deep-rapm

Regularized Adjusted Plus-Minus (RAPM) for NBA possession data — analytical ridge regression with optional recency weighting.

pip install deep-rapm

---

Overview

RAPM estimates each player's contribution per 100 possessions, controlling for the other nine players on the court. This package provides:

• Possession collection — pull and cache play-by-play data from the NBA Stats API
• Player metadata — build a player vocabulary with position information
• Analytical RAPM — exact ridge regression via the weighted normal equations
• Rolling RAPM — incremental Gram matrix updates for efficient time-series estimates

---

Data pipeline

Step 1 — collect possessions (~10 min per season):

collect-possessions --season 2022-23 --output-dir data/2022-23
collect-possessions --season 2023-24 --output-dir data/2023-24

Step 2 — build player vocab and position table:

collect-players --seasons 2021-22 2022-23 2023-24

Produces data/player_vocab.parquet and data/players.parquet.

---

Fitting RAPM

CLI

Season mode (uses pre-collected parquets):

solve-rapm                                    # 5 training seasons, alpha=2000
solve-rapm --seasons 2021-22 2022-23 2023-24  # specific seasons
solve-rapm --alpha 1000                       # tune regularisation
solve-rapm --half-life 365                    # recency weighting (1-year half-life)
solve-rapm --output-dir runs/rapm             # custom output directory

Date-range mode (auto-fetches and caches games from the NBA API):

solve-rapm --from-date 2024-10-01 --to-date 2025-04-15
solve-rapm --from-date 2023-10-01 --to-date 2025-04-15 --half-life 180

Output is saved to checkpoints/rapm/rapm.parquet and rapm_summary.json.

Python API

from pathlib import Path
from deep_rapm import fit_rapm, load_rapm

# Season mode
results = fit_rapm(
    data_dir=Path("data"),
    seasons=["2021-22", "2022-23", "2023-24"],
    player_vocab_path=Path("data/player_vocab.parquet"),
    player_table_path=Path("data/players.parquet"),
    alpha=2000,
    output_dir=Path("checkpoints/rapm"),
)

# Season mode with recency weighting (1-year half-life)
results = fit_rapm(
    data_dir=Path("data"),
    seasons=["2021-22", "2022-23", "2023-24"],
    player_vocab_path=Path("data/player_vocab.parquet"),
    player_table_path=Path("data/players.parquet"),
    alpha=2000,
    half_life_days=365,
    output_dir=Path("checkpoints/rapm"),
)

# Date-range mode
results = fit_rapm(
    data_dir=Path("data"),
    from_date="2024-10-01",
    to_date="2025-04-15",
    player_vocab_path=Path("data/player_vocab.parquet"),
    player_table_path=Path("data/players.parquet"),
    alpha=2000,
    half_life_days=180,
    output_dir=Path("checkpoints/rapm"),
)

# Load previously saved results
results = load_rapm(Path("checkpoints/rapm"))

qualified = results[results["qualified"]]
print(qualified.nlargest(10, "rapm")[["player_name", "orapm", "drapm", "rapm"]])

Output columns

All values are per 100 possessions.

Column	Description
orapm	Offensive RAPM — points added per 100 offensive possessions
drapm	Defensive RAPM — points prevented per 100 defensive possessions (positive = good defender)
rapm	Total RAPM = orapm + drapm
n_off / n_def	Offensive / defensive possession counts
qualified	True if ≥ 100 possessions in each role

Key parameters

Parameter	Default	Description
alpha	2000	Ridge penalty — higher shrinks estimates toward zero
half_life_days	None	Half-life for recency weighting (days). None = equal weights
min_poss	100	Minimum possessions each role to be flagged as qualified

Sample output (2018-19 through 2022-23, alpha=2000)

Player                  ORAPM   DRAPM    RAPM
Nikola Jokić            +7.74   +1.94   +9.68
Joel Embiid             +4.44   +4.56   +9.00
Stephen Curry           +6.09   +2.29   +8.38
Giannis Antetokounmpo   +4.33   +4.03   +8.35
LeBron James            +6.01   +2.03   +8.04
Alex Caruso             +0.96   +6.24   +7.20
Rudy Gobert             +0.20   +6.28   +6.48
Damian Lillard          +7.44   -0.52   +6.93

---

Rolling RAPM

fit_rolling_rapm fits RAPM at a sequence of evaluation dates using incremental Gram matrix updates — instead of rebuilding $X^\top W X$ from the full possession history at every date, it maintains the normal equations as running state and advances them forward in time. Each date step costs $O(k \cdot P^2)$ where $k$ is the number of new possessions (≈1,500/day) vs $O(n \cdot P^2)$ for a full recompute — roughly 650× fewer floating-point operations per step.

Weights combine exponential recency decay with a competition weight that down-weights blowout possessions:

$$w_i = 0.5^{\text{days_ago}_i / H} \cdot \exp!\left(-\left(\tfrac{|\text{score_diff}_i|}{\sigma}\right)^2\right)$$

CLI

python rolling_rapm.py --step-days 7 --half-life 365 --top 20 --ci-window 12 --output rolling_rapm.png --cache rolling_cache.parquet

Python API

from pathlib import Path
from deep_rapm import fit_rolling_rapm

df = fit_rolling_rapm(
    data_dir=Path("data"),
    seasons=["2022-23", "2023-24", "2024-25", "2025-26"],
    player_vocab_path=Path("data/player_vocab.parquet"),
    player_table_path=Path("data/players.parquet"),
    step_days=7,
    half_life_days=365,
    alpha=2000,
)
# df columns: date, player_id, player_name, orapm, drapm, rapm, n_off, n_def
print(df[df["date"] == df["date"].max()].nlargest(10, "rapm"))

Rolling RAPM parameters

Parameter	Default	Description
step_days	7	Days between evaluation dates
half_life_days	365	Recency weighting half-life (days)
alpha	2000	Ridge penalty
warmup_days	180	Skip first N days (insufficient data)
min_poss	100	Min possessions to include a player at a given date

---

Model

We model possession-level outcomes using a ridge-regularized linear model over player participation.

Let:

• $y_i \in \mathbb{R}$ denote the outcome for possession $i$ (e.g., points scored),
• $X \in \mathbb{R}^{n \times 2P}$ be the design matrix,
• $\beta \in \mathbb{R}^{2P}$ be player coefficients.

Each row $X_i$ encodes the 10 players on the court:

• 5 offensive players (indicator = 1 in offense block),
• 5 defensive players (indicator = 1 in defense block).

Thus, each row of $X$ contains exactly 10 ones.

We partition coefficients as:

$$\beta = \begin{bmatrix} \theta^{\text{off}} \ \theta^{\text{def}} \end{bmatrix}, \quad \theta^{\text{off}}, \theta^{\text{def}} \in \mathbb{R}^P.$$

---

Linear Model

We model:

$$y = \mu \mathbf{1} + X \beta + \varepsilon,$$

where:

• $\mu \in \mathbb{R}$ is an intercept (not penalized),
• $\varepsilon \sim (0, \sigma^2 I)$.

Equivalently, at the possession level:

$$\hat{y}i = \mu + \sum{j \in \text{off}(i)} \theta^{\text{off}}j + \sum{k \in \text{def}(i)} \theta^{\text{def}}_k.$$

---

Weighted Ridge Estimation

To incorporate recency or importance weighting, let:

$$W = \mathrm{diag}(w_1, \dots, w_n), \quad w_i > 0.$$

We estimate parameters via:

$$\min_{\mu, \beta} ; (y - \mu \mathbf{1} - X \beta)^\top W (y - \mu \mathbf{1} - X \beta) + \lambda |\beta|_2^2,$$

where:

• $\lambda > 0$ is the ridge penalty,
• the intercept $\mu$ is not penalized.

---

Closed-Form Solution

Define the weighted mean:

$$\bar{y}_w = \frac{\sum_i w_i y_i}{\sum_i w_i}, \quad \bar{X}_w = \frac{\sum_i w_i X_i}{\sum_i w_i}.$$

Center the data:

$$\tilde{y} = y - \bar{y}_w, \quad \tilde{X} = X - \bar{X}_w.$$

Then:

$$\hat{\beta} = (\tilde{X}^\top W \tilde{X} + \lambda I)^{-1} \tilde{X}^\top W \tilde{y},$$

$$\hat{\mu} = \bar{y}_w - \bar{X}_w^\top \hat{\beta}.$$

---

Interpretation (RAPM)

We report player impacts scaled per 100 possessions:

$$\text{ORAPM}_j = 100 \cdot \theta^{\text{off}}_j, \quad \text{DRAPM}_j = -100 \cdot \theta^{\text{def}}_j.$$

The negative sign in DRAPM arises because:

• $\theta^{\text{def}}_j$ represents contribution to opponent scoring,
• strong defenders have $\theta^{\text{def}}_j < 0$.

Thus, higher DRAPM corresponds to better defense.

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Summary

Component	Role
Offense coefficients $\theta^{\text{off}}$	Increase scoring
Defense coefficients $\theta^{\text{def}}$	Decrease opponent scoring
Ridge penalty $\lambda$	Stabilizes estimates under collinearity
Weights $w_i$	Time-decay or importance weighting

---

License

MIT