Chapter 16 Key Takeaways: Shot Quality Models
Executive Summary
Shot quality models quantify the expected value of basketball shots by combining probability of success with point value. These models separate shot selection (difficulty of shots taken) from shot-making (ability to convert shots relative to expectation), enabling more accurate player evaluation and strategic optimization.
Core Concepts
- [ ] Expected Points = P(make) x Point Value
- [ ] Shot quality measures difficulty, not outcome
- [ ] Shot-making measures skill beyond difficulty adjustment
- [ ] Zone-based hierarchy: Rim > Corner 3 > Above-break 3 > Mid-range
- [ ] Context factors: Defender distance, shot clock, touch time, dribbles
Key Formulas
Expected Points
xPoints = FG% x Point_Value
Example: - Corner 3: 0.39 x 3 = 1.17 xPts - Mid-range: 0.41 x 2 = 0.82 xPts
Logistic Regression for Shot Probability
P(make) = 1 / (1 + exp(-(b0 + b1*x1 + b2*x2 + ...)))
Shot Quality Metrics
Shot Quality Index (xFG%) = Average predicted probability across all shots
Shot-Making Index = Actual FG% - xFG%
Model Evaluation
Brier Score = mean((predicted - actual)^2)
Log Loss = -mean(actual*log(pred) + (1-actual)*log(1-pred))
Expected Points by Zone (League Averages)
| Zone | FG% | xPoints |
|---|---|---|
| Restricted Area | 63% | 1.26 |
| Corner 3 | 39% | 1.17 |
| Above-break 3 | 36% | 1.08 |
| Mid-range | 41% | 0.82 |
| Paint (non-RA) | 40% | 0.80 |
Key Difficulty Factors
Defender Distance
| Category | Distance | FG% Impact |
|---|---|---|
| Wide Open | 6+ feet | +8-10% |
| Open | 4-6 feet | +3-5% |
| Tight | 2-4 feet | Baseline |
| Very Tight | 0-2 feet | -5-8% |
Shot Clock
| Phase | Seconds | FG% vs Average |
|---|---|---|
| Early | 15+ | +4-5% |
| Mid | 8-14 | +0-2% |
| Late | 4-7 | -2-4% |
| Very Late | 0-3 | -8-12% |
Touch Time
- Catch-and-shoot (<2 sec): Highest FG%
- Quick (2-4 sec): Above average
- Moderate (4-6 sec): Average
- Extended (6+ sec): Below average
Model Building Checklist
-
Feature Selection - [ ] Shot location (x, y or distance + angle) - [ ] Defender distance at release - [ ] Shot clock - [ ] Touch time / dribbles - [ ] Shot type classification
-
Model Considerations - [ ] Exclude shooter identity for pure difficulty model - [ ] Include shooter for prediction model - [ ] Use temporal train-test splits - [ ] Evaluate calibration across probability bins
-
Validation Metrics - [ ] Log loss (calibration) - [ ] Brier score (accuracy) - [ ] AUC-ROC (discrimination) - [ ] Calibration plots by decile
Player Evaluation Framework
Shot Selection vs. Shot-Making Matrix
| Poor Shot-Making | Good Shot-Making | |
|---|---|---|
| Easy Shots | Underperformer | Role Player Value |
| Difficult Shots | Volume Scorer | Elite Creator |
Interpretation Guidelines
High xFG%, High Actual: Efficient role player or system beneficiary High xFG%, Low Actual: Underperforming, regression candidate Low xFG%, High Actual: Elite shot-maker, high skill Low xFG%, Low Actual: Inefficient volume scorer, role change needed
Applications
Offensive Strategy
- Maximize restricted area and three-point attempts
- Minimize long mid-range shots
- Create open shots through ball movement
- Prioritize early offense for higher xFG%
Player Evaluation
- Separate skill from opportunity
- Identify undervalued shot-makers
- Project players to new roles/systems
- Track development and decline
Defensive Analytics
- Measure shot quality forced
- Identify defenders who reduce opponent xPts
- Evaluate closeout effectiveness
- Design defensive schemes to minimize opponent xFG%
Team Building
- Target players whose skills fit system
- Avoid overpaying for system-inflated stats
- Build lineups with complementary profiles
- Project trade acquisitions accurately
Common Mistakes to Avoid
- Ignoring sample size: Need 300+ shots for stable shot-making estimates
- Conflating selection and making: High FG% can mean easy shots, not skill
- Ignoring context: Playoff performance differs from regular season
- Overfitting models: Include only stable, predictive features
- Ignoring shot creation: Difficult shot-takers often create for others
Quick Reference
Shot Value Hierarchy
- Dunks/layups at rim (1.30+ xPts)
- Wide-open corner 3 (1.20+ xPts)
- Open above-break 3 (1.10-1.15 xPts)
- Contested three (0.95-1.05 xPts)
- Open mid-range (0.85-0.90 xPts)
- Contested mid-range (0.70-0.80 xPts)
Model Performance Benchmarks
- Good log loss: < 0.65
- Good Brier score: < 0.22
- Good calibration: ±2% in each decile
Summary
Shot quality models are foundational tools in modern basketball analytics, enabling teams to optimize shot selection, accurately evaluate players, and design effective offensive and defensive strategies. The key insight is separating what shots players take (selection) from how well they convert them (making).