OpenSkill Rating and Balance Analysis

Problem

In multi-player or recurring matchups, raw win-loss records do not clearly separate stable skill from variance. rating-opening turns match results into comparable ratings to answer three questions: how strong a player or team is now, what the likely outcome of the next match is, and how to form fairer groups.

How It Works

The skill is based on the OpenSkill rating model. It represents a player by mu for skill and sigma for uncertainty, and computes a composite score as mu - 3 * sigma; higher values indicate stronger performance. The main actions are:
- rate: update ratings from match results.
- predict: estimate win/loss probability.
- balance: analyze player skills and recommend fairer groupings.

The underlying algorithm can be switched with --model, including the default pl, higher-precision bt-full, faster bt-part, and thurstone-full or thurstone-part. The implementation uses the Python script rating.py and the openskill library, making it suitable for wiring existing matchup data into rating, prediction, and team-balancing workflows.

Notes: ratings change with sample size, match records must be parseable and player identifiers must stay consistent, balance is a recommendation rather than a guaranteed optimum, and model choice affects precision and computation cost.