Shot Binning Technique

• Shot binning is a technique that partitions the offensive zone into discrete spatial segments to measure location-specific player and goaltender performance.
• It aggregates recency weighted shot outcomes to build skill-adjusted xG models, offering clearer insights into spatial shooting efficiency.
• The method improves predictive accuracy and tactical analysis by quantifying situational strengths and weaknesses across defined rink regions.

The shot binning technique refers to the partitioning of the playing surface—in particular, the offensive zone in ice hockey—into a fixed set of discrete spatial segments ("bins") to enable spatially resolved estimation of player and goaltender skill. This method supports the generation of skill-adjusted expected goals models by encoding how proficient a shooter or goaltender is from specific rink locations, providing a finer-grained account of location-dependent scoring talent than is possible from aggregate goal or shot data alone. Shot binning was notably operationalized in NHL analytics by the framework established by Shuckers and Curro and is a central component of recent skill-adjusted xG models for both shooters and goaltenders (Noel, 10 Nov 2025).

1. Principles and Mathematical Definition

The core concept of shot binning is to divide the relevant ice surface region, typically between the blue line and the goal line, into $B$ equal-width horizontal segments (bins). Each bin encompasses an area of the rink defined by coordinate boundaries, such that every shot event with a known $(x, y)$ location can be deterministically assigned to a unique bin. For instance, the rink might be partitioned into $B=9$ horizontal bins, as in Shuckers–Curro, with a possible additional "below-goal-line" bin for boundary cases (Noel, 10 Nov 2025).

Mathematically, let $s_i = (x_i, y_i)$ be the location of shot $i$. The bin assignment operator, $b(s_i): \mathbb{R}^2 \to \{1, \ldots, B\}$, indexes the spatial bin in which $s_i$ lies.

Skill features are then estimated individually for each bin by aggregating shots assigned to that location. For a given player or goaltender, and for each bin $b$, one computes:

• Weighted Cumulative xG in Bin: $$\mathrm{xG}_b = \sum_{i: b(s_i) = b} w_i \cdot \mathrm{xG}_i$$
• Weighted Cumulative Outcome in Bin: $$\mathrm{Goal}_b = \sum_{i: b(s_i) = b} w_i \cdot \mathrm{Outcome}_i$$ where $w_i$ is a recency weight for shot $i$.

2. Implementation in Skill-adjusted xG Models

The shot binning technique is used to form locational skill features for both shooters and goaltenders. For each player, separate statistics are maintained per bin, quantifying their talent when shooting from or defending each zone.

In the skill-adjusted NHL xG model (Noel, 10 Nov 2025), this process operates as follows:

• Discretize the offensive zone into nine equal horizontal bins between the blue line and the goal line.
• Assign each shot to its spatial bin.
• For each shooter (or goaltender), compute Goals Above Expected (GΔ) and Talent per bin using recency-weighted shot outcomes and predicted xG values:
  • $$\mathrm{G\Delta}_{b} = (\mathrm{Weighted\,Goals})_b - (\mathrm{Weighted\,xG})_b$$
  • $$\mathrm{Talent}_b = (\mathrm{Weighted\,Goals})_b / (\mathrm{Weighted\,xG})_b$$ (set to zero if denominator vanishes).
• The locational GΔ and Talent metrics are then concatenated across bins to yield the player's full spatial skill signature.
• Final skill feature vectors entering the xG model include locational (binned), overall (all bins), and situational (Gower-distance weighted) skill estimates.

3. Applications and Use Cases

Shot binning enables several methodological and practical advances in player and goaltender evaluation:

• Spatial Skill Profiling: By encoding player performance at each bin, analysts can quantify locational hot spots, cold spots, and versatility—e.g., a shooter with exceptional efficiency from high-danger areas but middling results from the perimeter.
• Fine-grained Input Features: When included as explicit features in gradient-boosted decision tree models (e.g., LightGBM in (Noel, 10 Nov 2025)), binned skill metrics enable the model to condition probability estimates not just on shot location, but also on a shooter's or goalie's context-specific efficacy.
• Enhanced Predictive Accuracy: The inclusion of binned skill features yields statistically significant improvements in predictive metrics:
  • For high-skill brackets, skill-adjusted models show relative log loss improvements of ≈4.6%, AUC improvements of ≈5.2%, and Brier score gains of ≈3.9% over unadjusted baselines, as measured on the 2021–2022 NHL holdout set (Noel, 10 Nov 2025).

4. Technical and Computational Considerations

Binning demands discretization granularity that balances spatial resolution against sample size per bin; excessive binning will lead to sparse or noisy estimates. In practice, 9 bins is a standard choice in NHL analytics, reflecting a compromise between spatial localization and statistical power.

For each player-binned combination, cumulative statistics are computed with a recency weighting scheme $w_i = i/n$ (the $i$th most recent of $n$ shots gets weight $i/n$), ensuring skill features reflect current rather than obsolete form.

The computation is modular and parallelizable: separate per-bin skill metrics can be calculated independently for each player and batch-mode updated as new shot data arrives.

5. Comparison with Alternative Encoding Schemes

Shot binning is one of several approaches to model spatial variation in shot and save probabilities:

Technique	Spatial Resolution	Statistical Stability
Shot binning (discrete)	Stepwise (bin-level)	Moderate (bin count)
Mixture-of-Gaussians	Continuous (soft regions)	Often higher (with regularization)
Spline/Kernel methods	Continuous (smooth functions)	Varies by smoothing

Unlike mixture-of-Gaussians (as in post-shot skill modeling for soccer (Baron et al., 2023)) or spline-based spatial smoothers, binning yields interpretable, direct summaries tied to concrete rink regions at the expense of some smoothing or “leakage” across neighboring areas.

6. Role in Contemporary and Future Skill-adjusted Analytics

The framework for shot binning, especially as adapted in (Noel, 10 Nov 2025), provides a reproducible foundation for integrating locational skill measures into skill-adjusted expected goals models in hockey. This technique supports advances in scouting, tactical analysis, and modeling by enabling:

• Direct interpretation of a player’s locational strengths and weaknesses.
• Model calibration for evolving play styles or rink-specific effects.
• Extensions to situational and context-aware skill modeling by combining binning with feature-distance weighting (e.g., Gower distance).

A plausible implication is that binning or its continuous analogs will remain core components of future skill-adjusted xG methodologies across invasion sports domains, supplementing global player-level summaries with precise, spatially contextualized skill indicators (Noel, 10 Nov 2025).