Source — the Draughts Competition Code (Russian Draughts Federation rules, items 3.16.4–3.16.9). Below are the exact definitions and a worked example on the same tournament position for every system.
The example used in every calculation below
The player played 5 rounds. Opponents' final tournament scores and the result of the game against each of them:
- A — 3 points, win
- B — 4 points, win
- C — 2.5 points, draw
- D — 3.5 points, loss
- E — 1.5 points, win
Shmulyan coefficient
First, the scores of opponents the player beat are summed; then the scores of opponents the player lost to are summed. The difference between these two totals is the player's coefficient (item 3.16.4).
Example: points from won games — 3 + 4 + 1.5 = 8.5. Points from the lost game — 3.5. Shmulyan coefficient = 8.5 − 3.5 = 5.
Sonneborn–Berger coefficient
Double the scores of opponents the player beat are summed, plus the scores of opponents the player drew with (item 3.16.5).
Example: 2 × 8.5 (wins) + 2.5 (draw) = 17 + 2.5 = 19.5.
Buchholz coefficient
The scores of all of the player's opponents are summed (item 3.16.6).
Example: 3 + 4 + 2.5 + 3.5 + 1.5 = 14.5.
Solkoff coefficient
The scores of all of the player's opponents are summed, excluding the best and the worst result (item 3.16.7).
Example: from the total of 14.5, the opponents' best result (4) and worst result (1.5) are excluded: 14.5 − 4 − 1.5 = 9.
Truncated Solkoff coefficient
The scores of all of the player's opponents are summed, excluding only the worst result. If coefficients are still tied, the 2 worst results are excluded, then 3, and so on, until places are decided (item 3.16.8).
Example: from the total of 14.5, only the worst result (1.5) is excluded: 14.5 − 1.5 = 13. If two players still tie, both additionally exclude their 2 worst results, and so on.
Riga coefficient system
The scores of opponents the player beat are summed and multiplied by 2. Then the scores of opponents the player drew with are summed and multiplied by 1.5. Then the scores of opponents the player lost to are summed. The sum of these three values is the player's coefficient (item 3.16.9).
Example: 2 × 8.5 (wins) + 1.5 × 2.5 (draw) + 3.5 (loss) = 17 + 3.75 + 3.5 = 24.25.
Source
These definitions are taken from the Draughts Competition Code (section 3.16, items 3.16.4–3.16.9). Which of these systems applies at a given Cup stage is decided by the tournament's chief arbiter; the site publishes the final figure exactly as it appears in the protocol.