The following is a proposal to (modestly) rearrange the section on tie breaks. I’ve attached a Word doc with red-lines.
The main change is to add a section 34E on adjustments for unplayed games. This is currently buried inside the description of Modified Median even though it applies to Solkoff and Median and should apply (but doesn’t on a literal reading) to Sonneborn-Berger and USAT. This also reorders the descriptions of Solkoff, Median and Modified Median so the simplest of the three is explained first rather than starting with the most complicated. The description of Sonneborn-Berger is moved up to the list of Swiss tie breaks rather than being described in the section on round robin tie breaks with a reference forward from the Swiss tie breaks.
This also is written to allow for a 3-1-0 score system by not hard-coding .5 for a draw into the rules.
Does anyone see a reason to keep the Opponent’s Performance in this? The PR is a junk statistic and I don’t see how averaging it across the opponents is going to change that.
34. Breaking Ties
34A. Introduction.
There is no perfect tiebreak system; each has its faults. In some events, especially large ones, ease and speed of calculation is a concern. In other events where time is not pressing, playoffs provide a better alternative to traditional tiebreak systems. Playoffs are often conducted at a faster time control than the tournament. See 34F12.
34B. Announcement.
When used, tiebreak systems should be posted at the site before the first round. There are several tiebreak systems that provide good and objective methods for directors to break ties for indivisible prizes.
Frequently, one tiebreak method alone will not break the tie, and it is necessary to use a secondary and sometimes even a tertiary method to produce a decision. Thus, at least the first two tiebreak systems should be posted. The director should be prepared to explain how the tiebreak systems work, as time permits.
34C. Monetary prizes.
Tiebreaks are not used for cash prizes, which are divided evenly among the tied players. An exception is a playoff, which may be used to determine cash prizes if notice of this is given in all detailed pre-tournament publicity. See also 32B, Distribution.
34D. Choice of tiebreak methods.
Different systems will yield different results, but the systems discussed here are not capricious or random. Each seeks to discover the first among equals, the player who has a somewhat better claim to a prize based on the strength of his or her opposition than others who earned the same score. Which system to choose depends on the nature of the tournament, its traditions, and the qualities required for the specific situations and conditions at hand.
One state chess association that has had a comprehensive list of tiebreaks for many years uses (in order):
Modified Median; Solkoff; Cumulative; Result between tied players; Most blacks; Kashdan; Sonneborn-Berger; and Coin flip. Having an ordered list that goes this deep can be useful.
34E. Adjusting for Unplayed Games
Many tiebreak calculations require adjustments for unplayed games (for byes, forfeits or withdrawals) as these provide different information than played games. There are adjustments for unplayed games by the player whose tiebreaks are being calculated (which tend to be specific to each tiebreak method), and sometimes for unplayed games by the player’s opponents (see 34E1).
34E1. Adjusting Scores for Unplayed Games of Opponents
Several of the more important tie breaks rely upon the scores of a player’s opponents. These need to be adjusted for any unplayed games (including missed rounds), which are treated as if they were a draw regardless of the number of points awarded in the tournament. These adjusted scores are used only when calculating opponent’s tiebreaks.
TD Tip:
An opponent who won the first two games, lost the third, withdrew and did not play rounds four or five would have an adjusted score of 3 points (1+1+0+0.5+0.5 =3).
34F. Calculating Swiss tiebreaks.
This section deals with various systems that have been used successfully at all levels of play. For team events see 34H, Team tiebreaks.
Unless a different method has been posted or announced before the start of the first round, players will expect the following sequence of tiebreak systems to be employed as the first four tiebreakers. Any variation to be used within the various systems should be posted also. These systems (and some additional ones) are explained in detail following the list.
1. Modified Median
2. Solkoff
3. Cumulative
4. Cumulative of Opposition
TD TIP: Pairing software can calculate tiebreaks automatically.
TD TIP: The TD should realize that in the unique case of multiple players all finishing the tournament with perfect scores (winning the maximum number of games possible in a tournament), the standard tiebreaking systems would not have the same relevance as they would in outcomes where the players finished with less-than perfect scores. Therefore, in the special case of more than one player finishing with a perfect score, the TD should make every effort possible to have a playoff among all players with perfect scores to determine the winner of the event. See 34F12.
34F1. Solkoff.
The Solkoff system uses the sum of the opponent’s adjusted scores (34E1). If the player has an unplayed game, it counts as an opponent with an adjusted score of 0.
34F2. Median
The Median system, also known as the Harkness system for inventor Kenneth Harkness, is the same as Solkoff (34F1) but discards the highest and lowest of the adjusted scores.
34F3. Modified Median
In the Modified Median system, the Median system (34F2) is used for players who tie with even scores (an even score is equal to exactly one half of the maximum possible score). The system is modified for players with non-even scores to disregard only the least significant opponents’ adjusted scores: the lowest adjusted score is discarded for tied players with plus scores and the highest adjusted score is discarded for tied players with minus scores.
For tournaments of nine or more rounds, the top two and bottom two adjusted scores are discarded for even-score ties, the bottom two scores for plus-score ties, and the top two scores for minus-score ties.
34F4. Cumulative.
To determine cumulative tiebreak score, simply add up the cumulative (running) score after each round. For example, if a player’s results were win, loss, win, draw, loss, the wall chart would show a cumulative score round by round as 1, 1, 2, 2.5, 2.5. The cumulative tiebreak total is 9 (1+1+2+2.5+2.5 = 9). If another player scored 2.5 with a sequence 1, 2, 2.5, 2.5, 2.5, the tiebreak points scored would be 10.5 (1+2+2.5+2.5+2.5 = 10.5). The latter player’s tiebreaks are higher because he or she scored earlier and presumably had tougher opposition for the remainder of the event.
The value of a win is subtracted from the sum for each unplayed win or full-point bye (22B); likewise, the value of a draw is subtracted from the sum for each unplayed draw or half-point bye.
For a tournament with accelerated pairings (28R2), the sum of rounds should start with round 2 since round 1 has harder pairings for the higher-rated players.
TD TIP: This system is ideal for large events, since it is very fast and easy to use. It also avoids the problem, common in Median and Solkoff, of having to wait for a lengthy last-round game between two non-contenders to end for top prizes to be decided. Another advantage is that last-round scores need not be included in calculating cumulative tiebreak points, since they have no effect on breaking the tie (both tied players will necessarily have the same last round score).
TD TIP: Cumulative tiebreaks can be calculated after the next to last round or while the last round is in progress.
34F5. Result between tied players (Head-to-head)
Self-explanatory if two tie, but useful only when they were paired and did not draw. If more than two tie, all results among tied players should be considered, with rank according to plus or minus, not percentage. For example, 3-1 (+2) beats 1-0 (+1).
34F6. Most blacks.
This counts the number of games played with black. (Games paired but not played don’t count).
34F7. Kashdan.
This system rewards aggressive play by scoring 4 tiebreak points for a win, 2 for a draw, 1 for a loss, and 0 for an unplayed game. Note that if players with no unplayed games tie, the one with fewer draws will come out ahead.
34F8. Sonneborn-Berger.
The Sonneborn-Berger system is also known as the partial-score method. Across all played games, sum the adjusted score (34E1) of the opponent by the score the player was awarded for the game. With the standard scoring system (W=1, D=0.5, L=0), this will be the sum of adjusted scores for players defeated plus half the sum of the adjusted scores of players drawn. Unplayed games (for any reason) count as zero.
TD TIP. The disadvantage of using this system in a Swiss is that losses are disregarded, and a player losing to a strong opponent deserves more credit than one losing to a weak opponent.
34F9. Cumulative scores of opposition.
The cumulative tiebreak points of each opponent are calculated as in 34F4 and these are added together.
34F10. Opposition’s performance.
(Has anyone actually used this? I can see using the player’s own PR, which in the absence of unplayed games is just a remap of the average rating of opposition). This method averages the performance ratings of the players’ opposition. Performance ratings are calculated by crediting the player with the opponent’s rating plus 400 points for a victory, the opponent’s rating minus 400 points for a loss, and the opponent’s rating for a draw. Results of tied players against each other should not be included, since this would give one of the players an unfair advantage. After the performance rating for each tied players’ opponents has been calculated, they are averaged. Both this system and 34E11 may be difficult to use when unrated players are in the tournament.
Example: A player who wins against a 1400 and a 1500, draws against a 1600, and loses to a 1700 would have a performance rating of 1650: (1400+400) + (1500+400) + 1600 + (1700–400) = 6600; 6600/4 = 1650.
34F11. Average rating of opposition.
This system averages the ratings of players’ opponents, the better tiebreak score going to the person who played the highest-rated average field. It sounds fair but has drawbacks. A tied player rated slightly above another will often have a very slightly higher-rated field and win the tiebreak by a statistically insignificant margin.
34F12. Speed play-off game(s).
The speed playoff, an exciting way to wind up a tournament, has been used as the first tiebreak to determine the title at several major events. See also 32F1, Tiebreaking and 32F, Trophies. A special playoff to break perfect-score ties does not need to be announced in the tournament publicity but should be announced to the players at the beginning of the tournament.
TD Tip:
The playoff does not have to be rated, and the time control can be faster than the time control used for the tournament (but should allow at least five minutes total playing time per player).
If the playoff is rated, it should be treated as a separate section in the rating report. Note that “Armageddon” playoffs (one player gets draw odds in return for less playing time) may not be rated.
34F13. Coin flip
This breaks all ties. (A computer program may be able to automate this).
34G. Round robin tiebreaks.
The most common method is the Sonneborn-Berger system (34F8). While the objection noted above (it rewards someone who does well against strong opponents and poorly against weaker ones), it is one of the few methods that can actually break ties in a round robin. The Head-to-Head tiebreak (34F5) is frequently used as well.
34H. Team tiebreaks.
34H1. Game (or match) points.
Since most team events in the United States are scored on match points, the easiest tiebreak is simply the total game points earned by the teams involved. However, it is of questionable value because the teams that face the weakest opposition are more likely to win their matches by large margins. If game scoring is primary, the number of matches won is a simple and fair tiebreak.
34H2. U.S. Amateur Team System.
For each round, the tiebreak points are the final adjusted score (34E1) of the opposing team multiplied by the number of points scored against that team. For example, if Team A scored 2.5-1.5 against Team B, which finished the tournament with 3 match points, Team A’s tiebreak for that round is 2.5 × 3 = 7.5. This system awards credit for an extra margin of victory without the drawbacks of using straight game points and is preferable.
34H3. Other systems.
Most of the individual tiebreak systems described in 34F are also suitable for team play, but they have the drawback of making the margin of victory meaningless in match-point scoring. Many players find a team event more exciting when every game can affect the team standings, even after a match has been won or lost.
34I. Reentry tiebreaks.
a. The reentered player must use the announced tiebreaks for the entry determined by 28S5,
Reentry scores.
b. The opponents of reentered players can use only the scores of whichever entry (the original entry or one of the reentries) that they played, when calculating the announced tiebreaks.
See also 32C5, Reentry prizes.
TD TIP: Due to the complexity of reentry tiebreaks directors and organizers need to consider very carefully the advisability of having both reentries and non-divisible prizes as options at the same event.
Tie breaks revised.docx (25.5 KB)