algo-rank-bayesian

# Bayesian Average Rating ## Overview Bayesian average combines an item's observed average rating with a prior (global average), weighted by review count. Formula: BR = (C × m + Σrᵢ) / (C + n) where m=global mean, C=confidence parameter, n=item reviews, Σrᵢ=sum of item ratings. Items with few reviews are pulled toward the global mean. ## When to Use **Trigger conditions:** - Ranking items by continuous ratings (1-5 stars) with varying review counts - IMDB-style "Top 250" lists that balance quality and popularity - Any rating aggregation where new items shouldn't dominate with few high ratings **When NOT to use:** - For binary (upvote/downvote) data (use Wilson Score instead) - When all items have similar review counts (simple average is sufficient) ## Algorithm ``` IRON LAW: The Prior Protects Against Small-Sample Extremes Without a prior, a single 5-star review makes an item "the best." The Bayesian average adds C "phantom votes" at the global mean m, shrinking small-sample items toward average. C controls shrinkage strength: higher C = more conservative (more phantom votes). Typical C = median review count across all items. ``` ### Phase 1: Input Validation Compute: global mean rating (m) across all items, choose C (phantom vote count). Collect per item: review count (n), average rating, or sum of ratings. **Gate:** m computed, C selected, item data available. ### Phase 2: Core Algorithm 1. Global mean: m = Σ(all ratings) / Σ(all review counts) 2. Bayesian average ...