Backgammon Galaxy (version 1) ratings explanation
1. Probability(P1 wins, given a decisive result) = 1 / (1 + 10^((P2_rating - P1_rating) / 800))
2. K = Min(16, Max(5, 32 - 0.012 * Average(P1_rating, P2_rating)))
3. Rating change if P1 wins match and PR: Match_length^0.75 * K * (1 - Probability(P1 wins, given a decisive result))
4. Rating change if P2 wins match and PR: Match_length^0.75 * K * Probability(P1 wins, given a decisive result)
5. Rating changes are zero-sum: If Player 1 gains X points, then Player 2 loses X points. For the above calculations in #3 and #4, the match loser loses the same number of rating points.
"Decisive result" means the same player wins both the match and the PR.

Example
Player 1: 1736.78
Player 2: 1628.80
Match length: 13

1. Probability(P1 wins, given a "decisive result") = 1 / (1 + 10^((1628.80 - 1736.78) / 800)) = 57.707843%

2. K = Min(16, Max(5, 32 - 0.012 * Average(1736.78, 1628.80))) = 11.80652

3. Rating change if Player 1 wins match and PR = 13^0.75 * 11.80652 * (1 - 0.57707843) = 34.19 points. So, Player 1 gains 34.19 points and Player 2 loses 34.19 points. New ratings: 1770.97 (Player 1), 1594.61 (Player 2).

4. Rating change if Player 2 wins match and PR = 13^0.75 * 11.80652 * 0.57707843 = 46.65 points. So, Player 2 gains 46.65 points and Player 1 loses 46.65 points. New ratings: 1690.13 (Player 1), 1675.45 (Player 2).

Note on the new Backgammon Galaxy version 2

Backgammon Galaxy version 2 rating changes are identical to version 1 rating changes if one player wins both the match and the PR. However, if the match winner is different than the PR winner, the match winner will gain half the rating change noted above and the match loser will lose half the rating change noted above.

Back to Ratings Calculators (FIBS, Backgammon Galaxy, Backgammon Studio Heroes)