Glossary

Definitions and formulas used throughout NetStats.

Player Metrics

Unified Archetype

Definition: A single label summarizing a player's role across scoring zone, ball-handling responsibility, and playmaking. Derived deterministically from three pre-computed cluster types: usage tier (how ball-dominant the player is), scoring zone (rim, perimeter, or mixed), and a playmaker overlay applied to the highest-distributing passing cluster. The result is one of 11 archetypes arranged in a 3×3 grid (role tier × scoring zone), with two Playmaker variants: Primary Creator and Secondary Creator.

Archetype Synergy

Definition: Composite score measuring how well two archetypes complement each other on the floor. Blends geometric coverage in 6-dimensional skill space (Ball Handling, Rim Finishing, Perimeter Shooting, Playmaking, Off-Ball Movement, Court Centrality) with an empirical lineup net-rating residual. Formula: Composite = 0.45 × coverage + 0.55 × empirical residual (pairs with < 100 shared minutes use coverage only).

Pass Out Degree

Definition: Number of unique teammates a player passes to (with at least 6 passes).

Pass In Degree

Definition: Number of unique teammates a player receives passes from (with at least 6 passes).

Scoring Style

Definition: One of 9 shot-chart-based clusters computed via Gaussian Mixture Model on each player's zone distribution. Determines the 'scoring zone' dimension of the unified archetype. Examples: Rim Finisher, Perimeter Shooter, Isolation Scorer, Mid-Range Specialist, etc.

Passing Role

Definition: One of 2 broad passing roles derived from network topology — pass volume and out-degree. Lead Distributor: high pass volume, initiates ball movement (associated with Primary Creator and Secondary Creator archetypes). Role Passer: lower volume, receives and finishes more than distributes.

Team Metrics

Team Entropy

Definition: Shannon entropy of outgoing pass distributions. Measures unpredictability of ball movement.

$$H = -\sum_{i} \sum_{j} p_{ij} \cdot \log_2(p_{ij})$$

Flux

Definition: Weighted average change in shooting percentage from passer to receiver.

$$\text{Flux} = \sum_{i,j} p_{ij} \cdot (FG\%_j - FG\%_i)$$

Clustering Coefficient

Definition: Measures how interconnected teammates are via triangles, accounting for pass weights. Uses the geometric mean of edge weights between triples.

$$ c_u = \frac{1}{\deg(u)(\deg(u)-1)} \sum_{v,w} \left( \hat{w}_{uv} \hat{w}_{uw} \hat{w}_{vw} \right)^{1/3} $$

where the normalized edge weights are:

$$ \hat{w}_{uv} = \frac{w_{uv}}{\max(w)} $$

Degree Centralization

Definition: Measures how much passing activity is concentrated in a single player.

$$C_D = \frac{\sum_{i}(d_{\max} - d_i)}{(n-1)(n-2)}$$