Chapter 13: Key Takeaways

Quick Reference Guide for Goalkeeper Analysis

Core Shot-Stopping Metrics

Metric Definitions

Key Formulas

Save Percentage: $$\text{Save \%} = \frac{\text{Saves}}{\text{Shots on Target}} \times 100$$

Goals Prevented: $$\text{GP} = \text{PSxG} - \text{Goals Conceded}$$

Goals Prevented per 90: $$\text{GP/90} = \text{GP} \times \frac{90}{\text{Minutes Played}}$$

Distribution Metrics

Distribution Style Classification

Sweeper-Keeper Metrics

Sweeper-Keeper Requirements

High-Line Systems: - Sweeper actions p90 > 1.0 - Pass completion > 80% - Comfortable under pressure

Low-Block Systems: - Sweeper actions less critical - Focus on shot-stopping - Strong aerial ability

Sample Size Guidelines

Metric Stabilization Points

Confidence Interval Reference

For save percentage with n shots: $$\text{SE} \approx \sqrt{\frac{p(1-p)}{n}}$$

95% CI: $\hat{p} \pm 1.96 \times \text{SE}$

Goalkeeper Style Profiles

Traditional Shot-Stopper

Modern Sweeper-Keeper

Bayesian Estimation

Beta-Binomial Model for Save Percentage

Prior: Beta(α, β) where α = prior saves, β = prior goals

Posterior: $$\text{Posterior} = \text{Beta}(\alpha + \text{saves}, \beta + \text{goals})$$

Posterior Mean: $$\hat{p} = \frac{\alpha + \text{saves}}{\alpha + \beta + \text{shots}}$$

Default Prior Values

Recruitment Checklist

For High-Line/Possession Teams

• [ ] Pass completion > 82%
• [ ] Long pass % < 40%
• [ ] Sweeper actions p90 > 1.0
• [ ] Comfortable under pressure
• [ ] Save % > 70%

For Low-Block/Defensive Teams

• [ ] Save % > 74%
• [ ] Aerial claim rate > 75%
• [ ] Strong 1v1 positioning
• [ ] Long kick accuracy > 55%
• [ ] Communication skills

Visualization Best Practices

Shot Map

• Show shot locations with outcome colors
• Size by xG
• Include goalkeeper position if available

Distribution Patterns

• Arrow plot showing pass origins and destinations
• Color by success/failure
• Highlight progressive passes

Radar Chart Metrics

1. Goals Prevented
2. Save Percentage
3. Pass Success Rate
4. Long Pass Accuracy
5. Sweeper Actions p90
6. Aerial Win Rate

Common Interpretation Pitfalls

Avoid These Mistakes

1. Ignoring Sample Size: 10-match samples are unreliable
2. Context-Free Comparison: Compare within similar systems
3. Single Metric Focus: Use comprehensive profiles
4. Ignoring Uncertainty: Always report confidence levels
5. Traditional Bias: Clean sheets ≠ goalkeeper quality

Best Practices

1. Use goals prevented over raw goals conceded
2. Report confidence intervals
3. Consider system context
4. Use multiple metrics
5. Acknowledge limitations

Quick Code Snippets

Basic Save Statistics

def get_save_stats(shots_faced, goals_conceded, xg_faced):
    saves = shots_faced - goals_conceded
    save_pct = saves / shots_faced if shots_faced > 0 else 0
    goals_prevented = xg_faced - goals_conceded
    return {
        'saves': saves,
        'save_pct': save_pct,
        'goals_prevented': goals_prevented
    }

Bayesian Save Percentage

def bayesian_save_pct(saves, shots, prior_alpha=10, prior_beta=3):
    post_alpha = prior_alpha + saves
    post_beta = prior_beta + (shots - saves)
    return post_alpha / (post_alpha + post_beta)

Distribution Analysis

def analyze_distribution(gk_passes):
    successful = gk_passes[gk_passes['pass_outcome'].isna()]
    long_passes = gk_passes[gk_passes['pass_length'] >= 40]
    return {
        'completion': len(successful) / len(gk_passes),
        'long_pct': len(long_passes) / len(gk_passes)
    }

Key Takeaways Summary

1. Use Goals Prevented over traditional metrics for shot-stopping evaluation

2. Distribution Matters - Modern goalkeepers must be evaluated as passers

3. System Context - No universal "best" profile; fit matters

4. Sample Size Awareness - Goalkeeper stats require patience

5. Bayesian Methods - Help with small samples

6. Multiple Metrics - Comprehensive profiles beat single numbers

7. Uncertainty Communication - Always report confidence levels

8. Trade-offs Exist - Sweeper-keepers may sacrifice aerial dominance

Benchmark Reference Table