Case Study 1: Building a Shot Quality Model for the Houston Rockets' Three-Point Revolution
Introduction
The Houston Rockets' embrace of three-point shooting and rim attacks in the mid-2010s represented a data-driven offensive philosophy built on shot quality principles. This case study examines how shot quality models informed this strategic transformation and evaluates its effectiveness.
Background
The Traditional Offense (Pre-2016)
League-wide shot distribution (2010): - Mid-range: ~35% of shots - Three-pointers: ~22% of shots - Restricted area: ~28% of shots - Other paint: ~15% of shots
Expected points by zone: | Zone | FG% | Point Value | Expected Points | |------|-----|-------------|-----------------| | Restricted Area | 63% | 2 | 1.26 | | Paint (non-RA) | 40% | 2 | 0.80 | | Mid-range | 41% | 2 | 0.82 | | Corner 3 | 38% | 3 | 1.14 | | Above-break 3 | 35% | 3 | 1.05 |
The Analytics Insight
Daryl Morey's front office identified a clear hierarchy: 1. Restricted area shots (1.26 xPts) - Highest value 2. Corner threes (1.14 xPts) - Second highest 3. Above-break threes (1.05 xPts) - Third highest 4. Mid-range shots (0.82 xPts) - Lowest value among common shots
The strategic implication: Eliminate mid-range shots entirely, maximize rim attempts and three-pointers.
Building the Shot Quality Model
Data Collection
Input features: - Shot location (x, y coordinates) - Defender distance at release - Shot clock time - Touch time before shot - Dribbles before shot - Shot type (catch-and-shoot, pull-up, etc.) - Player shooting ability
Model Architecture
P(make) = logistic(
b0 +
b1 * distance +
b2 * defender_distance +
b3 * shot_clock +
b4 * touch_time +
b5 * is_corner_3 +
player_fixed_effects
)
Feature Engineering
Spatial features: - Distance to basket (continuous) - Shot zone (categorical) - Angle to basket - Distance from three-point line (for near-line shots)
Contextual features: - Defender distance buckets (0-2, 2-4, 4-6, 6+ feet) - Shot clock phase (early/mid/late/very late) - Score differential - Quarter/overtime indicator
Player features: - Historical shooting percentage by zone - Three-point specialist indicator - Rim finishing grade
Model Training and Validation
Dataset
- Training data: 2010-2015 league-wide shots (500,000+ attempts)
- Validation: 2015-16 season (held out)
- Features: 25 predictive variables
Model Performance
| Metric | Value | Interpretation |
|---|---|---|
| Log Loss | 0.63 | Good probability calibration |
| Brier Score | 0.21 | Low prediction error |
| AUC-ROC | 0.68 | Reasonable discrimination |
| R-squared | 0.18 | Explains 18% of variance |
Calibration Results
| Predicted FG% | Actual FG% | Count | Error |
|---|---|---|---|
| 30-35% | 32.8% | 45,000 | +0.3% |
| 35-40% | 37.2% | 62,000 | -0.3% |
| 40-45% | 42.1% | 78,000 | -0.4% |
| 45-50% | 47.5% | 55,000 | +0.0% |
| 50-55% | 52.3% | 40,000 | -0.2% |
| 55-60% | 57.8% | 35,000 | +0.3% |
| 60-65% | 62.1% | 48,000 | -0.4% |
| 65-70% | 66.9% | 32,000 | -0.6% |
The model showed excellent calibration across probability ranges.
Implementation: The Rockets Transformation
Shot Distribution Changes
| Season | Mid-Range % | Three-Point % | Rim % | Other |
|---|---|---|---|---|
| 2012-13 | 28.2% | 28.5% | 31.0% | 12.3% |
| 2014-15 | 18.5% | 35.8% | 32.5% | 13.2% |
| 2016-17 | 10.2% | 43.2% | 35.1% | 11.5% |
| 2018-19 | 4.2% | 50.2% | 34.8% | 10.8% |
Expected Points Impact
2012-13 Shot Quality:
xPts = 0.282(0.82) + 0.285(1.08) + 0.310(1.26) + 0.123(0.80)
= 0.23 + 0.31 + 0.39 + 0.10
= 1.03 xPts per shot
2018-19 Shot Quality:
xPts = 0.042(0.82) + 0.502(1.08) + 0.348(1.26) + 0.108(0.80)
= 0.03 + 0.54 + 0.44 + 0.09
= 1.10 xPts per shot
Improvement: +0.07 xPts per shot = +7 points per 100 shots
Player Acquisition Decisions
James Harden trade (2012): - High-volume scorer - Elite rim attacker - Developing three-point shooter - Shot profile aligned with analytics vision
Role player targets: - Prioritized floor-spacing shooters - Targeted corner three specialists - De-emphasized mid-range scorers
Results Analysis
Offensive Efficiency
| Season | Off Rating | League Rank | xPts/Shot |
|---|---|---|---|
| 2012-13 | 106.3 | 8th | 1.03 |
| 2014-15 | 108.4 | 5th | 1.05 |
| 2016-17 | 111.8 | 2nd | 1.08 |
| 2017-18 | 114.7 | 1st | 1.11 |
| 2018-19 | 113.8 | 2nd | 1.10 |
Shot-Making Analysis
The Rockets didn't just take better shots - they also made them:
2017-18 Season: - Expected FG%: 48.2% - Actual FG%: 49.1% - Shot-making above expected: +0.9%
Key players exceeding expectations: | Player | xFG% | Actual FG% | Differential | |--------|------|------------|--------------| | James Harden | 47.5% | 49.2% | +1.7% | | Chris Paul | 49.1% | 51.8% | +2.7% | | Eric Gordon | 44.8% | 45.9% | +1.1% |
Three-Point Volume vs. Efficiency
| Season | 3PA/Game | 3P% | Expected 3P% | Differential |
|---|---|---|---|---|
| 2016-17 | 40.3 | 35.7% | 35.2% | +0.5% |
| 2017-18 | 42.3 | 36.2% | 35.5% | +0.7% |
| 2018-19 | 45.4 | 35.6% | 35.3% | +0.3% |
The team maintained efficiency even at historic volume.
Model Insights for Strategy
Defender Distance Findings
The model revealed that open threes were significantly more valuable than contested mid-range shots:
| Shot Type | Avg Defender Dist | FG% | xPts |
|---|---|---|---|
| Open 3 (6+ ft) | 7.2 ft | 40.1% | 1.20 |
| Contested 3 (2-4 ft) | 3.1 ft | 33.5% | 1.01 |
| Open mid-range | 6.5 ft | 45.2% | 0.90 |
| Contested mid-range | 3.0 ft | 36.8% | 0.74 |
Key insight: Even contested threes outperformed contested mid-range shots.
Shot Clock Analysis
| Shot Clock | Rim FG% | 3P FG% | Optimal Strategy |
|---|---|---|---|
| Early (15+ sec) | 67% | 38% | Rim attack preferred |
| Mid (8-14 sec) | 63% | 36% | Either acceptable |
| Late (4-7 sec) | 58% | 34% | Take available shot |
| Very Late (0-3 sec) | 51% | 30% | Three slightly preferred |
Strategic application: Early offense prioritized rim attacks; late clock favored three-point attempts.
Limitations and Challenges
What the Model Missed
- Opponent adaptation: Teams learned to defend the Rockets' tendencies
- Playoff adjustments: Defenses became more physical in playoffs
- Player fatigue: High three-point volume may have affected late-game shooting
- Shot creation burden: Harden's isolation heavy-lifting showed diminishing returns
2018 Western Conference Finals
Regular season vs. Warriors: - 3PA: 42.3/game - 3P%: 36.2%
Conference Finals vs. Warriors: - 3PA: 44.8/game - 3P%: 30.4%
Game 7: 7/44 from three (15.9%) - model predicted ~35%
Post-hoc analysis: The model didn't account for: - Elite switching defense - Playoff physicality - High-pressure variance - Shot quality degradation against elite defense
Lessons Learned
For Model Building
- Include opponent quality: Shot quality varies by defensive opponent
- Context matters: Regular season models may not transfer to playoffs
- Confidence intervals: High-variance outcomes need uncertainty quantification
- Update regularly: Shot quality relationships evolve with rule changes
For Strategic Implementation
- Diversification: Over-reliance on one shot type creates vulnerabilities
- Player skills matter: Model assumes shots are interchangeable; they aren't
- Adaptation: Opponents adjust to predictable strategies
- Balance: Extreme optimization may have diminishing returns
Conclusion
The Rockets' shot quality-driven transformation demonstrated the power of analytics in basketball strategy. Their sustained offensive excellence validated the core principles of expected points optimization. However, the playoff struggles revealed limitations of models that don't account for high-stakes variance and opponent adaptation.
Shot quality models remain essential tools for understanding offensive efficiency, but successful implementation requires nuanced application that recognizes their limitations.
Discussion Questions
- How might the Rockets have modified their approach to account for playoff variance?
- What role should player skill differentiation play in shot quality optimization?
- How can shot quality models better incorporate opponent defensive quality?
- Is there an optimal level of shot selection extremity, or should teams maximize expected value regardless of variance?
- How have other teams adapted to or countered the Rockets' approach?
Data Exercise
Using the shot quality principles from this case study:
-
Calculate the expected points for a team with this distribution: - 35% at rim (64% FG) - 25% mid-range (40% FG) - 40% three-pointers (36% FG)
-
Optimize the distribution to maximize expected points while keeping total shots constant.
-
Calculate the expected improvement in points per 100 shots.