Table

Elo, rated by sides. A side's rating is the average of the players on it, which at singles is simply the player.

Every match is marked on a scale from 0 to 1. The two ratings say what each side was expected to score before it started, the scoreline says what each actually scored, and the difference between those two numbers is the rating change. Both players on a side are credited with the same result.

One match, taken apart:

1. 1 The two sides

   This is a doubles session, so each side averages two players. After this step the working reads only these two numbers, never the four behind them.

   You1040 and 960

   1000

   Them920 and 880

   900

2. 2 What you were expected to score

   Your side is 100 above theirs, which on the 0 to 1 scale is worth 0.640. Level sides would each be on 0.5. A gap of 400 is ten-to-one odds, and every gap between falls off the same curve.

   1 ÷ (1 + 10^{−100 ÷ 400})

   0.640

   Expected score by rating gap

   10.50

   −400level+400

   The curve is steepest around level, so the first hundred points of a gap change the odds far more than the fifth hundred does. A side far enough ahead is already expected to win, and winning tells the table little it did not know.

3. 3 What the result scored

   You win 21–10, taking 21 of the 31 points played. A win is worth three quarters of the 1 on its own, the same for any win. The last quarter is set by that share of the points, which is a ratio rather than a count, so a game to 11 and a game to 21 are marked the same way.

   Your share of the points, 21 ÷ 31

   0.677

   ×The margin's share of the score

   0.250

   =What the margin adds

   0.169

   +The win itself

   0.750

   =What the result scored

   0.919

   How a score divides

   • The win 0.750
   • The margin you took 0.169
   • The margin you left 0.081

   The win is three quarters of the bar whatever the scoreline, so the heaviest defeat still sits below the narrowest win and a losing record can never climb above a winning one. Only the last quarter is open, and 21–10 took 0.677 of it.

4. 4 The change

   Take what the result scored in step three, subtract what step two expected of you, and that difference is the whole of the movement. Multiplying it by 20 turns a fraction into rating points.

   What the result scored

   0.919

   −What you were expected to score

   0.640

   =Beat expectation by

   0.279

   ×How far this match can move you

   20

   =Your rating change

   +5.6

   You and your partner each gain 5.6. Both of them lose the same. Had you been the side rated 900 instead, the identical scoreline would have been worth +11.2, because beating a side rated above you is the harder thing to have done.

   The 20 is not a constant. It is what one game to 21 is worth to a player past their first ten matches. A game to 11 is worth 11 ÷ 21 of that, and those first ten matches are worth double.

Your first ten matches are placement matches, and the rating moves at double speed through them to find its level quickly. That doubling is counted per player rather than per side, so a newcomer partnered with a regular moves twice as far as the regular does on the very same result. A P beside a name in the table below means those ten are not done.

Every point your side scored, added up across every match you played. A point counts the same whether the match was won or lost.

Equal totals are separated by wins, and then by whoever needed fewer matches to get there.