"algo-rank-elo"

Elo Rating System

Overview

Elo assigns numerical ratings that update after each pairwise comparison. Winner gains points, loser loses points. The amount exchanged depends on expected vs actual outcome. Originally for chess, now used for sports, games, and A/B preference testing. Update runs in O(1) per match.

When to Use

Trigger conditions:

• Ranking items from pairwise comparison data (A vs B outcomes)
• Building competitive rating systems for games or sports
• Crowdsourced quality evaluation through pairwise preferences

When NOT to use:

• When you have absolute scores, not pairwise comparisons (use direct ranking)
• When team dynamics matter more than individual skill (use TrueSkill)

Algorithm

IRON LAW: Elo Assumes Each Matchup Is Independent and Stationary
Rating changes are based on surprise: beating a higher-rated opponent
gains more points than beating a lower-rated one. K-factor controls
update speed: high K (32) = volatile, fast adaptation. Low K (16) =
stable, slow adaptation. Choose K based on how quickly skill changes.

Phase 1: Input Validation

Initialize all participants at base rating (typically 1500). Collect match results: winner, loser (or draw). Gate: Valid match data, no self-matches.

Phase 2: Core Algorithm

1. Expected score: E_A = 1 / (1 + 10^((R_B - R_A)/400))
2. Actual score: S_A = 1 (win), 0.5 (draw), 0 (loss)
3. Update: R_A_new = R_A + K × (S_A - E_A)
4. Process all matches sequentially (order matters for sequential Elo)

Phase 3: Verification

Check: total rating points conserved (zero-sum). Rating distribution is reasonable (no extreme values from data errors). Gate: Ratings conserved, top-ranked items pass sanity check.

Phase 4: Output

Return sorted ratings with confidence indicators.

Output Format

{
  "ratings": [{"id": "player_A", "rating": 1720, "matches": 50, "wins": 35, "losses": 15}],
  "metadata": {"k_factor": 32, "initial_rating": 1500, "total_matches": 500}
}