Penalty Kick Predictor

Setup

common to both modes

Ball: Adidas Teamgeist, 14-panel thermally bonded, size 5.
Coefficients: team-supplied table, not independently calibrated.
Physical parameters: assumed values (see below), not measured for this ball.

Prediction model Assumed physical parameters

mass m (kg)

radius R (m)

air density ρ (kg/m³)

viscosity μ (Pa·s)

Noise σ (m)

MC trials N

Seed

Observed positions (rows x / y / z, columns t)

t = 0

t = 0.05

t = 0.10

Six later coordinates cannot identify all spin and aerodynamic parameters. Results are conditional on the supplied table, the axis assumption and the assumed ball parameters.

Reference generator model

speed |v₀| (m/s)

elevation (°)

azimuth (°)

S₀

φ (rad)

Spin rate implied by S₀: —

The predictor only reads the three noisy positions and the declared table; it never sees the hidden truth.

Results

—

Side view (x–z)

Top view (x–y)

Goal plane (y–z)

Coefficient table and interpolation

Spin parameter along the trajectory, S(t)

Status

Marginal distribution of y_g

Marginal distribution of z_g