Chapter 24: Injury Risk and Load Management - Exercises

Section A: Injury Data Fundamentals (Questions 1-7)

Exercise 1: Injury Report Analysis

Analyze the following injury report data for a team over one season:

a) Calculate the total games lost to injury b) Calculate the percentage of total team games lost (82 games × 15 roster spots) c) Classify injuries by severity tier

Exercise 2: Injury Rate Calculation

A player has played 280 games over 4 seasons with the following injury history: - Season 1: 78 games (4 missed to injury) - Season 2: 65 games (17 missed) - Season 3: 72 games (10 missed) - Season 4: 65 games (17 missed)

a) Calculate the player's career injury rate (games missed / total possible games) b) Is there a trend in his injury rate? c) How does this compare to the league average (~12-15 games missed per season)?

Exercise 3: Data Quality Assessment

Discuss the limitations of official NBA injury reports for analytical purposes: a) What information is missing from standard reports? b) How might teams obscure injury information? c) What additional data sources would improve injury analysis?

Exercise 4: Injury Classification

Create a classification system for basketball injuries that would support analytical work: a) Define at least 5 severity tiers with expected recovery times b) Create body part categories relevant to basketball movements c) Distinguish between contact and non-contact injuries

Exercise 5: Historical Injury Tracking

Design a data schema for tracking player injury history: a) What fields would you include? b) How would you handle injuries that span multiple seasons? c) How would you track re-injuries to the same body part?

Exercise 6: Wearable Data Integration

A player's wearable device records the following during a practice: - Total distance: 4.2 miles - High-speed running distance (>15 mph): 0.8 miles - Accelerations (>3 m/s^2): 45 - Decelerations (>3 m/s^2): 52 - Jump count: 38

a) Calculate summary metrics (acceleration per mile, jumps per mile) b) What thresholds might indicate overexertion? c) How would you compare this to game-day loads?

Exercise 7: Return-to-Play Data

A player recovering from a hamstring strain has the following return-to-play progression:

a) Evaluate the progression rate b) Is the Day 7 pain level concerning? c) When would you recommend return to game action?

Section B: Load Management Modeling (Questions 8-15)

Exercise 8: Acute-Chronic Workload Ratio

Calculate the Acute-Chronic Workload Ratio (ACWR) for a player with the following weekly loads (arbitrary units):

a) Calculate the 4-week chronic load (weeks 1-4) b) Calculate the acute load for week 5 c) Calculate the ACWR for week 5 d) Does this ACWR fall in the "danger zone"?

Exercise 9: Exponentially Weighted Moving Average

Using the same data from Exercise 8, calculate the EWMA-based ACWR: a) Calculate 7-day EWMA acute load (use decay factor 2/(7+1) = 0.25) b) Calculate 28-day EWMA chronic load (use decay factor 2/(28+1) = 0.069) c) Compare to the rolling average ACWR

Exercise 10: Rest Day Optimization

A team plays the following schedule over 10 days: - Day 1: Game - Day 2: Travel - Day 3: Game - Day 4: Off - Day 5: Practice - Day 6: Game - Day 7: Off - Day 8: Practice - Day 9: Game - Day 10: Game (back-to-back)

For a 33-year-old star player who played heavy minutes: a) Calculate optimal rest distribution b) Which practices should he skip? c) Should he sit out the back-to-back?

Exercise 11: Minutes Restriction Protocol

Design a minutes restriction protocol for a player returning from a calf strain: a) Starting minutes limit b) Weekly increase rate c) Conditions for advancement vs. regression d) Target timeline to full minutes

Exercise 12: Positional Load Differences

Compare expected load profiles for different positions:

a) Which position has the highest overall load? b) How should load management differ by position? c) Design position-specific thresholds

Exercise 13: Schedule Density Analysis

Analyze the following schedule segment: - 4 games in 5 nights - 3 travel days (>500 miles) - 2 back-to-backs - 1 rest day

a) Calculate a "schedule difficulty" score b) What rest strategies would you recommend? c) How does this compare to league-average difficulty?

Exercise 14: Recovery Monitoring

A player shows the following recovery metrics the morning after a game: - Sleep duration: 6.2 hours (typical: 7.5) - HRV: 45 ms (typical: 55) - Self-reported fatigue: 7/10 (typical: 4) - Muscle soreness: 8/10 (typical: 3)

a) Calculate a composite recovery score b) Is this player ready for practice? c) What intervention would you recommend?

Exercise 15: Season-Long Load Planning

Design a season load management plan for a 30-year-old star player: a) Target games played (out of 82) b) Distribution of rest games (front-load, back-load, even) c) Back-to-back policy d) Minutes per game targets by month e) All-Star break considerations

Section C: Injury Prediction Models (Questions 16-23)

Exercise 16: Feature Engineering

From the following raw data, create 5 engineered features for injury prediction: - Game logs with minutes, distance, accelerations - Injury history (dates, types, recovery times) - Age, height, weight, position - Sleep and HRV data - Schedule information

Exercise 17: Target Variable Definition

Compare different target variable definitions for injury prediction: a) Binary: Injured within 7 days (yes/no) b) Multi-class: No injury / Minor / Major c) Continuous: Days until next injury d) Survival: Time-to-event

Which is most useful for load management decisions?

Exercise 18: Baseline Injury Rates

Calculate expected injury rates for a player based on: - Age: 28 - Position: SF - Injury history: 2 significant injuries in 6 seasons - Minutes per game: 34

Using base rates from the chapter, estimate: a) Probability of missing 10+ games this season b) Probability of season-ending injury c) Expected games missed

Exercise 19: Model Evaluation Metrics

An injury prediction model produces the following confusion matrix:

Calculate: a) Accuracy b) Precision (for injury prediction) c) Recall (sensitivity) d) F1 score e) Is this model useful for load management? Why or why not?

Exercise 20: Cost-Sensitive Classification

Assign costs to the injury prediction outcomes: - True Positive (correctly predict injury): Benefit = +$X - False Positive (predict injury when healthy): Cost = $Y - False Negative (miss injury): Cost = $Z - True Negative (correctly predict no injury): Benefit = +$W

a) What are reasonable values for X, Y, Z, W? b) How do these costs affect model threshold selection? c) Calculate expected value for threshold p = 0.3 vs p = 0.5

Exercise 21: Time Series Cross-Validation

Design a cross-validation scheme for an injury prediction model: a) Why can't we use standard k-fold CV? b) How would you handle the temporal nature of the data? c) What is the appropriate prediction horizon? d) How do you avoid data leakage?

Exercise 22: Survival Analysis Application

A player has survived 3 seasons without an ACL injury. Using survival analysis concepts: a) What is the hazard rate if 5% of similar players tear their ACL each season? b) What is his cumulative survival probability through year 3? c) What is the conditional probability of ACL tear in year 4?

Exercise 23: Model Calibration

Your injury prediction model shows the following calibration: - When it predicts 20% injury risk, actual rate is 35% - When it predicts 50% injury risk, actual rate is 60% - When it predicts 80% injury risk, actual rate is 75%

a) Is this model well-calibrated? b) How would you adjust predictions? c) What is the expected calibration error?

Section D: Economic Analysis (Questions 24-30)

Exercise 24: Injury Cost Calculation

Calculate the cost of an injury for a player with: - Salary: $25 million/year - Games missed: 25 - Team projected wins without injury: 52 - Team projected wins with injury: 48 - Playoff revenue per home game: $2 million

a) Direct salary cost of games missed b) Potential playoff revenue impact c) Total estimated injury cost

Exercise 25: Load Management ROI

A team implements a load management program costing $2 million annually: - Sport science staff: $800K - Wearable technology: $400K - Additional recovery equipment: $300K - Data systems: $500K

Expected benefits: - Reduce games lost to injury by 150 per season - Average player salary: $8M/year

Calculate: a) Cost savings from reduced injuries b) Net ROI c) Break-even injury reduction

Exercise 26: Rest Game Decision

A star player ($35M salary) has an elevated injury risk indicator: - Base injury probability: 5% - Elevated probability if plays: 15% - Expected injury cost: $10M (missed games + performance decline)

If he rests: - Lost win probability: 3% - Each win worth $500K to team

Calculate: a) Expected cost if he plays b) Expected cost if he rests c) Optimal decision

Exercise 27: Contract Implications

A team is negotiating a max contract with a player who has injury history: - Base max: 5 years, $200M - Historical injury rate: 25% of games missed - League average: 12%

a) Calculate expected games played over contract b) What contract protection mechanisms would you recommend? c) How should injury history affect contract value?

Exercise 28: Insurance Analysis

A team is considering injury insurance for a $40M player: - Premium: $2M annually - Coverage: 80% of salary for games missed beyond 20 - Deductible: First 20 games

For a player expected to miss 15 games: a) Calculate expected insurance payout b) Is the insurance worth the premium? c) At what expected games missed does insurance become valuable?

Exercise 29: Playoff Health Optimization

A team is preparing for playoffs starting in 3 weeks: - Star player has minor knee soreness - If rests now: 95% healthy for playoffs - If plays through: 70% healthy for playoffs - Playoff revenue at stake: $15M - Remaining regular season games: 6 - Each regular season win worth: $200K

Calculate optimal strategy.

Exercise 30: Multi-Year Planning

Design a 5-year injury management strategy for a team with: - Core players aged 26, 28, 30, 32 - Total payroll: $140M - Current injury prevention budget: $1M

a) Recommended budget by year b) Priority investments c) Expected savings d) Key performance indicators

Section E: Applied Problems (Questions 31-35)

Exercise 31: Real-Time Load Monitoring

Design a real-time load monitoring system for game use: a) What metrics would you track during the game? b) What thresholds trigger alerts? c) How do you communicate with coaching staff? d) How do you balance performance and safety?

Exercise 32: Post-Injury Projection

A 27-year-old star point guard just tore his ACL: - Pre-injury stats: 24 PPG, 8 APG, 5.5 Win Shares - Career: 5 seasons, 380 games

Project: a) Expected recovery timeline b) First season back performance c) Career trajectory adjustment d) Long-term injury risk implications

Exercise 33: Case Study Analysis

Analyze Kawhi Leonard's load management approach: a) What was his injury history prior to load management? b) How did the Raptors manage his load in 2018-19? c) What were the results? d) What can other teams learn from this approach?

Exercise 34: Youth Development Consideration

A 19-year-old rookie is showing early fatigue signs mid-season: - Playing 28 MPG (high for rookie) - Load metrics elevated - No current injury but declining performance

Design a management plan that balances: a) Long-term development b) Current season contribution c) Injury prevention d) Team dynamics

Exercise 35: Comprehensive Risk Assessment

Create a comprehensive injury risk assessment for this player:

a) Calculate overall risk score b) Identify top 3 risk factors c) Recommend management strategy d) Set appropriate rest targets

Answer Key Guidelines

Quantitative exercises should show complete calculations. Design exercises should demonstrate understanding of principles with practical application. Case analyses should integrate multiple chapter concepts.

Section focus areas: - Data fundamentals: Exercises 1-7 - Load management: Exercises 8-15 - Prediction models: Exercises 16-23 - Economics: Exercises 24-30 - Applications: Exercises 31-35