Tie-break Formulas
Swiss Tournaments
It is not unusual for Swiss tournaments to end up with several players tied with the same number of points. To establish a finish order, the following tie-break formulas are applied in order:
- Modified Median
- Solkoff
- Cumulative
- Cumulative opponent's score.
There is no perfect tie-break system; each has its faults. The tie-break systems used by the SCC are the ones commonly recommended by chess federations around the world. Here is a brief description of each of the tie-break criteria:
Modified Median
Of the two median tiebreaks, this is the more standard now. It evaluates the strength of a player's opposition by summing the final scores of his or her opponents and then discarding either the highest of these scores, the lowest, or both, depending on the tied player's score.
For players who tie with even scores (that is, their number of wins and losses is the same), both high and low are discarded. For tied players with plus scores, only the lowest is discarded, and for players with minus scores only the highest is discarded.
For tournaments of nine or more rounds, the top two scores are discarded (or the bottom two scores, or all four, as determined by the same even/plus/minus criteria above).
These scores are adjusted for any unplayed games, which count a half point each. If the player involved in the tie has any unplayed games, they count as opponents with adjusted scores of 0.
Solkoff
This is just like the Median except that no opponents' scores are discarded. Popular with tournaments of only a few rounds.
Cumulative Score
This is easy to calculate by hand, and has been popular for that reason. To get this value just add up the cumulative (running) score for each round. The theory is that players who win their games in the early rounds (and therefore end up with higher cumulative scores than players with the same score who win later rounds) have had to face tougher opposition throughout the tournament.
Cumulative Scores of Opposition
This uses the cumulative scores calculated as above, but for the tied players' opponents rather than for the tied players themselves.
Round Robin Tournaments
Ties in Round Robin tournaments (like our club championship) are resolved using the Sonneborn-Berger system. For each player in the tie, add the final scores of all the opponents the player defeated and half the final scores of all the opponents with whom the player drew. If a tie remains after applying the Sonneborn-Berger test, we look at the number of won games and finally the result of direct encounters.