Effective Field-Goal Percentage (eFG%)

• Effective Field-Goal Percentage (eFG%) is a refined shooting efficiency metric that adjusts traditional FG% by valuing three-pointers at 1.5 times, offering a comprehensive performance measure.
• Advanced estimation techniques like Rao-Blackwellization, spatial point processes, and Bayesian hierarchies reduce variance and yield deeper insights into shot quality and strategic shot selection.
• eFG% is applied to assess shot selection, defensive impacts, temporal dependencies, and integrates deep learning to provide actionable insights for optimizing player and team performance.

Effective Field-Goal Percentage (eFG%) is a core metric in basketball analytics that extends traditional field-goal percentage by adjusting for the additional value of made three-point shots. As quantitative analysis of the sport has evolved with advances in player tracking, spatio-temporal data, and Bayesian spatial modeling, eFG% has emerged not only as a descriptive boxscore statistic but as a focal point for advanced research into shot efficiency, tactical optimization, and statistical inference. Recent developments leverage conditional estimators, spatial point processes, deep learning models, and time series analysis to provide deeper context for shot quality, selection, and defense, creating a more stable and predictive representation of player and team efficiency.

1. Definition and Classical Computation

Effective field-goal percentage modifies raw shooting percentage to reflect that three-point field goals are worth 1.5 times as much as two-point field goals. The standard formula is:

$$\mathrm{eFG\%} = \frac{\mathrm{FGM} + 0.5 \times \mathrm{3PM}}{\mathrm{FGA}}$$

where FGM is the total field goals made, 3PM is the made three-point field goals, and FGA is the total field goal attempts. This adjustment provides a more comprehensive measure of shot quality than FG% alone, particularly useful in comparing players or teams with varying shooting profiles, such as strong perimeter shooters versus high-volume post scorers (Shiiku et al., 6 Oct 2025).

2. Conditional and Variance-Reduced Estimation

Traditional FG% (and by extension, eFG%) implicitly treats all shot attempts as identically distributed Bernoulli trials, ignoring contextual and shot-specific factors. Research by Marty and Lucey introduces the Rao-Blackwellized FG% (RB-FG%) estimator, which leverages post-shot release probabilities computed from spatiotemporal trajectory data (entry angle, shot depth, left-right deviation) to reduce estimator variance (Daly-Grafstein et al., 2018). Under a Beta-Bernoulli hierarchical model:

• Each shot $X_i$ is modeled as $X_i \sim \text{Bern}(p_i)$, with $p_i \sim \text{Beta}(\theta v, (1-\theta)v)$.
• The RB-FG% estimator uses the conditional expectation:

$\text{RB-FG\%} = \frac{1}{N} \sum_{i=1}^N p_i$

Here, $p_i$ is the modeled probability of a make derived from detailed trajectory data. By Rao-Blackwellization, mean squared error of the estimator is reduced:

$$\mathrm{MSE}(\hat{\theta}_{RB}) \leq \mathrm{MSE}(\hat{\theta})$$

When extended to eFG%, incorporating per-shot probability and appropriate weighting for shot type yields a more stable and predictive measure, particularly valuable in low sample sizes or early-season estimation.

3. Shot Selection, Spatial Intensity, and Bayesian Point Process Models

The spatial patterning and selection of shot attempts have direct consequences for eFG%. A marked spatial point process framework models both the intensity (frequency) and mark (accuracy) of shot attempts across the court. The shot intensity is expressed as:

$\lambda(s) = \lambda_0 \exp\{ X(s)^\top \beta \}$

and shot success follows:

$$\text{logit}[\theta(s)] = \xi \lambda(s) + Z(s)^\top \alpha$$

Here, $\lambda(s)$ is the shot attempt intensity at location $s$, $X(s)$ are spatial covariates (e.g., shot type basis), $\xi$ quantifies dependence between frequency and accuracy, and $Z(s)$ incorporates contextual effects (Jiao et al., 2019). A positive $\xi$ (observed for ~80% of top shooters) signifies that players are more accurate in high-frequency areas, forming “hot zones” that elevate eFG%. Bayesian inference with Markov chain Monte Carlo yields credible intervals for $\xi$, $\beta$, and $\alpha$, and model fit is assessed via Deviance Information Criterion and Logarithm of Pseudo-Marginal Likelihood.

A Functional Bayesian Additive Regression Trees (FBART) and Adaptive FBART (AFBART) framework further extends these spatial models by representing shot intensity surfaces with flexible, nonparametric tree ensembles and adaptive bases (Cao et al., 10 Mar 2025). These techniques give granular uncertainty quantification, capture nonlinearities, and facilitate identification of latent spatial shot selection patterns, informing strategic improvements to eFG% via targeted shot allocation.

4. Defensive Impact and Spatio-Temporal Trajectory Analysis

Defensive contest affects shooting efficiency and, consequently, eFG%. Large-scale trajectory analysis models defender proximity, contest angle, and physical attributes to estimate how defensive pressure alters shot trajectory parameters—entry angle, depth, and left-right variance (Bornn et al., 2019). Bayesian quadratic regression fits the shot path:

$$E(Z_i) = \beta_0 + \beta_1 x_i + \beta_2 y_i + \beta_3 x_i^2 + \beta_4 y_i^2 + \beta_5 x_i y_i$$

Research demonstrates that tighter contests increase trajectory variance (e.g., shot depth variance rises 56%) and systematically bias outcomes toward lower success rates. Perimeter defensive metrics are refined via regression on modeled shot-make probabilities rather than binary outcomes:

$Y_{ijk} = \beta_0 + \alpha_j + \gamma_k$

where $Y_{ijk}$ is shot probability for shooter $j$ vs defender $k$. Conditioning on estimated probabilities yields lower variance and more reliable defender ratings than conventional opponent FG% metrics. Applied to eFG%, this framework accommodates contextual defensive effects, enhancing tactical evaluations of player and team shooting quality.

5. Time Series and Sequential Models of Shooting Efficiency

eFG% can exhibit temporal dependence across games and within games, driven by momentum and “hot hand” effects. A doubly self-exciting Poisson time series model, adhering to the INGARCH(1,1) type, accounts for autocorrelation in made field goals and, by extension, adjusted shooting efficiency (Briz-Redón, 2023). At the game level:

$Y_{g} \sim \text{Poisson}(\lambda_g)$

$$\lambda_g = \exp[\alpha_S + \alpha_H I_{\text{Home}_g} + \kappa_S \lambda_{g-1} I_{g>1} + \eta_S Y_{g-1} I_{g>1}]$$

and analogously at the minute level. Bayesian estimation employs a divide-and-conquer approach with Wasserstein barycenters to manage computational complexity. Model fit statistics (WAIC) confirm superior inference for players exhibiting momentum. Temporal autocorrelation in eFG% indicates that efficiency should be interpreted beyond static averages, especially for “streaky” shooters.

6. Contextual Applications: Clutch-Time Performance and Strategic Insights

Analysis of clutch-time efficiency in Japan's B.League examines eFG% by region (“In the Paint,” “Mid-Range,” “3-Point Area”) and situational windows (Shiiku et al., 6 Oct 2025). Empirical findings reveal:

• eFG% > 50% for Paint and 3-Point Area persists both in clutch and non-clutch periods.
• Mid-Range eFG% declines substantially under pressure, reflecting increased contest and lower probability.
• Three-point eFG% drops significantly in clutch time ($t_{46} = -3.004$, $p = 0.004$), not entirely offset by spatial selection.

Correlation between clutch-time three-point eFG% and win percentage is weak (r = 0.28, p = 0.18), while non-clutch three-point efficiency shows a stronger association with wins (r = 0.63, p = 0.006). Tactical implications include prioritizing high-efficiency shot creation in late-game scenarios, avoiding low-percentage mid-range isolations, and optimizing lineups for resilience to defensive pressure. K-means clustering classifies players into archetypes (“Balanced Contributors,” “Perimeter Shooters,” etc.) to further tailor strategic choices.

7. Integration with Deep Learning and Micro-Action Evaluation

Deep learning architectures working on raw spatio-temporal data provide continuous prediction of possession quality, facilitating dynamic assessment of eFG% in context (Sicilia et al., 2019). The DeepHoops model estimates the probability of terminal actions, yielding expected points values (EPV):

$$\text{EPV}(\tau) = \sum_{z \in Z} P(z | \text{context}) v(z)$$

and evaluates micro-actions’ impact via:

$$\text{EPA}(\text{action}, \tau) = \text{EPV}(\tau + \epsilon) - \text{EPV}(\tau - \epsilon)$$

This methodology quantifies how off-ball screens, cuts, and passes improve shot quality, offering a direct way to augment eFG% with action-level context. Integration with existing boxscore metrics yields enriched performance evaluation and can inform both player development and tactical design.

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In summary, effective field-goal percentage (eFG%) represents a foundational and evolving construct in basketball analytics, connecting spatial modeling, probability theory, defensive contest, temporal dynamics, and machine-learning–enabled contextual analysis. The metric’s conceptual underpinnings, advanced estimators, and practical applications continue to be refined through the integration of trajectory tracking, Bayesian inference, and deep neural architectures, providing increasingly stable, reliable, and actionable insights into basketball efficiency and strategy.