Badminton & Table Tennis Win Probability Calculator (Rally Scoring)

How it works

Each rally is won with probability p (or p_serve / p_receive). The game is a walk over the score grid: first to the target, win by 2, with a golden point at the cap (badminton 30). P(game) = sum of the probabilities of every path ending in your win; with a single p and no cap, P(game) = Σ C(T−1+j, j)·p^T·q^j (j = 0…T−2) + C(2T−2, T−1)·p^(T−1)·q^(T−1) · p²/(p²+q²). Match: best of 3 = g²(3 − 2g); best of 5 = g³(1 + 3(1−g) + 6(1−g)²); best of 7 = g⁴(1 + 4(1−g) + 10(1−g)² + 20(1−g)³).

Under rally scoring every rally gives a point to whoever wins it, so a game is a race to the target (21 in badminton, 11 in table tennis and PAR squash) that must be won by 2. Badminton caps the race: at 29-all the next rally wins 30-29. From 4 January 2027 the BWF switches to the 3×15 system: games to 15, win by 2 from 14-all, capped at 21 (at 20-all the next rally wins). The calculator walks through every possible score exactly, so it handles the cap, a live score and different serve and receive rates. With one rally share the server does not matter. With separate rates the serving rule matters: in badminton and squash the rally winner serves next, while in table tennis serve switches every two points and every point from 10-all. Match odds then chain the games, with the next game’s first server set by each sport’s rule. Because a longer game is a longer race, the same rally edge is worth more over 21 points than over 11, and more in a best of 5 than a best of 3. The tables list the likely game and match scores and how the odds move with your rally share. The results assume independent rallies and a fixed skill gap.

Worked example

You win 52% of rallies in a badminton game to 21, best of 3. Adding every path through the score grid (with the 30-point cap) gives a 60.4% chance of winning a game, and the game reaches 20-all 12.1% of the time. The match probability is g² × (3 − 2g) = 0.6041² × 1.7917 = 65.4%: 36.5% to win 2-0 and 28.9% to win 2-1. The most likely single score is a 21-18 win (6.7%). Under the 3×15 format that starts in January 2027 the same 52% gives 58.9% per game and 63.2% per match. The same 52% in a table-tennis game to 11 gives only 57.7% per game, because the shorter race leaves more room for luck.

Sources: Badminton — scoring system, 30-point cap and serving rules (Wikipedia) · Table tennis — scoring, deuce and service rotation (Wikipedia) · BWF — Members approve 3×15 scoring system (effective 4 January 2027) · BWF Council proposal: 3×15 scoring system with setting to 21

Frequently asked questions