ManaCore

Card Impact Analysis: Progressive Model Complexity

This R-based analysis evaluates individual card impact on game outcomes using a progressive modeling approach:

1. Version 0 (V0) – Baseline: win ~ has_card + elo_diff + elo_mean
2. Version 1 (V1) – Adds deck archetype: win ~ has_card + elo_diff + elo_mean + archetype
3. Optional Bayesian Hierarchical Model – Shrinks estimates for rare cards toward global mean using rstanarm.
4. Optional L2-regularized logistic regression - across all cards simultaneously.

The framework outputs odds ratios (OR), p-values, archetype-adjusted win-rate lifts (ΔP), and other statistics for deeper insight into card effectiveness.

Model Versions

Version 0: Baseline

• Formula: win ~ has_card + elo_diff + elo_mean
• Simple, fast model estimating card effect.
• Outputs OR, standard error, and p-values.

Version 1: + Archetype

• Formula: win ~ has_card + elo_diff + elo_mean + archetype
• Controls for deck archetype.
• Computes archetype-adjusted win-rate lift (ΔP) per card.
• ΔP also calculated at mean covariate values.

Optional: Bayesian Hierarchical

• Requires rstanarm.
• Formula: win ~ scale(elo_diff) + scale(elo_mean) + archetype + (1 + scale(elo_diff) | card_id),.
• Pools information across cards for stable effect estimates.
• Outputs posterior OR, credible intervals, and significance flags.

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Key Metrics

Metric	Description
v0_or / v1_or	Odds ratio for having card (V0 or V1)
v1_win_rate_lift_pct	Archetype-adjusted ΔP in %
v1_win_rate_lift_mean_pct	ΔP at mean covariate values
v*_p / v*_p_adj	Raw and FDR-adjusted p-values
v*_significant_raw / v*_significant_fdr	Significance flags
n_games	Number of games card appears in
confidence	High/medium/low based on sample size & OR stability
bayes_or	Bayesian hierarchical OR (if available)
bayes_or_lower / bayes_or_upper	95% credible interval
bayes_significant	Credible positive/negative flag

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Interpreting Results

• Odds Ratios (OR)

  • OR > 1 → Card increases win probability
  • OR < 1 → Card decreases win probability

• Win-Rate Lift (ΔP)

  • Positive → Card improves win probability, adjusted for archetype
  • Compare v1_win_rate_lift_pct across cards to identify top performers

• Confidence Levels

  • High: ≥200 games & stable OR from V0 → V1
  • Medium: ≥100 games & moderate stability
  • Low: Few games or inconsistent estimates

• Bayesian Estimates

  • Shrinks rare-card estimates toward global mean
  • Useful for cards with limited data

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Model Comparison

• AIC improvement: Difference in model fit between V0 and V1
• OR stability: Compare V0 and V1 OR to flag inconsistent effects
• Separation warnings: Cards with extreme coefficients (potential perfect prediction)

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