Chapter 10 Key Takeaways: Plus-Minus and On/Off Analysis

Essential Concepts Summary

Plus-minus and on/off analysis measure team performance with and without specific players on the court. These metrics capture total player impact regardless of whether contributions appear in box scores, but they suffer from confounding factors that motivated the development of adjusted methods covered in later chapters.

Core Formulas Reference

Raw Plus-Minus

$$\text{Plus-Minus} = \text{Team Points Scored}_{\text{player on}} - \text{Team Points Allowed}_{\text{player on}}$$

Purpose: Point differential during player's minutes Level: Can be calculated per game, season, or career

Net Rating

$$\text{Net Rating} = \text{Offensive Rating} - \text{Defensive Rating}$$

Where: $$\text{Offensive Rating} = \frac{\text{Points Scored}}{\text{Possessions}} \times 100$$

$$\text{Defensive Rating} = \frac{\text{Points Allowed}}{\text{Possessions}} \times 100$$

Possession Estimation

$$\text{Possessions} \approx \text{FGA} - \text{OREB} + \text{TOV} + 0.44 \times \text{FTA}$$

On/Off Differential

$$\text{On/Off Diff} = \text{Net Rating}_{\text{on}} - \text{Net Rating}_{\text{off}}$$

This can be decomposed: $$\text{On/Off Diff} = (\text{ORtg}_{\text{on}} - \text{ORtg}_{\text{off}}) - (\text{DRtg}_{\text{on}} - \text{DRtg}_{\text{off}})$$

Key Metrics Summary

Interpretation Benchmarks

Team Net Rating (Per 100 Possessions)

Individual On/Off Differential

Important: Differential depends heavily on backup quality, not just player ability.

Sources of Plus-Minus Noise

1. Sample Size Limitations

Standard Error Estimate: $$SE \approx \frac{37}{\sqrt{\text{Possessions}/100}}$$

2. Teammate Quality Confounding

Players sharing court with better teammates will have inflated plus-minus regardless of individual contribution.

Example: - Five players with true impacts: +5, +3, +1, -1, -3 - When they play together: All show +5 raw plus-minus - Cannot distinguish individual contributions

3. Opponent Quality Variation

• Starters typically face opponent starters
• Bench players face opponent benches
• Opponent quality affects results regardless of player ability

4. Score and Context Effects

• Garbage time inflates some players' plus-minus
• Clutch situations have tiny samples but outsized importance
• Score effects change play style

Lineup Analysis Guidelines

Sample Size Requirements

Lineup Evaluation Framework

1. Identify lineups with sufficient minutes
2. Calculate efficiency (ORtg, DRtg, Net Rtg)
3. Consider context (opponent quality, game situation)
4. Calculate confidence intervals before drawing conclusions

Confidence Interval Calculation

$$\text{95\% CI} = \text{Net Rating} \pm 1.96 \times SE$$

Example: 200 minutes, +15 Net Rating - Possessions: ~400 - SE: 37/sqrt(4) = 18.5 - 95% CI: -21 to +51 (too wide for conclusions)

On/Off Analysis Best Practices

Before Drawing Conclusions, Check:

• [ ] Sample size sufficient (1000+ minutes preferred)
• [ ] Teammate quality context understood
• [ ] Opponent quality distribution examined
• [ ] Garbage time impact considered
• [ ] Confidence intervals calculated
• [ ] Multiple seasons examined if available

Red Flags

1. Extreme values with small samples: +25 in 150 minutes is noise
2. Contradictory evidence: Great plus-minus but poor box scores (investigate)
3. Garbage time inflation: Check score differential during minutes
4. Unsustainable teammate shooting: On-court 3P% far above baseline

The Path to Adjusted Metrics

Why Raw Plus-Minus Is Insufficient

1. Cannot isolate individual contribution
2. Confounded by teammates and opponents
3. High noise, low signal (r=0.30-0.40 year-to-year)
4. Misleading for players on very good or very bad teams

Adjusted Plus-Minus Concept

Use regression to estimate individual contributions:

$$\text{Team Net Rating} = \sum_{i \in \text{teammates}} \beta_i - \sum_{j \in \text{opponents}} \beta_j + \epsilon$$

Where $\beta_i$ represents each player's estimated individual impact.

Regularized Adjusted Plus-Minus (RAPM)

Addresses collinearity through ridge regression: - Adds penalty for extreme estimates - Shrinks values toward zero (or prior) - Requires multi-year data for stability

Covered in detail in Chapter 14

Contextual Factors to Consider

Regular Season vs. Playoffs

Position-Specific Considerations

Point Guards: - Often show highest on/off due to playmaking leverage - Control possession outcomes - Create downstream effects for teammates

Centers: - Defensive impact often exceeds offensive - Rim protection creates team-wide effects - May show larger DRtg differentials

Wings: - More balanced offensive/defensive contributions - Defensive switching affects multiple positions - Two-way impact harder to isolate

Common Mistakes to Avoid

Mistake 1: Treating On/Off as Absolute Value

Problem: Comparing players across different teams by on/off differential Solution: Recognize differential depends on backup quality

Mistake 2: Ignoring Confidence Intervals

Problem: Drawing firm conclusions from small samples Solution: Always calculate and report uncertainty

Mistake 3: Attributing Team Performance to Individuals

Problem: Assuming good team Net Rating means each player is good Solution: Use lineup analysis and adjustment methods

Mistake 4: Treating Playoffs Like Regular Season

Problem: Expecting regular season metrics to predict playoff outcomes Solution: Acknowledge smaller samples and adjustment potential

Mistake 5: Ignoring Context When Comparing

Problem: Comparing players with different roles, teammates, opponents Solution: Control for context or use adjusted methods

Quick Reference: Analytical Questions

Chapter Summary Statement

Plus-minus and on/off analysis capture player impact that box scores miss by measuring team performance outcomes. However, raw plus-minus is noisy and confounded by teammate quality, opponent quality, and sample size. These limitations motivate adjusted plus-minus methods that use regression to isolate individual contributions. Raw on/off analysis serves as an important input and diagnostic tool, but should not be used as the sole measure of player value.

Looking Ahead

Part 3 of this textbook introduces adjusted plus-minus methods:

• Chapter 14: Regularized Adjusted Plus-Minus (RAPM)
• Chapter 15: Modern All-in-One Metrics (RPM, RAPTOR, EPM)
• Chapter 16: Tracking-Enhanced Impact Metrics

These approaches address the limitations identified in this chapter through statistical adjustment and data integration.