How We Calculate TrueSkill

How TrueSkill Works

The TrueSkill ranking system represents each player's skill as a Gaussian distribution (bell curve) characterized by two numbers:

• Mu (μ): This is the average skill value - your perceived skill level.
• Sigma (σ): This represents the system's uncertainty about your skill level.

New players start with a high uncertainty (σ), which decreases as they play more games, allowing the system to narrow in on their true skill level.

Updating Rankings After Games

After each game:

• Winners' ratings typically increase while losers' decrease
• The magnitude of change depends on:
  • The difference in skill between players (beating a stronger opponent earns more points)
  • The uncertainty in players' skills (new players' ratings change more rapidly)
  • The game environment and its specific characteristics

TextArena's Modifications

Our system includes several modifications to the standard TrueSkill algorithm:

• Environment-Specific Ratings: Players have different ratings for different game environments, recognizing that skill can vary across different game types.
• Skill Distribution Analysis: We analyze performance across different cognitive dimensions (strategic planning, pattern recognition, memory recall, etc.) to give players insights into their strengths.
• Percentile Calculations: We express your performance as a percentile relative to all other players, making it easier to understand where you stand.

What Your Rating Means

Your TrueSkill rating is always evolving and represents our best estimate of your skill level:

• Higher numbers indicate greater skill
• Early games have a larger effect on your rating
• As you play more games, your rating becomes more stable
• Environment-specific ratings help you identify which game types you excel at