Chapter 17 Quiz

Instructions: Select the single best answer for each question unless otherwise stated. Answers are provided at the end.

Q1. What does a Voronoi diagram partition the pitch into?

(a) Equal-area rectangles (b) Regions where each point is closest to a specific player (c) Regions based on player velocity (d) Hexagonal cells centred on each player

Q2. The computational complexity of Fortune's sweep-line algorithm for computing a Voronoi diagram with $n$ sites is:

(a) $O(n)$ (b) $O(n \log n)$ (c) $O(n^2)$ (d) $O(n^2 \log n)$

Q3. Which of the following is a limitation of the standard (unweighted) Voronoi diagram in soccer?

(a) It cannot handle more than 11 players (b) It ignores player velocity and physical capabilities (c) It requires 3D positional data (d) It can only be computed for rectangular pitches

Q4. The Delaunay triangulation is the geometric dual of:

(a) The convex hull (b) The Voronoi diagram (c) The pitch control surface (d) The expected threat grid

Q5. In the Fernandez--Bornn pitch control model, the influence function for a player is modelled as a:

(a) Uniform distribution (b) Bivariate Gaussian distribution (c) Poisson distribution (d) Exponential distribution

Q6. The parameter $\Delta t$ in the Fernandez--Bornn model represents:

(a) The time since kickoff (b) The frame rate of tracking data (c) A look-ahead time for predicting future position (d) The duration of a pressing sequence

Q7. In the influence function, the covariance matrix $\Sigma_i$ is elongated along the velocity direction because:

(a) Players are taller than they are wide (b) Players can cover more ground in the direction they are moving (c) The ball travels faster than players (d) The pitch is longer than it is wide

Q8. Pitch control $\mathrm{PC}_A(x)$ for team A at a point $x$ is defined as:

(a) $I_A(x) - I_B(x)$ (b) $I_A(x) / I_B(x)$ (c) $I_A(x) / (I_A(x) + I_B(x))$ (d) $\max(I_A(x), I_B(x))$

Q9. In Spearman's time-to-intercept model, pitch control is determined by:

(a) The total distance of each player from the ball (b) Which team's nearest player can arrive at each point first (c) The number of players in each half of the pitch (d) The team currently in possession

Q10. A typical grid resolution for real-time pitch control computation is:

(a) 0.1 m cells (1050 x 680 grid) (b) 1 m cells (105 x 68 grid) (c) 2 m cells (53 x 34 grid) (d) 10 m cells (11 x 7 grid)

Q11. Space creation is defined as:

(a) A player carrying the ball into open space (b) A player's movement that increases the area available to a team-mate (c) The total area of the pitch not occupied by any player (d) The difference between the two teams' total Voronoi areas

Q12. In the counterfactual method for measuring space creation, what is "frozen"?

(a) All players on the defending team (b) The ball (c) The space-creating player's position (d) All players except the ball carrier

Q13. The weighted exploitation metric combines space quantity with:

(a) Player salary (b) Expected threat (xT) at the reception location (c) The number of passes in the build-up (d) Match minute

Q14. Which off-ball run type involves movement away from the opponent's goal to receive between the lines?

(a) Penetrating run (b) Lateral run (c) Dropping run (d) Decoy run

Q15. A decoy run is characterised by:

(a) The player receiving the ball at the end of the run (b) The player pulling defenders out of position without expecting to receive (c) The player running toward their own goal (d) The player exchanging positions with a team-mate

Q16. In the penetrating-run detection algorithm, which threshold determines whether a player is running toward goal?

(a) The minimum distance from goal (b) The minimum velocity component toward goal ($v_{\min}$) (c) The maximum acceleration (d) The player's jersey number

Q17. The run quality score $Q_{\text{run}}$ is a weighted combination of:

(a) Goals, assists, and key passes (b) Depth gained, space created, defenders engaged, and positional value change (c) Speed, acceleration, and deceleration (d) Pass completion rate and progressive passes

Q18. The Dangerous Space Matrix (DSM) combines which three factors?

(a) Distance to goal, shot angle, and xG (b) Pitch control, expected threat, and defender density (c) Possession percentage, pass accuracy, and pressing intensity (d) Player speed, acceleration, and stamina

Q19. In the defender-density function $D_{\text{def}}(x, y)$, the parameter $\sigma_d$ controls:

(a) The maximum speed of defenders (b) The spatial decay of each defender's coverage (c) The total number of defenders (d) The width of the penalty area

Q20. Spatial entropy in the final third measures:

(a) The total number of entries into the final third (b) The unpredictability/diversity of a team's attack patterns (c) The average speed of attacks (d) The number of players committed to each attack

Q21. The maximum entropy for $K$ zones is:

(a) $K$ (b) $K^2$ (c) $\log K$ (d) $1/K$

Q22. Pitch-control-weighted expected threat (PC-xT) is computed by:

(a) Multiplying pitch control by xT at each grid cell and summing (b) Taking the maximum of pitch control and xT (c) Subtracting xT from pitch control (d) Dividing xT by pitch control

Q23. Spatial value added (SVA) of an action is:

(a) The xG generated by the action (b) The change in PC-xT before and after the action (c) The distance the ball travelled (d) The number of opponents bypassed

Q24. Which of the following is NOT a valid strategy for reducing the computational cost of pitch control evaluation?

(a) Using a coarser grid (b) Ignoring players far from the ball (c) Evaluating only every 5th frame (d) Increasing $\Delta t$ to 30 seconds

Q25. A team consistently creates 50 m$^2$ of dangerous space in the final third per possession but has a low exploitation rate of 8 %. The most likely tactical diagnosis is:

(a) The team cannot create chances (b) The team creates space but fails to play passes into it (c) The defence is too compact (d) The goalkeeper is underperforming

Answer Key