Musrank

MusRank is a skill-rating system for Mus that focuses on match length noise with a Weng-Lin / TrueSkill-style core. Outcomes are treated as win/loss only (no margin-of-victory signal).

Installation

npm install --save musrank

Quick start

import { rating, rate } from 'musrank'

const a1 = rating()
const a2 = rating()
const b1 = rating()
const b2 = rating()

const [[a1p, a2p], [b1p, b2p]] = rate([a1, a2], [b1, b2], {
  rank: [1, 2],
})

2v2 parameter exploration

Run a local sweep (2v2 only, no draws) and print a table with the result, parameter config, and Elo-style mu change:

npm run build
node exploration/matches-sim.mjs

The script runs two scenarios (A wins, B wins) for several parameter sets and prints a console table with:

• result: scenario (A wins / B wins)
• params: named parameter preset (tau values or beta scaling)
• config: JSON of the preset options
• eloChangeA / eloChangeB: average mu change per team

The model: two layers of uncertainty

Layer 1 — Hand-level randomness (β₀)

Each hand has:

• card randomness
• bidding variance

We model this base noise as β₀. Larger β₀ means outcomes are blurrier; smaller β₀ means skill dominates.

Layer 2 — Match aggregation (β(L))

Mus is played to L juegos (points). More games average out randomness, so the match-level noise shrinks with L.

Conceptually:

beta(L) = beta0 / sqrt(L)

Or with a reference match length:

beta(L) = beta0 * (Lref / L) ^ alpha

Where L is the number of juegos. Short matches are noisy; long matches are reliable.

Example (intuition): if beta(10) = 1.0

• L = 2 → beta(2) ≈ 2.24 (chaotic, weak evidence)
• L = 4 → beta(4) ≈ 1.58 (still swingy)
• L = 20 → beta(20) ≈ 0.71 (stable, decisive)

What “more β” vs “less β” means

• More β → more chaos. Upsets are common, a win provides weak evidence.
• Less β → more determinism. Upsets are rare, a win is strong evidence.

In Mus terms: short matches → high β, long matches → low β.

Think of it like this:

• beta(L) defines the noise (how much to trust a win/loss result)

So the same result gives:

• a small update in a short match (high β)
• a large update in a long match (low β)

Defaults you’ll choose later

These are the two core knobs:

1. β₀ — base hand randomness
2. σ₀ — prior uncertainty for new players

Rule of thumb: start with sigma0 ≈ 1–2 × beta(10) so new players can move meaningfully after a few matches.

Why this approach fits Mus

• Short matches are noisy by nature — β(L) encodes that.
• Ratings update fast for new players, slowly for established ones — σ₀ encodes that.

That separation keeps the math principled and lets Mus behave like Mus.