algo-rank-trueskilllisted

# TrueSkill Rating System ## Overview TrueSkill (Microsoft Research) models each player's skill as a Gaussian distribution N(μ, σ²) where μ is estimated skill and σ is uncertainty. Supports teams and multiplayer (not just 1v1). Conservative rating = μ - 3σ. Uncertainty decreases with more games. Uses Bayesian inference via message passing. ## When to Use **Trigger conditions:** - Rating players in team-based or multiplayer (3+ participant) games - Building matchmaking systems that balance match quality - When you need uncertainty estimates alongside skill ratings **When NOT to use:** - For simple 1v1 ranking with no uncertainty (Elo is simpler) - For non-competitive ranking (product ratings — use Wilson Score) ## Algorithm ``` IRON LAW: Skill Rating Has TWO Components — Mean AND Uncertainty TrueSkill represents skill as N(μ, σ²). New players have high σ (uncertain). After many games, σ shrinks (confident). The conservative rating μ - 3σ ensures players are ranked by their LIKELY MINIMUM skill, not their estimated average. Never use μ alone for ranking. ``` ### Phase 1: Input Validation Initialize: μ₀ = 25, σ₀ = 25/3 (default). Collect match results with team compositions and finishing order. **Gate:** Valid match results, team compositions defined. ### Phase 2: Core Algorithm 1. For each match, compute expected outcome from team skill distributions 2. Compare actual vs expected outcome 3. Update each player's (μ, σ) using Bayesian update: - μ shifts toward perform