Chapter 8 Key Takeaways: Shooting Efficiency Metrics

Essential Concepts Summary

Shooting efficiency metrics quantify how effectively players and teams convert scoring opportunities into points. The progression from basic Field Goal Percentage through Effective Field Goal Percentage to True Shooting Percentage represents increasing sophistication in capturing the full picture of scoring efficiency.

Core Formulas Reference

Field Goal Percentage (FG%)

$$FG\% = \frac{FGM}{FGA} \times 100$$

Purpose: Basic shooting accuracy measure Limitation: Treats all field goals equally regardless of point value

Effective Field Goal Percentage (eFG%)

$$eFG\% = \frac{FGM + 0.5 \times 3PM}{FGA} \times 100$$

Purpose: Accounts for extra value of three-pointers Interpretation: The FG% a player would need shooting only twos to produce same points per shot

True Shooting Percentage (TS%)

$$TS\% = \frac{PTS}{2 \times (FGA + 0.44 \times FTA)} \times 100$$

Purpose: Comprehensive efficiency including free throws Gold Standard: Most complete single measure of scoring efficiency

True Shooting Attempts (TSA)

$$TSA = FGA + 0.44 \times FTA$$

The 0.44 Factor: Weighted average accounting for: - Two-shot fouls (2 FTA = 1 possession) - Three-shot fouls (3 FTA = 1 possession) - And-one free throws (1 FTA, no extra possession) - Technical free throws (no possession cost)

Free Throw Rate (FTr)

$$FTr = \frac{FTA}{FGA}$$

Purpose: Measures foul-drawing ability relative to shot attempts

Three-Point Attempt Rate (3PAr)

$$3PAr = \frac{3PA}{FGA}$$

Purpose: Shot distribution metric showing three-point reliance

Points Per Shooting Attempt (PPS)

$$PPS = \frac{PTS}{TSA}$$

Purpose: Direct measure of points produced per scoring attempt

Expected Value (EV)

$$EV = FG\% \times \text{Point Value}$$

Purpose: Expected points per shot type

Three-Point Break-Even

$$\text{Break-Even 3P\%} = \frac{2}{3} \times 2P\%$$

Purpose: Three-point percentage needed to equal two-point efficiency

Key Metrics Summary

Efficiency Benchmarks

True Shooting Percentage (Modern Era)

Note: League average TS% is approximately 56-57% in the 2020s era.

Effective Field Goal Percentage

Free Throw Rate

Shot Zone Efficiency Reference

Expected Value by Zone (League Average)

The Mid-Range Dead Zone

Mid-range shots (10-22 feet, excluding three-pointers) typically yield: - Lowest expected value in basketball - ~0.80-0.86 points per attempt - Below both rim attempts (1.28+) and three-pointers (1.05+)

The Three-Point Revolution

Historical Three-Point Attempt Evolution

Why Three-Point Shooting Increased

1. Mathematical advantage: Higher EV than mid-range
2. Spacing benefits: Opens driving lanes
3. Analytics adoption: Front offices recognized value
4. Player development: Youth training emphasized shooting
5. Rule changes: Freedom of movement helped shooters

Efficiency Analysis Checklist

Before Evaluating a Player

• [ ] Calculated TS% (not just FG%)
• [ ] Considered shot volume (TSA/game or Usage)
• [ ] Examined shot distribution (3PAr, zone breakdown)
• [ ] Compared to era-appropriate benchmarks
• [ ] Accounted for role context (primary vs. secondary scorer)
• [ ] Checked free throw rate contribution

Quality Control Questions

1. Is the sample size sufficient for reliability?
2. What is the player's role and team context?
3. How does efficiency compare to usage level?
4. Are efficiency metrics consistent with shot profile?
5. What does zone-specific analysis reveal?

Common Mistakes to Avoid

Mistake 1: Using FG% for Perimeter Players

Problem: FG% penalizes three-point shooters Solution: Always use eFG% or TS% for overall efficiency

Mistake 2: Ignoring Free Throws in Efficiency

Problem: eFG% misses free throw contribution Solution: TS% captures complete scoring picture

Mistake 3: Comparing Volume and Efficiency Separately

Problem: High efficiency at low volume is different from high efficiency at high volume Solution: Consider efficiency in context of TSA or Usage Rate

Mistake 4: Applying Modern Benchmarks to Historical Players

Problem: League average TS% has changed over time Solution: Compare to era-appropriate averages

Mistake 5: Treating Expected Value as Deterministic

Problem: EV analysis assumes large samples; variance matters Solution: Acknowledge variance especially in small samples (playoffs)

Key Relationships

TS% vs. eFG%

$$TS\% - eFG\% \approx \text{Free Throw Contribution}$$

Players with high FTr will have TS% noticeably higher than eFG%.

eFG% vs. FG%

$$eFG\% - FG\% = \frac{0.5 \times 3PM}{FGA} \times 100$$

The "three-point bonus" - increases with both 3PM and 3PAr.

Volume-Efficiency Trade-off

As usage increases: - Shot difficulty typically increases - Efficiency tends to decrease - Exceptional players maintain high efficiency despite volume

Historical Context

Elite TS% Seasons (High Volume)

League Average TS% by Era

Quick Reference Conversions

From FG% to Approximate TS%

For players with typical shot distributions:

TS% ≈ FG% + 7-10%

From eFG% to Expected PPS

Expected PPS ≈ eFG% × 2 / 100

(50% eFG% = 1.00 PPS)

From TS% to Expected PPS

PPS = TS% × 2 / 100

(60% TS% = 1.20 PPS)

Chapter Summary Statement

True Shooting Percentage represents the gold standard for measuring scoring efficiency because it incorporates all scoring methods: two-pointers, three-pointers, and free throws. Understanding the relationship between TS%, eFG%, and shot distribution enables proper evaluation of players across different roles and eras. The three-point revolution transformed shot selection by revealing the mathematical superiority of three-pointers over mid-range shots, fundamentally changing how basketball is played.

Looking Ahead

Chapter 9 introduces advanced box score metrics like PER, Game Score, and Usage Rate that incorporate shooting efficiency alongside other statistics to create comprehensive player evaluation frameworks. These metrics build on the efficiency concepts established here while attempting to capture a player's complete statistical contribution.