Chapter 15 Exercises: Player Tracking Data

Overview

These exercises cover player tracking fundamentals, spatial analytics, speed and distance metrics, defensive tracking, and practical applications.

Section A: Tracking Fundamentals (Exercises 1-8)

Exercise 1: Coordinate Systems

The NBA court uses a coordinate system with the basket at origin.

a) If a player is at (15, 8), calculate their distance from the basket. b) Convert court coordinates to shot zone classification. c) What is the angle to the basket from position (20, 10)?

Exercise 2: Frame Rate Analysis

Tracking data captures 25 frames per second.

a) How many data points are generated in a 48-minute game for one player? b) If each frame includes x, y position, what is the data volume per game? c) Why might teams downsample to 5 frames per second for some analyses?

Exercise 3: Speed Calculation

Given positions at consecutive frames: - Frame 1: (10.0, 5.0) - Frame 2: (10.5, 5.2)

a) Calculate displacement between frames. b) Calculate instantaneous speed (assuming 25 fps). c) Convert to miles per hour.

Exercise 4: Distance Traveled

A player's positions over 5 frames (at 25 fps): (0, 0), (2, 1), (5, 2), (8, 4), (10, 5)

a) Calculate total distance traveled. b) Calculate average speed over this period. c) How does this differ from displacement?

Exercise 5: Closest Defender

Ball handler at (10, 5). Defenders at: - D1: (12, 6) - D2: (8, 4) - D3: (15, 10)

a) Calculate distance to each defender. b) Identify the closest defender. c) Classify the contest level (wide open, open, tight, very tight).

Exercise 6: Team Spacing

Five offensive players at: (25, 5), (-25, 5), (0, 20), (15, -5), (-15, -5)

a) Calculate the convex hull area (approximate or exact). b) Compare to league average spacing (~250 sq ft). c) How does spacing affect EPV?

Exercise 7: Paint Touch Detection

Define the paint as the rectangle: -8 < x < 8, 0 < y < 19.

Given player trajectory crossing through the paint: (10, 15), (5, 17), (2, 18), (0, 16), (-3, 14)

a) Which positions are in the paint? b) How many frames (at 25 fps) was the player in the paint? c) Calculate time spent in paint.

Exercise 8: Ball Movement

Ball positions over 4 frames: (20, 10), (10, 5), (5, 3), (2, 1)

a) Calculate ball speed at each transition. b) Was this likely a pass or dribble? Explain. c) Estimate pass distance.

Section B: Offensive Tracking (Exercises 9-15)

Exercise 9: Touch Analysis

Player touched ball 45 times in a game with these distributions: - Front court touches: 38 - Elbow touches: 12 - Post touches: 8 - Paint touches: 18

a) Calculate touch location percentages. b) What player type does this suggest? c) Compare to positional averages.

Exercise 10: Time of Possession

Player averaged 4.2 minutes of time of possession per game.

a) If they played 32 minutes, what percentage of their minutes were holding ball? b) How does this compare to typical values by position? c) Calculate expected dribbles (assuming 0.8 dribbles/second while holding).

Exercise 11: Drives and Pull-Ups

Tracking data shows: - Drives per game: 12 - Points per drive: 1.05 - Pull-up attempts: 8 - Pull-up efficiency: 0.42

a) Calculate total points from drives and pull-ups. b) Compare to league averages. c) Which skill should this player emphasize?

Exercise 12: Off-Ball Movement

Player's average speed when not holding the ball: 4.2 mph League average: 3.8 mph

a) Calculate the percentage difference from average. b) Estimate extra distance traveled per game (35 minutes of off-ball time). c) Why might more off-ball movement be valuable?

Exercise 13: Catch and Shoot Analysis

Player's catch-and-shoot attempts: - Wide open (6+ ft): 85 attempts, 42% FG - Open (4-6 ft): 62 attempts, 38% FG - Tight (2-4 ft): 28 attempts, 32% FG

a) Calculate eFG% for each category. b) Calculate weighted average catch-and-shoot efficiency. c) How does defender distance affect this player's shooting?

Exercise 14: Dribble Analysis

Before shots: - 0 dribbles: 48% of shots, 45% FG - 1-2 dribbles: 32% of shots, 42% FG - 3+ dribbles: 20% of shots, 38% FG

a) Calculate expected points per shot for each dribble category. b) What does this suggest about shot selection? c) Recommend an optimal dribble distribution.

Exercise 15: Screen Setting

Player sets 8 screens per game: - Slip to basket: 2 per game, 1.4 pts/play - Roll: 4 per game, 1.2 pts/play - Pop: 2 per game, 1.0 pts/play

a) Calculate total screen-related value per game. b) How might this show up (or not) in box scores? c) Design a metric to credit screen setting value.

Section C: Defensive Tracking (Exercises 16-22)

Exercise 16: Matchup Analysis

Player defended these opponent possessions: - vs. Point Guards: 45 possessions, 1.05 PPP allowed - vs. Shooting Guards: 80 possessions, 0.95 PPP allowed - vs. Small Forwards: 35 possessions, 1.10 PPP allowed

a) Calculate weighted average defensive efficiency. b) Which assignment is most favorable for this defender? c) How does matchup distribution affect defensive reputation?

Exercise 17: Contest Analysis

Player's shot contests: - Altered (tight, missed): 42 - Made despite contest: 28 - No contest: 15

a) Calculate contest rate. b) Calculate opponent FG% on contested shots. c) Evaluate defensive effectiveness.

Exercise 18: Help Defense

Tracking shows player provided help defense 25 times per game: - Successful rotations (no score): 18 - Failed rotations (score anyway): 7

a) Calculate help defense success rate. b) Estimate points saved per game. c) Why is this valuable but hard to capture?

Exercise 19: Rim Protection

Center defended 12 shots at the rim per game: - Altered (missed): 7 - Made: 5 - Fouled: 2

a) Calculate rim protection FG% allowed. b) Compare to league average (~65% at rim). c) Estimate impact on team defense.

Exercise 20: Perimeter Defense

Wing defender metrics: - Steals: 1.5 per game - Deflections: 3.2 per game - Opponent isolation PPP: 0.85

a) Evaluate this defender's ball pressure. b) How do steals/deflections relate to isolation defense? c) What aspects of defense aren't captured here?

Exercise 21: Defensive Speed

Player's average defensive speed: 4.0 mph Player's max defensive speed: 12.5 mph Defensive distance per game: 2.8 miles

a) Compare to positional averages. b) Calculate acceleration capability from average to max. c) Why might defensive speed matter?

Exercise 22: Closeout Analysis

Player's closeouts to shooters: - On time (contested): 35 - Late (open shot): 12 - Too aggressive (blown by): 8

a) Calculate closeout success rate. b) What adjustment would you recommend? c) Design a closeout quality metric.

Section D: Advanced Applications (Exercises 23-30)

Exercise 23: Spatial Advantage

Calculate spatial advantage from this possession: - Initial spacing: 280 sq ft - After ball movement: 350 sq ft - Initial closest defender: 4 ft - After pass: 7 ft

a) Calculate spacing improvement percentage. b) Classify defender distance change (improvement category). c) Estimate EPV change from these improvements.

Exercise 24: Transition Analysis

Fast break data: - Transition possessions: 15 per game - Points per transition: 1.25 - Half-court possessions: 85 per game - Points per half-court: 1.02

a) Calculate total points from each play type. b) What's the value of generating extra transition opportunities? c) How does pace affect transition frequency?

Exercise 25: Load Management

Player's physical tracking over a week: | Game | Minutes | Distance | Sprints | Top Speed | |------|---------|----------|---------|-----------| | Mon | 35 | 2.8 mi | 45 | 15.2 mph | | Wed | 32 | 2.5 mi | 38 | 14.8 mph | | Fri | 38 | 3.1 mi | 52 | 15.5 mph |

a) Calculate cumulative load metrics. b) Identify concerning trends (if any). c) Recommend rest/load adjustments.

Exercise 26: Two-Man Game Analysis

Pick-and-roll partnership data: | Action | Frequency | PPP | |--------|-----------|-----| | Ball handler shot | 35% | 0.98 | | Pass to roller | 25% | 1.15 | | Kick to corner | 20% | 1.08 | | Reset | 20% | 0.85 |

a) Calculate weighted average PPP. b) Identify optimal action allocation. c) What defensive coverage might change this?

Exercise 27: Gravity Measurement

When Star Player is on court: - Teammate open 3PA increase: +4 per game - Teammate rim attempts increase: +2 per game - Teammate catch-and-shoot %: +3%

a) Estimate total teammate value added. b) How would you attribute this to the star? c) Design a "gravity" metric.

Exercise 28: Fatigue Analysis

Player's efficiency by quarter: | Quarter | TS% | Speed (mph) | Shot Dist | |---------|-----|-------------|-----------| | Q1 | 62% | 4.5 | 12.5 ft | | Q2 | 58% | 4.2 | 13.8 ft | | Q3 | 55% | 4.0 | 15.2 ft | | Q4 | 52% | 3.7 | 16.5 ft |

a) Identify fatigue indicators. b) Calculate efficiency loss from Q1 to Q4. c) Recommend workload management.

Exercise 29: Play Type Classification

Use tracking features to classify play types:

a) Identify likely play type for each. b) What features distinguish isolation from pick-and-roll? c) Design a classification algorithm approach.

Exercise 30: Comprehensive Player Profile

Create a tracking-based player profile from this data: - Average speed: 4.3 mph - Distance per game: 2.9 miles - Touches per game: 62 - Time of possession: 5.2 min - Drives: 8 per game - Catch-and-shoot 3P%: 39% - Defensive matchup PPP: 0.92

a) Classify this player's role. b) Identify strengths and weaknesses. c) Compare to positional archetypes.

Section E: Research Problems (Exercises 31-35)

Exercise 31: Data Quality Assessment

Tracking data has occasional missing frames (2% missing rate).

a) How would you handle missing data for speed calculations? b) What biases might missing data introduce? c) Design an interpolation approach.

Exercise 32: Feature Engineering

Design new features from tracking data for: a) Ball movement quality b) Defensive switching efficiency c) Transition opportunity creation

Exercise 33: Model Development

Outline an approach to predict: a) Shot make probability from tracking features b) Defensive assignment quality c) Injury risk from physical load

Exercise 34: Visualization Design

Design visualizations for: a) Player movement patterns (heat map) b) Team spacing over time c) Defensive coverage breakdown

Exercise 35: Integration Project

Design a system that integrates tracking data with: a) Box score statistics b) Video review workflow c) Coaching decision support

Answer Key Hints

Exercise 1a: Distance = sqrt(15^2 + 8^2) = sqrt(225 + 64) = sqrt(289) = 17 feet

Exercise 3b: Speed = displacement / time = sqrt(0.5^2 + 0.2^2) / (1/25) = 0.539 * 25 = 13.47 ft/s

Exercise 5b: D2 at (8,4) is closest: distance = sqrt(4 + 1) = sqrt(5) ≈ 2.24 feet

Full solutions available in the instructor's manual.