Chapter 16 Exercises: Shot Quality Models

Overview

These exercises cover expected points calculations, shot difficulty factors, model building, and practical applications of shot quality metrics.

Section A: Expected Points Fundamentals (Exercises 1-8)

Exercise 1: Basic Expected Points

Calculate expected points for each shot:

a) Calculate xPoints for each shot. b) Rank shots by expected value. c) Which shot has highest expected value?

Exercise 2: Zone-Based Expected Points

League average FG% by zone: - Restricted area: 63% - Paint (non-RA): 40% - Mid-range: 41% - Corner 3: 39% - Above-break 3: 36%

a) Calculate expected points per shot for each zone. b) Why do teams prioritize restricted area and corner 3s? c) Calculate expected points per 100 shots for a player taking 40% at rim, 20% mid-range, 40% three-pointers.

Exercise 3: Shot Distribution Analysis

Two players with same PPG (20.0):

Player A: 8 FGA/g at rim (65%), 6 FGA mid-range (42%), 4 FGA three (35%) Player B: 4 FGA/g at rim (65%), 4 FGA mid-range (42%), 10 FGA three (38%)

a) Calculate expected points per game for each player. b) Calculate actual vs. expected efficiency. c) Which player has better shot selection?

Exercise 4: Defender Distance Impact

League FG% by defender distance: - Wide Open (6+ ft): 48% - Open (4-6 ft): 43% - Tight (2-4 ft): 38% - Very Tight (0-2 ft): 33%

For a player taking 100 three-point attempts: - 30 wide open - 40 open - 25 tight - 5 very tight

a) Calculate expected makes. b) Calculate expected points. c) Compare to league average (36% on all 3PA).

Exercise 5: Shot Clock Analysis

FG% by shot clock: - Early (15+ sec): 52% - Mid (8-14 sec): 48% - Late (4-7 sec): 43% - Very Late (0-3 sec): 35%

A team averages 90 FGA per game with this distribution: - Early: 25%, Mid: 50%, Late: 20%, Very Late: 5%

a) Calculate expected FG%. b) Calculate actual vs. expected if team shoots 47%. c) Recommend shot selection adjustments.

Exercise 6: Touch Time Analysis

FG% by touch time before shot: - Catch-and-shoot (<2 sec): 48% - Quick (2-4 sec): 44% - Moderate (4-6 sec): 41% - Extended (6+ sec): 38%

a) Why does FG% decline with touch time? b) If a player increases catch-and-shoot attempts from 30% to 50% of total shots, estimate efficiency gain. c) What player types might not fit this pattern?

Exercise 7: Dribbles Before Shot

FG% by dribbles: - 0 dribbles: 48% - 1-2 dribbles: 44% - 3-5 dribbles: 40% - 6+ dribbles: 36%

A point guard's shot distribution: - 0 dribbles: 20%, 1-2: 35%, 3-5: 30%, 6+: 15%

a) Calculate expected FG%. b) If the player can increase 0-dribble shots to 30%, estimate new expected FG%. c) Discuss tradeoffs of this recommendation.

Exercise 8: Combined Factor Analysis

Shot with these characteristics: - Distance: 18 feet (mid-range, base 41%) - Defender: 3 feet (tight, multiply by 0.90) - Touch time: 5 seconds (moderate, multiply by 0.98) - Dribbles: 2 (multiply by 0.99)

a) Calculate combined expected FG%. b) Calculate expected points. c) Compare to a wide-open corner three (39% base).

Section B: Model Building (Exercises 9-15)

Exercise 9: Feature Engineering

Design features for a shot quality model from this data: - Shot location (x, y) - Shooter ID - Defender positions - Shot clock - Score differential

a) List 10 potentially predictive features. b) Identify which are continuous vs. categorical. c) Propose interaction terms.

Exercise 10: Logistic Regression Basics

The logistic regression model: P(make) = 1 / (1 + exp(-(b0 + b1distance + b2defender_dist)))

With coefficients: b0 = 0.5, b1 = -0.05, b2 = 0.15

Calculate P(make) for: a) Shot at 10 feet with defender at 4 feet b) Shot at 20 feet with defender at 6 feet c) Shot at 5 feet with defender at 2 feet

Exercise 11: Model Evaluation

Model predicts these probabilities for 10 shots: [0.65, 0.45, 0.55, 0.70, 0.35, 0.60, 0.40, 0.75, 0.30, 0.50]

Actual outcomes (1=make, 0=miss): [1, 0, 1, 1, 0, 0, 1, 1, 0, 1]

a) Calculate log loss. b) Calculate Brier score. c) Evaluate calibration (do 60% probability shots go in ~60% of the time?).

Exercise 12: Train-Test Split

You have 50,000 shots from a season.

a) Design a train-test split strategy. b) Why is random splitting potentially problematic for basketball data? c) Propose an alternative (e.g., temporal, player-based).

Exercise 13: Cross-Validation

Design 5-fold cross-validation for shot quality model:

a) How should folds be constructed? b) What metrics should be computed on each fold? c) How do you select the final model?

Exercise 14: Feature Importance

Model shows these feature importances: 1. Distance to basket: 35% 2. Defender distance: 22% 3. Shot type: 15% 4. Shot clock: 10% 5. Shooter ability: 8% 6. Other: 10%

a) Interpret these importances. b) Which features might be undervalued? c) How would you use this for player evaluation?

Exercise 15: Model Calibration

Your model predicts: - 100 shots at 30% probability: 25 made (expected 30) - 100 shots at 50% probability: 55 made (expected 50) - 100 shots at 70% probability: 65 made (expected 70)

a) Evaluate calibration for each bucket. b) Is the model over- or under-confident? c) Propose calibration adjustment.

Section C: Player Evaluation (Exercises 16-22)

Exercise 16: Shot Quality Differential

Player's shot statistics: - Attempts: 500 - Makes: 230 - Expected makes (from model): 210

a) Calculate actual FG%. b) Calculate expected FG%. c) Calculate shot-making above expected.

Exercise 17: Shot Selection Evaluation

Two shooters with same expected points per shot (1.05):

Player X: High volume (15 FGA), 1.02 actual xPts/shot Player Y: Low volume (8 FGA), 1.08 actual xPts/shot

a) Who has better shot selection? b) Calculate total expected points per game for each. c) Discuss volume vs. selectivity tradeoff.

Exercise 18: Shot Creation Credit

Player creates shots for teammates: - Assists: 8 per game - Assisted shot xPts: average 1.15 - Own shots xPts: average 1.00

a) Calculate total shot creation value. b) How much credit should the passer receive? c) Compare to a player with better own shots (1.10) but fewer assists (4).

Exercise 19: Defensive Shot Quality

Defender's opponents take shots with: - Average xPts: 0.95 (vs. league average 1.05) - Made rate: 42% (vs. expected 44%)

a) Calculate shot quality reduction. b) Calculate shot-making reduction (beyond quality). c) Total defensive impact.

Exercise 20: Three-Point Value Analysis

Player's three-point profile: - Corner 3: 45 attempts, 42% FG - Above-break 3: 120 attempts, 36% FG - Pull-up 3: 40 attempts, 32% FG

a) Calculate expected points by shot type. b) Calculate actual points by shot type. c) Recommend shot distribution adjustment.

Exercise 21: Rim Finishing Analysis

Player's shots at rim: - Uncontested: 50 attempts, 75% - Contested (no rim protector): 40 attempts, 55% - Contested (with rim protector): 30 attempts, 45%

a) Calculate expected points for each category. b) Compare to league averages. c) Identify strengths and weaknesses.

Exercise 22: Shot Quality Trends

Player's monthly shot quality:

a) Calculate shot-making differential by month. b) Identify shot quality trends. c) What might explain the variations?

Section D: Advanced Applications (Exercises 23-30)

Exercise 23: Play Type Analysis

Expected points by play type: | Play Type | Freq | xPts | Actual Pts | |-----------|------|------|------------| | Transition | 15% | 1.15 | 1.22 | | P&R Handler | 25% | 0.98 | 1.02 | | P&R Roller | 10% | 1.20 | 1.15 | | Isolation | 20% | 0.92 | 0.88 | | Post-up | 10% | 0.95 | 0.98 | | Spot-up | 20% | 1.08 | 1.05 |

a) Calculate total expected and actual PPP. b) Identify over/under-performing play types. c) Recommend play type distribution changes.

Exercise 24: Lineup Shot Quality

Five-man lineup shot quality: - Lineup A: xPts 1.12, actual 1.08 - Lineup B: xPts 1.02, actual 1.10 - Lineup C: xPts 1.08, actual 1.06

a) Which lineup creates best shots? b) Which lineup converts best relative to shot quality? c) How should this inform lineup decisions?

Exercise 25: Clutch Shot Analysis

Player's shot quality in clutch (last 5 min, within 5 pts): - Regular season clutch: xPts 1.00, actual 1.05 - Playoffs clutch: xPts 0.95, actual 0.92

a) Evaluate clutch shot selection. b) Evaluate clutch shot-making. c) Is this player a "clutch performer"?

Exercise 26: Shot Quality Aging

Player's shot quality by age: | Age | xFG% | Actual FG% | 3PA% | |-----|------|------------|------| | 25 | 48% | 50% | 35% | | 27 | 49% | 51% | 40% | | 29 | 48% | 49% | 45% | | 31 | 47% | 46% | 50% | | 33 | 45% | 43% | 52% |

a) Analyze shot selection changes with age. b) Analyze shot-making changes with age. c) Project shot quality at age 35.

Exercise 27: Trade Analysis

Acquiring player's shot profile: - xPts/shot: 1.02 - Volume: 12 FGA/game - Shot creation for others: +0.05 xPts/assisted shot

Team's current: - xPts/shot: 0.98 - Available shots: 10 FGA/game for new player

a) Calculate expected offensive improvement. b) Account for shot creation impact. c) Value the acquisition in wins.

Exercise 28: Defensive System Analysis

Team defense allows: - Open 3s: 12 per game, 38% (league avg open: 40%) - Contested 3s: 18 per game, 32% (league avg: 34%) - Rim attempts: 25 per game, 58% (league avg: 63%) - Mid-range: 15 per game, 42% (league avg: 41%)

a) Calculate expected points allowed from shot quality. b) Calculate actual points allowed on these shots. c) Evaluate defensive shot quality impact.

Exercise 29: Shot Quality Model Improvement

Your current model has: - Log loss: 0.65 - Brier score: 0.22 - R-squared: 0.15

Proposed improvements: a) Add shooter fixed effects b) Add shot type interactions c) Use gradient boosting instead of logistic regression

Predict impact of each improvement and justify.

Exercise 30: Comprehensive Analysis

Using all shot quality concepts, analyze a hypothetical player:

Stats: - 18 PPG on 14 FGA - 48% FG (league avg: 47%) - Shot distribution: 35% rim, 20% mid-range, 45% three - Defender distance avg: 4.5 feet - xFG% from model: 46% - Creates 3.5 "open" shots for teammates per game

a) Calculate shot quality metrics. b) Evaluate shot-making ability. c) Evaluate shot selection. d) Evaluate shot creation. e) Provide overall assessment and recommendations.

Answer Key Hints

Exercise 1: - Shot A: 0.65 × 2 = 1.30 xPts - Shot B: 0.45 × 2 = 0.90 xPts - Shot C: 0.38 × 3 = 1.14 xPts - Shot D: 0.32 × 3 = 0.96 xPts

Exercise 2a: - Restricted: 0.63 × 2 = 1.26 xPts - Paint: 0.40 × 2 = 0.80 xPts - Mid-range: 0.41 × 2 = 0.82 xPts - Corner 3: 0.39 × 3 = 1.17 xPts - Above-break 3: 0.36 × 3 = 1.08 xPts

Exercise 10a: P(make) = 1 / (1 + exp(-(0.5 - 0.05×10 + 0.15×4))) = 1 / (1 + exp(-(0.5 - 0.5 + 0.6))) = 1 / (1 + exp(-0.6)) = 1 / 1.549 = 0.645 or 64.5%

Full solutions available in the instructor's manual.