-Rating presence (Off − Def, neg-good convention) + offensive pair chemistry summed over all 10 pairs − defensive pair chemistry summed over all 10 pairs. Q-Rating presence is the leave-one-out swap on the trained Q model with attention pooling over lineups (closer analog to RAPM than the action decomposition).

What it is. A team-season summary of the roster's Q-Rating quality, centered so the sign is meaningful. Raw team Q-Rating is a possession-weighted sum of every roster player's Q-Rating (action + presence). Detrended = raw minus the season league mean. Positive means the roster grades above the league that year, negative means below.

How it's computed. For each (team, season): weighted mean over the roster of each player's total-impact (action + presence − opponent-side presence, good-direction on both sides), weighted by that player's possessions with that team that year. The result is multiplied by 5 to put it on per-100-poss scale (five players share each possession). Detrending subtracts the season-wide league mean so ~50% of teams end up on each side of zero.

How to read it. Semantically parallels Team RAPM (already zero-centered). +2 means "roster grades ~2 pts/100 poss above the league that year," −3 means "3 below." The trajectory chart on the team page shows total plus off/def breakdown, with Team RAPM overlaid as a reference line.

Limitations. Aggregates the whole roster equally by possessions played, so it doesn't distinguish starter-heavy vs bench-heavy usage. Presence uses career-average magnitudes broadcast across seasons, so team-season snapshots reflect the long-run quality of the players on the roster rather than that specific year's form.

What it is. Per (team, season, action bucket) rate of how much value each team generated from each of the ~30 offensive and defensive action buckets, centered against the season league mean per bucket. Surfaces two views on the team page: "Season strengths" ranks the current-season buckets from most above to most below league, and "By season" shows a heatmap of every season the team has on record.

How it's computed. For each (team, season, bucket): sum every roster player's per-bucket Q-Rating coefficient weighted by their possessions with that team that year, divided by total team possessions. Detrend by subtracting the season league mean per bucket. Green cells indicate the team was above league on that bucket that year; red indicates below.

How to read it. Bucket rows in the heatmap are sorted by how identity-defining the bucket is over the team's history, so signature strengths and weaknesses float to the top. Low-volume specialty buckets (3pt corner pullup, midrange post hook, foul-take, etc.) swing more than high-volume ones (rim finishes, midrange catches).

Limitations. Only sees action-level credit, not presence. Two teams with identical action profiles but different rim protection would look identical here even though their defense is not.

What it is. A per-event marginal: how much value did this player's actual decisions add above what the league-average action distribution would produce in the same state context? Headline number is the doubly-robust (DR) marginal in points per event. Three estimators reported: importance sampling (IS), self-normalized IS (WIS), and doubly-robust (DR). DR is the headline.

How it's computed. For each event we have (state, observed action, reward). Behavior policy π_b(a|s,p) is a learned neural classifier. Target policy is the state-conditional empirical league action frequency (no player conditioning), bucketed into six contexts: clutch / blowout / early-clock / late-clock / transition / normal. IS weight = π_target(a|s) / π_b(a|s,p), clipped at 20. DR baseline = Σ_a π_target(a|s) × Q_calibrated(s, a, neutral_player), where Q is per-action-bucket calibrated via post-hoc OLS so each bucket's predicted Q matches observed event-reward expectation. Marginal = observed_avg_reward − DR_value. 95% CI is from 200-sample bootstrap.

What this measures. Per-event scoring efficiency relative to league policy in the same situation. Positive = player's actual decisions outperform league defaults in their state mix.

Limitations. Per-event efficiency, not total impact: pure passers (Jokić, CP3) and defensive stars rank lower than their RAPM would suggest because the metric only measures the per-shot/per-action value-add, not playmaking or defense. Low-event samples (rookie years, partial seasons) have wide CIs; the lower-bound column is the statistically distinguishable view.

What it is. Per-player aggregate of how often the action they chose matches the action with the highest predicted Q from the Q-Rating model. Three views: top-1 rate (chose the best action), top-3 rate (chose one of the top three), and avg rank percentile (1.0 = always optimal, 0.0 = always worst).

How it's computed. For each event the actor took action a in state s, we evaluate Q(s, a', actor) for every valid action a' in the action vocabulary, compute the rank of the chosen action among all alternatives, and report the percentile = 1 − rank/(N_actions − 1). Per-player aggregation averages over all their decisions.

Limitations. "Best" is defined by the Q model, so this measures agreement with Q, not absolute optimality. Players whose role pushes them into low-Q decisions (e.g. forced isolation possessions late-shot-clock) will score lower even if their decision was the best of bad options.

What it is. A neural classifier that learns π_b(a | state, player): which action does this specific player tend to choose in this specific state? Used as the denominator in the OPE importance-sampling weights.

How it's computed. Same lineup-attention encoder as the Q model, but the output head is a softmax over the action vocabulary instead of a scalar Q. Trained on cross-entropy against the observed action; achieves ~38% top-1 and ~68% top-3 accuracy on held-out events.

Why we care. Without a learned π_b, IS weights would have to fall back to a uniform action prior, which inflates variance dramatically for high-volume players whose action mix is far from uniform.

RAPM-style numbers are in points per 100 possessions. A +5 RAPM player is roughly +5 net points per 100 possessions compared to a league-average player on a neutral team. League scoring runs ~115 per 100, so +5 is genuinely elite (top-10ish in any given season). For defense, more negative is better: a −3 DRAPM player concedes 3 fewer points per 100 than average. QR-DQN skill advantage is in different units (points per event, not per 100 possessions). Play Types percentages are shares of a player's offensive actions; defensive rates are per 100 defensive possessions they were on the floor for.

NBA play-by-play covering the 2000-01 through 2025-26 regular seasons, 5.49M possessions across 30,815 games, parsed into per-event tuples with the 5-on-5 lineup, action, actor, and reward. Models implemented in scikit-learn (ridge with box-score prior, K-fold CV), PyTorch (Q-network with lineup attention, distributional QR-DQN, lineup GNN, prefix transformer for possession value, Kalman filter for career trajectories), LightGBM (win probability, expected FG%), and a closed-form Gaussian-Gaussian Bayesian solve for the RAPM prior step. Ratings regenerate end-to-end from raw play-by-play, no hand curation.