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🧮 Rating Algorithms

RatingKit ships with fourteen drivers. Every bundled driver supports teams and multiple teams through RatingKit's normalized match representation.

📋 Algorithm Matrix

Key Rating Deviation Volatility Team support Multi-team support
elo ✅ — — ✅ ✅
elo_mov ✅ — — ✅ ✅
fide ✅ — — ✅ ✅
uscf ✅ — — ✅ ✅
glicko ✅ ✅ — ✅ ✅
glicko2 ✅ ✅ ✅ ✅ ✅
weng_lin ✅ ✅ — ✅ ✅
bradley_terry ✅ — — ✅ ✅
plackett_luce ✅ — — ✅ ✅
thurstone_mosteller ✅ — — ✅ ✅
dwz ✅ — — ✅ ✅
egf ✅ — — ✅ ✅
ingo ✅ — — ✅ ✅
fifa ✅ — — ✅ ✅

🎯 Selection Guide

Elo

Use elo when you need a familiar, predictable rating change and do not need uncertainty tracking.

Margin-of-Victory Elo

Use elo_mov when scores are available and a larger winning margin should generally create a larger update.

Glicko-2

Use glicko2 for chess servers, ladders, and competitive queues where uncertainty and volatility matter.

Weng-Lin

Use weng_lin for team games, uneven teams, substitutes, and multiplayer environments that benefit from Bayesian uncertainty.

Plackett-Luce

Use plackett_luce for free-for-alls, races, battle royale placements, and matches containing several ranked teams.

Thurstone-Mosteller

Use thurstone_mosteller when a Gaussian performance model fits the domain.

⚙️ Algorithm Options

Edit algorithm_options in config/rating-kit.php:

'algorithm_options' => [
    'elo' => [
        'k_factor' => 32.0,
        'scale' => 400.0,
    ],
    'glicko2' => [
        'tau' => 0.5,
        'epsilon' => 0.000001,
    ],
    'weng_lin' => [
        'beta' => 200.0,
    ],
],

👥 Team Aggregation

'team_aggregation' => 'average',

Supported values:

  • average: weighted average team rating
  • sum: weighted sum of team ratings

average is usually preferable when teams of different sizes can compete.

⚖️ Team Distribution

Elo-family and pairwise drivers can distribute a team update using:

'team_distribution' => 'participation',

Supported values:

  • equal
  • participation
  • rating_weighted

Bayesian drivers use each competitor's uncertainty as part of their update.

⚠️ Federation-Style Drivers

fide, uscf, dwz, egf, ingo, and fifa are configurable practical adaptations for application use. They are not assertions of federation certification, and an application with formal federation requirements should verify every rule against the applicable current regulations.

↕️ Rating Direction

Most algorithms use higher-is-better ratings. The Ingo-style driver uses lower-is-better values. RatingKit applies the configured direction to leaderboards, individual ranks, conservative scores, predictions, and peak/best rating helpers.

'algorithm_directions' => [
    'ingo' => 'asc',
],