Glossary

Definitions and formulas used throughout NetStats.

Player Metrics

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).

Hub Score

Definition: Measures offensive centrality and overall ball involvement.

$$ \begin{align*} \text{Hub} =\ & 0.25 \cdot Z_{\text{Touches}} \\ &+ 0.20 \cdot Z_{\text{Total Passes}} \\ &+ 0.15 \cdot Z_{\text{Assists}} \\ &+ 0.15 \cdot Z_{\text{Pass Out Degree}} \\ &+ 0.10 \cdot Z_{\text{Pass In Degree}} \\ &+ 0.10 \cdot Z_{\text{Time of Possession}} \\ &+ 0.05 \cdot Z_{\text{Points}} \end{align*} $$

Black Hole Score

Definition: Identifies players who stop ball movement and reduce efficiency.

$$ \begin{align*} \text{Black Hole} =\ & 0.25 \cdot Z_{\text{Passes Received} - \text{Passes Made}} \\ &+ 0.20 \cdot (1 - Z_{\text{Points per Touch}}) \\ &+ 0.15 \cdot (1 - Z_{\text{Assists}}) \\ &+ 0.15 \cdot Z_{\text{Time of Possession}} \\ &+ 0.15 \cdot Z_{\text{Avg Sec per Touch}} \\ &+ 0.10 \cdot Z_{\text{Avg Dribbles per Touch}} \end{align*} $$

Source Score

Definition: Highlights initiators and ball movers early in possessions.

$$ \begin{align*} \text{Source} =\ & 0.30 \cdot Z_{\text{Passes Made}} \\ &+ 0.20 \cdot Z_{\text{Pass Out Degree}} \\ &+ 0.20 \cdot Z_{\text{Assists}} \\ &+ 0.15 \cdot (1 - Z_{\text{Passes Received}}) \\ &+ 0.10 \cdot (1 - Z_{\text{Points}}) \\ &+ 0.05 \cdot (1 - Z_{\text{Time of Possession}}) \end{align*} $$

Conduit Score

Definition: Recognizes players who connect others and maintain ball flow.

$$ \begin{align*} \text{Conduit} =\ & 0.25 \cdot Z_{\text{Passes Received}} \\ &+ 0.25 \cdot Z_{\text{Passes Made}} \\ &+ 0.15 \cdot Z_{\text{Pass Out Degree}} \\ &+ 0.15 \cdot Z_{\text{Pass In Degree}} \\ &+ 0.10 \cdot (1 - Z_{\text{Points}}) \\ &+ 0.10 \cdot (1 - Z_{\text{Assists}}) \end{align*} $$

Sink Score

Definition: Measures finishing behavior—players who end possessions by scoring.

$$ \begin{align*} \text{Sink} =\ & 0.30 \cdot Z_{\text{Points}} \\ &+ 0.20 \cdot Z_{\text{Passes Received}} \\ &+ 0.15 \cdot (1 - Z_{\text{Passes Made}}) \\ &+ 0.15 \cdot (1 - Z_{\text{Pass Ratio}}) \\ &+ 0.10 \cdot Z_{\text{Points per Touch}} \\ &+ 0.10 \cdot (1 - Z_{\text{Assists}}) \end{align*} $$

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.

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