Chapter 22 Quiz: Match Strategy and Tactics

Instructions

Answer all 25 questions. Each question is worth 1 point. A passing score is 18/25 (72%). For multiple-choice questions, select the single best answer unless otherwise indicated.

Question 1

What algorithm is used to solve the assignment problem when matching observed player positions to formation template positions?

A) Dijkstra's algorithm B) Hungarian algorithm C) K-means clustering D) Gradient descent

Answer: B

Explanation: The Hungarian algorithm solves the assignment problem in $O(n^3)$ time, finding the permutation of players to template positions that minimizes total squared displacement. This is an instance of the linear sum assignment problem.

Question 2

In the formation compactness analysis, what do the eigenvalues of the covariance matrix of player positions represent?

A) The number of players in each defensive line B) The speed at which the formation changes C) The spread of the team shape along the principal axes D) The probability of each formation template

Answer: C

Explanation: The eigenvalues $\lambda_1 \geq \lambda_2$ of the covariance matrix measure the variance (spread) of player positions along the first and second principal components. Large eigenvalues indicate a stretched formation; small eigenvalues indicate compactness.

Question 3

Why is it important to separate in-possession, out-of-possession, and transition phases before detecting formations?

A) Because tracking data is only available during in-possession phases B) Because formations differ substantially between these phases C) Because the Hungarian algorithm only works for one phase at a time D) Because FIFA regulations require separate reporting for each phase

Answer: B

Explanation: Teams systematically adopt different shapes depending on their phase of play. A team may play a 4-3-3 in possession but compact into a 4-5-1 out of possession. Mixing phases would produce a meaningless average formation.

Question 4

What is the primary purpose of a tactical fingerprint?

A) To identify individual player strengths and weaknesses B) To predict the exact final score of a match C) To characterize a team's playing style across measurable dimensions D) To track player fitness levels throughout a season

Answer: C

Explanation: A tactical fingerprint is a multidimensional profile (feature vector) that quantifies a team's playing style across dimensions such as possession, pressing intensity, directness, and width. It enables systematic comparison between teams.

Question 5

When computing standardized tactical fingerprints, why do we use z-scores rather than raw values?

A) Z-scores are easier to compute B) Z-scores allow comparison across leagues and seasons with different baselines C) Raw values are not available in most datasets D) Z-scores eliminate the need for data cleaning

Answer: B

Explanation: Standardization using z-scores ($z = (x - \mu) / \sigma$) removes the effect of different scales and league-specific baselines, allowing meaningful comparison of tactical profiles across different competitions and time periods.

Question 6

What does PPDA (Passes Per Defensive Action) measure?

A) A team's passing accuracy under pressure B) The number of passes a team makes in the defensive third C) The number of passes a team allows the opponent before making a defensive action D) The ratio of passes to shots in a match

Answer: C

Explanation: PPDA measures how many passes a team allows the opponent to make in the opponent's own half before engaging with a defensive action (tackle, interception, foul). Lower PPDA indicates more intense pressing.

Question 7

In opponent analysis, what is the purpose of computing betweenness centrality in the passing network?

A) To identify the most accurate passer B) To find the player who connects the most passing sequences (key pivot player) C) To determine which player scores the most goals D) To measure the total distance covered by each player

Answer: B

Explanation: Betweenness centrality measures how often a node (player) lies on the shortest path between other nodes in the network. High betweenness centrality identifies pivot players who are critical to the team's build-up play.

Question 8

Which of the following is NOT a typical component of defensive vulnerability mapping?

A) Spatial vulnerability (xG conceded by pitch zone) B) Temporal vulnerability (xG conceded by time interval) C) Transitional vulnerability (counter-press effectiveness) D) Nutritional vulnerability (player diet analysis)

Answer: D

Explanation: Defensive vulnerability mapping encompasses spatial (where on the pitch), temporal (when in the match), transitional (during phase changes), and personnel (individual player weaknesses) vulnerabilities. Nutritional analysis is not part of tactical vulnerability mapping.

Question 9

What statistical method does Section 22.4.2 recommend for detecting tactical change points during a match?

A) Linear regression B) Binary segmentation with likelihood-ratio test C) Principal component analysis D) Bayesian network inference

Answer: B

Explanation: The chapter uses binary segmentation with a likelihood-ratio test to detect change points in tactical metric time series. This method evaluates every possible split point and selects the one that maximizes the likelihood ratio between the segmented and unsegmented models.

Question 10

In the context of in-game tactical adjustments, what does the "feedback loop" consist of?

A) Observe, Analyze, Recommend, Implement, Monitor B) Plan, Do, Check, Act C) Collect, Clean, Model, Deploy D) Scout, Recruit, Train, Evaluate

Answer: A

Explanation: The in-game tactical feedback loop consists of five stages: Observe (data systems detect the current tactical state), Analyze (compare patterns to pre-match expectations), Recommend (suggest adjustments), Implement (coaching staff decides), and Monitor (track the effect of changes).

Question 11

According to research cited in the chapter, when do losing teams benefit most from making substitutions?

A) After the 75th minute B) Before the 58th minute C) At half-time only D) In the final 5 minutes

Answer: B

Explanation: Research has consistently shown that losing teams benefit from earlier substitutions, typically before the 58th minute, as this provides more remaining time for the substitute to influence the match outcome.

Question 12

What is the Substitution Impact Score (SIS)?

A) The number of goals scored after a substitution B) The difference in predicted contribution between the incoming and outgoing player C) The win probability change after a substitution D) The physical fitness difference between two players

Answer: B

Explanation: SIS is defined as $\text{SIS}(p_{\text{on}}, p_{\text{off}}, t, \text{state}) = \hat{Y}(p_{\text{on}}, t, \text{state}) - \hat{Y}(p_{\text{off}}, t, \text{state})$, quantifying the expected improvement from replacing one player with another given the current match context.

Question 13

In the fatigue model presented in Section 22.5.4, which of the following is NOT an input variable?

A) Total distance covered B) High-speed running distance C) Number of high-intensity accelerations D) Player's transfer market value

Answer: D

Explanation: The fatigue model uses total distance, sprint distance, number of accelerations, and minutes played as inputs. Transfer market value is an economic metric unrelated to physical fatigue modeling.

Question 14

Why does the chapter frame multi-substitution decisions as a dynamic programming problem?

A) Because each substitution is independent of the others B) Because the decision to use one substitution affects the value of remaining substitutions C) Because dynamic programming is faster than other methods D) Because FIFA requires sequential substitution decisions

Answer: B

Explanation: With 3-5 substitutions available, the problem is sequential: using one substitution changes the team's composition and reduces the remaining substitution budget, creating interdependencies that require dynamic programming (Bellman equation) or simulation to optimize.

Question 15

How is game state (GS) formally defined in Section 22.6?

A) The current minute of the match B) The current score differential from the perspective of a given team C) The formation currently being used D) The number of substitutions remaining

Answer: B

Explanation: Game state is defined as $\text{GS}(t) = g_{\text{team}}(t) - g_{\text{opponent}}(t)$, the goal difference from the perspective of the team being analyzed. Common states are winning (GS > 0), drawing (GS = 0), and losing (GS < 0).

Question 16

Why are game-state-adjusted metrics important?

A) They are required by football governing bodies B) They correct for the confounding effect of score on team behavior C) They are easier to compute than raw metrics D) They only apply to knockout tournaments

Answer: B

Explanation: Raw metrics are confounded by game state: a team that frequently leads will naturally show lower attacking output (because they manage the game) and higher defensive metrics. Adjusting for game state reveals true underlying capability independent of score context.

Question 17

In a win probability model, which of the following features would typically have the STRONGEST effect on win probability?

A) Venue (home/away) B) Score difference combined with time remaining C) Number of corner kicks D) Ball possession in the last 5 minutes

Answer: B

Explanation: Score difference is the strongest predictor of match outcome, and its effect interacts with time remaining (a 1-0 lead is much more valuable at 89 minutes than at 10 minutes). Together, these are the dominant features in any win probability model.

Question 18

What does a Markov chain model of score progression assume?

A) That goals are scored at a constant rate B) That the probability of the next state depends only on the current state, not the history C) That both teams have equal scoring ability D) That no substitutions occur during the match

Answer: B

Explanation: The Markov property states that the transition probabilities depend only on the current state, not the path taken to reach it. For score progression, this means the probability of the next goal depends on the current score difference but not on the history of goals.

Question 19

According to the chapter, what finding did Brechot and Flepp (2020) report about losing teams in the Bundesliga?

A) Losing teams defend more effectively after going behind B) Losing teams systematically over-commit to attack, conceding more xG than they generate C) Losing teams make better substitution decisions D) Losing teams have higher pressing success rates

Answer: B

Explanation: The research found that losing teams over-react by pushing too many players forward, which opens defensive spaces and leads to conceding more xG than the additional attacking xG generated. This suggests a more moderate response to losing might be more effective.

Question 20

Which visualization technique does the chapter recommend as most effective for communicating tactical information to coaches?

A) 3D scatter plots B) Pitch-overlaid visualizations (heat maps, pass maps, shot maps) C) Spreadsheet tables with detailed statistics D) Pie charts of possession distribution

Answer: B

Explanation: The chapter emphasizes "use the pitch as the canvas" as the primary visualization principle. Football people think spatially, so overlaying data on pitch diagrams leverages their spatial intuition and communicates information more effectively than abstract charts.

Question 21

What is the recommended maximum duration for a half-time analytical briefing?

A) 1 minute B) 3-5 minutes C) 10-15 minutes D) There is no time limit

Answer: B

Explanation: The chapter specifies that half-time presentations should be 3-5 minute briefings with key data points and visualizations, reflecting the extremely limited time available during the half-time interval.

Question 22

Which of the following is a key principle for building trust between analysts and coaching staff?

A) Always present complex statistical models to demonstrate expertise B) Start with the coach's questions, not your models C) Avoid showing video because it is subjective D) Present definitive conclusions without mentioning uncertainty

Answer: B

Explanation: The chapter emphasizes starting with the coach's questions rather than leading with analytical models. Additionally, being honest about uncertainty, validating findings against video, and providing insights (not instructions) are critical for building trust.

Question 23

What is the score effect vector $\Delta \mathbf{v}_s$?

A) The change in score during a match B) The difference between a team's tactical fingerprint in game state $s$ and their fingerprint when drawing C) The velocity of the ball during a goal-scoring sequence D) The expected goals generated in game state $s$

Answer: B

Explanation: The score effect vector is defined as $\Delta \mathbf{v}_s = \mathbf{v}_s - \mathbf{v}_0$, measuring how much a team's tactical profile shifts when in game state $s$ compared to when drawing. Teams with large magnitude score effect vectors are more strategically adaptive.

Question 24

In the context of formation analysis, what does the ratio $\lambda_1 / \lambda_2$ of the covariance eigenvalues indicate?

A) The number of players in each line B) The elongation of the team shape C) The speed of formation transitions D) The probability of the formation being correct

Answer: B

Explanation: The eigenvalue ratio $\lambda_1 / \lambda_2$ measures how elongated the team shape is. A ratio close to 1 indicates a roughly circular spread (compact in all directions), while a high ratio indicates the team is stretched along one axis---typically the length axis during counter-attacks.

Question 25

What is the difference between Euclidean distance and cosine similarity when comparing two tactical fingerprints?

A) They always give the same result B) Euclidean distance measures absolute difference in values; cosine similarity measures directional similarity regardless of magnitude C) Cosine similarity is always larger than Euclidean distance D) Euclidean distance only works for 2D data

Answer: B

Explanation: Euclidean distance captures the magnitude of difference between two vectors (how far apart they are in the feature space). Cosine similarity measures the angle between two vectors, capturing whether teams have similar profiles regardless of intensity. Two teams could have high cosine similarity (similar style direction) but large Euclidean distance (different intensity levels).