Backgammon Ratings

The rating change scales with the square root of the match length. A 4-point match is worth twice a 1-point match; 9 points is worth 3×; 16 points is worth 4×.

Match length is whatever was agreed at invitation — not the final score. A 5-point match counts as 5 whether it ended 5-0 or 5-4.

Experience is the running sum of completed-match lengths. At experience ≥ 400 the experience factor is 1 — it stops affecting the rating change.

Below 400 the factor is max(1, 5 − (E + n)/100), where E is experience before the match and n is the match length. Experience 300 doubles the rating change; 200 triples it; 0 multiplies it by 5.

Underdog win probability: U = 1 / (10^(|P1−P2|·√n / 2000) + 1); favorite: F = 1 − U.

If the favorite wins, ΔP = 4 · PE · √n · U. If the favorite loses, ΔP = 4 · PE · √n · F. Symmetric for the underdog. So beating a much stronger player gains far more than beating a weaker one, and losing to a much stronger player costs much less.