Winrate Matrix Explanation

Structure of a Cell in the Matrix

Each cell in the matrix displays 3 pieces of information:

1. Confidence Interval (at the top)

Example: "46.9% - 51.4%"

• What is it?: A range of possible values with 95% confidence
• Calculation: Based on the statistical formula for confidence interval of a proportion
• Meaning:
  • With 95% certainty, the true winrate is between 46.9% and 51.4%
  • The wider the interval, the less data we have (fewer matches)
  • The narrower the interval, the more data we have (more matches)

Why is it useful?

Indicates the reliability of the winrate. A winrate of 60% with an interval of 40%-80% is less reliable than a winrate of 55% with an interval of 53%-57%.

2. Actual Winrate (in the middle, large)

Example: "49.1%"

• What is it?: The percentage of wins in this specific matchup
• Calculation: (wins / total_matches) × 100
• Meaning:
  • For this specific matchup (e.g., Archetype A vs Archetype B)
  • How many times Archetype A won against Archetype B
  • Example: 49.1% = Archetype A wins approximately 49 times out of 100 against Archetype B

Special case: Mirror Match

When an archetype plays against itself (same archetype in row and column), the winrate should be close to 50% (or 50% ± a few % due to draws). If it's very different from 50%, there might be an issue with the data.

3. Number of Matches (at the bottom)

Example: "1872 matches"

• What is it?: The total number of matches played in this matchup
• Meaning:
  • The more matches, the more reliable the winrate
  • The fewer matches, the wider the confidence interval will be

"OVERALL" Column

In the "OVERALL" column, you see:

• Overall winrate: The winrate of this archetype against all other archetypes
• Total matches: The total number of matches played by this archetype (all matchups combined)

Comparison: Cell vs OVERALL

• Specific cell: Winrate in a specific matchup (e.g., Archetype A vs Archetype B)
• OVERALL: Average winrate of the archetype against all others

Calculation Code

The confidence interval is calculated using the standard statistical formula:

$p = $wins / $matchCount;  // Win proportion
$z = 1.96;                  // 95% confidence level
$margin = $z * sqrt(($p * (1 - $p)) / $matchCount) * 100;

$min = max(0, ($p * 100) - $margin);
$max = min(100, ($p * 100) + $margin);

The more matches there are, the smaller the margin of error, so the interval is narrower.