Spatial Shot Quality Telemetry and Expected Threat (xT) Quantification

1. The Geometry of Shot Quality

Every shot attempt in our live database is mapped into a continuous coordinate space $(x, y)$ measured in metres from the goal line. Two fundamental spatial parameters govern the baseline probability: Euclidean distance to the centre of the goal line $d = \sqrt{(105 - x)^2 + (34 - y)^2}$, and the visible shot angle $\theta = \arctan\left(\frac{7.32 \cdot (105 - x)}{(105 - x)^2 + (y - 30.34)(y - 37.66)}\right)$.

2. Feature Weighting Vector

Our gradient-boosted decision trees incorporate 14 contextual variables for every shot event:

• Shot Type: Strong foot (1.00), weak foot (0.82), header (0.58), rebound / volley (0.76).
• Assist Pattern: Through-ball behind defensive line (+0.18 xG uplift), cutback cross from endline (+0.14 xG uplift), high aerial cross (-0.08 xG penalty).
• Defensive Pressure Cone: Density of opponent defenders situated inside the triangle formed between the ball and both goal posts.
• Goalkeeper Vector: Goalkeeper positioning relative to the optimal bisector line.

3. Field Tilt and Non-Shot Expected Threat (xT)

Field tilt measures the territorial dominance of a side by computing the share of total final-third passes: $\text{Field Tilt} = \frac{\text{Passes}_{A, \text{Final3rd}}}{\text{Passes}_{A, \text{Final3rd}} + \text{Passes}_{B, \text{Final3rd}}}$. When combined with Markovian grid transitions, xT isolates teams that generate sustained territorial siege before shots are taken.