Exercises: Injuries and Their Impact

Exercise 1: Position Weighting

Assign position weights (0-1 scale) to the following positions and justify your choices:

a) Starting center b) Slot cornerback c) Third-down running back specialist d) Starting punter e) Nickel linebacker

For each, consider: - Play frequency - Replacement availability - Scheme importance - Historical performance variance

Exercise 2: Quarterback Tier Classification

Classify the following quarterbacks into tiers (Elite, Good, Average, Below Average) based on recent performance:

a) A quarterback with 4,500 yards, 35 TDs, 10 INTs b) A quarterback with 3,200 yards, 22 TDs, 12 INTs c) A quarterback with 3,800 yards, 25 TDs, 8 INTs d) A first-round rookie starting Week 1 e) A journeyman starter with career 85 passer rating

Explain your reasoning and estimate the point impact if each was replaced by an average backup.

Exercise 3: Injury Status to Probability

Convert the following injury scenarios to miss probabilities:

a) "Questionable" with Full-Full-Limited practice pattern b) "Doubtful" with DNP-DNP-DNP pattern c) "Questionable" with Limited-Limited-Full pattern d) No designation but missed Wednesday for "rest" e) "Questionable" with DNP-Limited-Limited pattern

Exercise 4: Basic Injury Adjustment

Calculate the spread adjustment for the following scenario:

Team A Injuries: - Starting QB (Elite tier): Questionable, 40% miss probability - WR1 (Pro Bowl caliber): Out - Starting RT: Questionable, 60% miss probability

Given: - Elite QB over average backup: 5 points - Pro Bowl WR1 over backup: 1.5 points - Starting RT over backup: 0.8 points - Position weights: QB=1.0, WR=0.25, RT=0.30

Calculate the total expected adjustment.

Exercise 5: Compound Effect Analysis

A team has the following injured players:

• LT: Out (100% miss)
• LG: Questionable (50% miss)
• C: Questionable (50% miss)

a) Calculate the probability of each scenario (0, 1, 2, or 3 OL out) b) Calculate the base impact for each scenario c) Apply compound multipliers (15% increase per additional OL) d) Calculate the expected adjustment

Exercise 6: Backup Quality Assessment

Two teams lose their starting quarterbacks:

Team A: - Starter: Elite tier (+6 value) - Backup: Experienced veteran with 15 career starts (+2 value)

Team B: - Starter: Good tier (+4 value) - Backup: Undrafted third-year player with 0 starts (-1 value)

a) Calculate the spread adjustment for each team b) Which team is affected more? Why? c) How should this impact predictions for games between these teams?

Exercise 7: Practice Report Analysis

Analyze the following practice reports and predict game participation:

Player A (Hamstring): - Monday: DNP - Wednesday: DNP - Thursday: Limited - Friday: Full - Saturday: Full - Status: Questionable

Player B (Ankle): - Monday: Limited - Wednesday: Limited - Thursday: Limited - Friday: Limited - Saturday: Limited - Status: Questionable

Player C (Concussion): - Monday: DNP - Wednesday: DNP - Thursday: DNP - Friday: DNP - Saturday: DNP - Status: Out

Estimate play probability for A and B. What's different about C's situation?

Exercise 8: In-Game Injury Analysis

A starting quarterback (estimated +4 points over backup) is injured at the following points. Calculate the remaining game impact:

a) Start of 2nd quarter (45 minutes remaining) b) Halftime (30 minutes remaining) c) Start of 4th quarter (15 minutes remaining) d) 2 minutes remaining in the 4th quarter

Use the formula: Impact = Full_Impact × (Time_Remaining / 60)

Exercise 9: Return From Injury

A star running back returns from a 4-week hamstring injury. His normal value is +1.2 points per game.

a) Estimate his value for his first game back (assume 80% capacity) b) Estimate his value for his second game back (assume 90% capacity) c) By what game should you expect full value? d) How would this analysis differ for a player returning from ACL surgery?

Exercise 10: Market Response Analysis

The following line movements occurred after injury news:

a) Calculate the market-implied impact for each injury b) Which adjustment seems most/least reasonable? c) Identify potential market inefficiencies

Exercise 11: Multi-Week Injury Tracking

Track a hypothetical team through three weeks:

Week 1: Fully healthy - Model prediction: -4.5

Week 2: QB questionable (60% play), WR2 out - Base adjustment: ? - New prediction: ?

Week 3: QB out, WR2 out, CB1 questionable (40% miss) - Base adjustment: ? - New prediction: ?

Assume: QB value = +4 pts, WR2 value = +0.5 pts, CB1 value = +0.8 pts

Exercise 12: Injury Model Validation

You built an injury model that made the following predictions vs actual results:

a) Calculate the mean absolute error b) Calculate the correlation between predicted and actual c) Is your model systematically over- or under-estimating? d) What might explain the outlier (Game 4)?

Exercise 13: Defensive Injury Impact

Analyze the impact of defensive injuries:

Scenario: A team loses their top edge rusher (8 sacks, 15 QB hits in 12 games)

a) Estimate the per-game pass rush value lost b) How does this translate to expected points? c) Compare to losing an average edge rusher d) How might the offense adjust their game plan?

Exercise 14: Playoff Injury Analysis

A team entering playoffs has the following injury situation:

• Starting LT: Season-ending injury in Week 17
• WR1: Recovering from Week 16 injury, questionable
• Starting FS: Healthy but played through injury for 4 weeks

a) Calculate the direct injury adjustment b) How should you factor in the "playing through injury" for the FS? c) How do playoff stakes change your analysis?

Exercise 15: Building an Injury Database

Design a database schema for tracking injuries:

a) What tables would you need? b) What fields would each table contain? c) How would you link injuries to games? d) What queries would be most useful for analysis?

Provide pseudocode or SQL-like structure.

Exercise 16: Historical Injury Analysis

Using hypothetical data, analyze injury patterns:

Team X Injury History (last 3 seasons): - Season 1: 52 player-games missed - Season 2: 78 player-games missed - Season 3: 45 player-games missed - League average: 58 player-games missed

a) Is Team X above or below average in injuries? b) What factors might explain variance? c) Should you project forward based on this data? d) How might injury history affect preseason predictions?

Exercise 17: Uncertainty Quantification

For a game with significant injury uncertainty:

Home Team: QB questionable (40% miss), if plays likely limited Away Team: Fully healthy

a) Model both scenarios (QB plays vs doesn't) b) Calculate expected spread under each scenario c) How should uncertainty widen your confidence interval? d) At what probability does the "plays" scenario dominate predictions?

Exercise 18: Cross-Sport Comparison

Compare injury impact across sports:

a) Why is QB injury impact larger in NFL than star player injury in NBA? b) How does roster size affect injury impact? c) How do playoff formats change injury analysis? d) What can NFL analysts learn from other sports' injury analysis?

Exercise 19: Ethical Considerations

Discuss the ethical dimensions of injury analysis:

a) Should analysts share injury-related predictions publicly? b) How should "inside information" about injuries be handled? c) What are the privacy considerations for injured players? d) How might injury analysis affect team medical decisions?

Exercise 20: Comprehensive Injury Model

Build a complete injury adjustment for the following game:

Home Team (-3.5): - QB: Healthy (Elite tier) - RB1: Out (Above average tier) - WR1: Questionable, 50% (Pro Bowl tier) - LT: Out (Average tier) - CB1: Questionable, 30% (Good tier)

Away Team: - QB: Questionable, 60% (Good tier, average backup) - All others healthy

a) Calculate home team expected adjustment b) Calculate away team expected adjustment c) Calculate net adjustment to the spread d) What is your adjusted spread prediction? e) How confident are you in this prediction?

Challenge Exercise: Real-Time Injury System

Design a real-time injury adjustment system:

Requirements: 1. Ingest injury report data automatically 2. Update player values based on injury history 3. Calculate team adjustments for each game 4. Track prediction accuracy over time 5. Identify market inefficiencies

Deliverables: - System architecture diagram - Data model specification - Key algorithm pseudocode - Validation strategy

Submission Guidelines

For each exercise: 1. Show calculations step-by-step 2. State assumptions clearly 3. Interpret results in context 4. Identify limitations of your analysis 5. For programming exercises, include commented code