| PR Diff | 1 pt | 3 pt | 5 pt | 7 pt | 9 pt | 11 pt | 13 pt |
|---|
Statistical Findings: Analysis of 3.3 million matches shows that PR difference is the primary driver of outcomes - skill advantage creates substantial win rate differences, with a 10-point PR gap producing win probabilities ranging from 59.7% to 73.4% depending on match length. Even smaller PR differences of 5-7 points consistently show meaningful impacts across all match types, demonstrating how player skill level directly correlates with competitive success.
Variance Reduction Effect: Match length acts as a variance reducer. In 1-point matches, luck dominates (win rates cluster around 50-67%). In 13-point matches, the same PR differences produce win rates spanning 50-83%, demonstrating how extended play reduces randomness and lets skill express itself.
Data Source: Over 3.3 million matches from Backgammon Studio Heroes (anonymized), with 2.4 million human vs human matches. Most reliable data points have more than 10,000 matches per category. Note that curves become less smooth at higher PR differences (particularly above 15), especially for longer match lengths, due to smaller sample sizes. For example, 13-point matches have fewer than 1,000 samples at PR differences above 13. Research by Art Benjamin and Hal Heinrich published in Math Overboard magazine.