Tie-breaking in Swiss-system tournaments

Last updated

Swiss system tournaments, a type of group tournament common in chess and other board games, use various criteria to break ties between players who have the same total number of points after the last round. This is needed when prizes are indivisible, such as titles, trophies, or qualification for another tournament. Otherwise players often share the tied spots, with cash prizes being divided equally among the tied players.


Some tiebreakers used in other group tournaments are also used in Swiss-system tournaments, while others exploit the particular features of the Swiss system. If the players are still tied after one tie-break system is used, another system is used, and so on, until the tie is broken. Most of the methods are numerical methods based on the games that have already been played or other objective factors, while some methods require additional games to be played. In chess, where results are simply win/loss or draw, strength of schedule is the idea behind the methods based on the games already played: that the player that played the harder competition to achieve the same number of points should be ranked higher. In other games, results may supply more data used for breaking ties.

Median / Buchholz / Solkoff

The Median system is also known as the Harkness System, after its inventor Kenneth Harkness, or the Median-Buchholz System. [1]

For each player, this system sums the number of points earned by the player's opponents, excluding the highest and lowest. If there are nine or more rounds, the top two and bottom two scores are discarded. Unplayed games by the opponents count ½ point. Unplayed games by the player count zero points.

Modified Median

The Modified Median system is similar to the Median system, except:


This system is the same as the Median system, except that no scores are discarded. [3] Ephraim Solkoff did not invent this system. He introduced it to the United States in 1950, but it was used in England prior to that. [4]


To calculate this, sum the running score for each round. For example, if a player has (in order) a win, loss, win, draw, and a loss; his round-by-round score will be 1, 1, 2, 2½, 2½. The sum of these numbers is 9. Additionally, one point is subtracted from the sum for each unplayed win, and ½ point is subtracted for each unplayed draw. In the previous example, if the fourth-round draw was instead a ½ point bye, then ½ point would be subtracted and the final sum would be 8½.

This system places more weight on games won in the early rounds and the least weight on games won in the final rounds. The rationale for this system is that a player who scored well early in the tournament has most likely faced tougher opponents in later rounds and should therefore be favored over a player who scored poorly in the start before subsequently scoring points against weaker opponents. [5]

A practical benefit of the cumulative system is that it is simple to track with pen and paper when running a large tournament. Of course in the age of computers and smart phones, instead of accumulating points scored against weak players, we could just calculate who had the toughest schedule as with the Solkoff and median systems. An alternative explanation for the popularity of the cumulative system is that it is easier for coaches, players and the audience to follow the potential scores and prizes, as the point totals don't vary and only need to be added to from round to round.

Cumulative opponent's score

This sums the cumulative scores of the player's opponents. [6]

Result between tied players

If the tied players played each other, if one of them won then that player finishes higher on tie-break. [7]

Most games with the black pieces

The player that had the black pieces the most times finishes highest on tie-breaks. [8]

Most wins (Baumbach)

The player with the most wins finishes highest on tie-breaks. This is used as the first tie-break rule for individual tournaments in ICCF.


Invented by Isaac Kashdan, this system awards four points for a win, two points for a draw, one point for a loss, and none for an unplayed game. As a result, if players with no unplayed games tie, the one with fewer draws finishes higher on the tie-break (i.e. a win and a loss is better than two draws). [9]

Sonneborn–Berger score

Add the scores of every opponent the player beats and half of the score of every opponent the player draws. [10] The system was named after William Sonneborn and Johann Berger, but it was invented by Oscar Gelbfuhs. [11] The system is the main tie-breaking system in round robin tournaments, but is also used in Swiss tournaments. It is also called the Neustadtl score.

What we call the Sonneborn-Berger system was not invented by Sonneborn or Berger, and it was not originally designed for tie-breaking. It was invented by Oscar Gelbfuhs about 1873 to be used as a weighted score in round-robin tournaments. It would be used instead of the raw score for final places. In 1886 Sonneborn criticized the system and suggested an improvement that would give a better-weighted score. His suggestion was to add the square of the player's points to the amount calculated as above. In 1887 and 1888 Berger studied Gelbfuhs' system and the suggestion of Sonneborn. This improvement became known as the Sonneborn-Berger system.[ citation needed ]

When the system is used to break ties between equally scoring players, adding in the square of the player's raw score does no good, so the Sonneborn improvement is omitted. However, the system has retained the Sonneborn-Berger name. [12]

Opponent's performance

This method uses the average performance rating of the player's opponents. The "performance rating" of a player is basically the rating the player would receive if they had started the tournament without a rating. [13]

Average rating of opposition

The average rating of the player's opponents. [14]

Brightwell Quotient

The Brightwell Quotient used in the World Othello Championship uses a formula based on strength of schedule and margin of victory within games; it also allows for byes. (Not relevant in games such as chess without a defined margin of victory.)

Time of loss

Among tied players, the player whose first loss came last gets priority. If player A's first loss was in round 4 and player B's first loss was in round 2, player A gets priority. This was a tiebreaker used by Pokémon Organized Play in 2004-2005.


If a player arrives after the first round is paired, the player loses priority. This tiebreaker is currently used by Pokémon Organized Play.

Speed play-off games

The tie is broken by one or more games played with fast time control, or Fast chess.

Single fast game

FIDE rules provide for a single fast decisive game, known as Armageddon. White gets more time on the clock, but must win (i.e. a draw counts as a win for Black). The player who wins the draw of lots may choose which color they play.

Coin flip

As a last resort, ties are broken by a random process such as a coin flip. [15]

Order of tiebreak criteria

Harry Golombek points out deficiencies in most of the tie-break systems and recommends a playoff if there is time. If not, he recommends Sonneborn-Berger and then the player who has the most wins. For Swiss tournaments, he recommends the Buchholz system and the Cumulative system. [16]

For Swiss tournaments for individuals (not teams), FIDE's 2019 recommendations are: [17]

  1. Buchholz Cut 1 (the Buchholz score reduced by the lowest score of the opponents);
  2. Buchholz (the sum of the scores of each of the opponents of a player);
  3. The greater number of wins;
  4. The greater number of wins with Black pieces, not counting forfeits.

The U.S. Chess Federation recommends these as the first four tie-breaking methods to be used: [18]

  1. Modified Median
  2. Solkoff
  3. Cumulative
  4. Cumulative opponent's score

See also

Related Research Articles

In chess, there are a number of ways that a game can end in a draw, neither player winning. Draws are codified by various rules of chess including stalemate, threefold repetition, and the fifty-move rule. Under the standard FIDE rules, a draw also occurs in a dead position, most commonly when neither player has sufficient material to checkmate the opponent.

A game of chess can end in a draw by agreement. A player may offer a draw at any stage of a game; if the opponent accepts, the game is a draw. In some competitions, draws by agreement are restricted; for example draw offers may be subject to the discretion of the arbiter, or may be forbidden before move 30 or 40, or even forbidden altogether. The majority of draws in chess are by agreement.

<span class="mw-page-title-main">36th Chess Olympiad</span> 2004 chess tournament in Calvià, Spain

The 36th Chess Olympiad, organized by the Fédération Internationale des Échecs (FIDE) and comprising an open and a women's tournament, as well as several events designed to promote the game of chess, took place between October 14 and October 31, 2004, in Calvià on the Spanish island of Mallorca. There were 129 teams in the open event and 87 in the women's event. In total, 1204 players were registered.

A Swiss-system tournament is a non-eliminating tournament format that features a fixed number of rounds of competition, but considerably fewer than for a round-robin tournament; thus each competitor does not play all the other competitors. Competitors meet one-on-one in each round and are paired using a set of rules designed to ensure that each competitor plays opponents with a similar running score, but does not play the same opponent more than once. The winner is the competitor with the highest aggregate points earned in all rounds. With an even number of participants, all competitors play in each round.

The Sonneborn–Berger score is a scoring system often used to break ties in chess tournaments. It is computed by summing the conventional score of each defeated opponent, and half the conventional score of each drawn opponent.

<span class="mw-page-title-main">37th Chess Olympiad</span> 2006 chess tournament in Turin, Italy

The 37th Chess Olympiad, organized by FIDE and comprising an open and a women's tournament, as well as several other events designed to promote the game of chess, took place between May 20 and June 4, 2006, in Turin, Italy. There were 148 teams in the open event and 103 in the women's event. In total, 1307 players were registered.

The Buchholz system is a ranking or scoring system in chess developed by Bruno Buchholz in 1932, for Swiss system tournaments. It was originally developed as an auxiliary scoring method, but more recently it has been used as a tie-breaking system. It was probably first used in the 1932 Bitterfeld tournament. It was designed to replace the Neustadtl score.

In a group tournament, unlike a knockout tournament, there is no scheduled decisive final match. Instead, all the competitors are ranked by examining the results of all the matches played in the tournament. Typically, points are awarded for each match, with competitors ranked based either on total number of points or average points per match.

<span class="mw-page-title-main">38th Chess Olympiad</span> 2008 chess tournament in Dresden, Germany

The 38th Chess Olympiad, organized by FIDE and comprising an open and a women's tournament, as well as several other events designed to promote the game of chess, took place from 12 to 25 November 2008 in Dresden, Germany. There were 146 teams in the open event and 111 in the women's event. In total, 1277 players were registered.

<span class="mw-page-title-main">Johann Berger</span> Austrian chess player (1845–1933)

Johann Nepomuk Berger was an Austrian chess master, theorist, endgame study composer, author and editor.

<span class="mw-page-title-main">30th Chess Olympiad</span> 1992 chess tournament in Manila, Philippines

The 30th Chess Olympiad, organized by FIDE and comprising an open and a women's tournament, as well as several other events designed to promote the game of chess, took place between June 7 and June 25, 1992, at the Philippine International Convention Center in Manila, Philippines.

<span class="mw-page-title-main">23rd Chess Olympiad</span> 1978 chess tournament in Buenos Aires, Argentina

The 23rd Chess Olympiad, organized by FIDE and comprising an open and a women's tournament, as well as several other events designed to promote the game of chess, took place between October 25 and November 12, 1978, in Buenos Aires, Argentina.

<span class="mw-page-title-main">Chess tournament</span> Series of competitive chess games

A chess tournament is a series of chess games played competitively to determine a winning individual or team. Since the first international chess tournament in London, 1851, chess tournaments have become the standard form of chess competition among serious players.

A chess rating system is a system used in chess to estimate the strength of a player, based on their performance versus other players. They are used by organizations such as FIDE, the US Chess Federation, International Correspondence Chess Federation, and the English Chess Federation. Most of the systems are used to recalculate ratings after a tournament or match but some are used to recalculate ratings after individual games. Popular online chess sites such as chess.com, Lichess, and Internet Chess Club also implement rating systems. In almost all systems, a higher number indicates a stronger player. In general, players' ratings go up if they perform better than expected and down if they perform worse than expected. The magnitude of the change depends on the rating of their opponents. The Elo rating system is currently the most widely used.

Norway Chess is an annual closed chess tournament, typically taking place in the May to June time period every year. The first edition took place in the Stavanger area, Norway, from 7 May to 18 May 2013. The 2013 tournament had ten participants, including seven of the ten highest rated players in the world per the May 2013 FIDE World Rankings. It was won by Sergey Karjakin, with Magnus Carlsen and Hikaru Nakamura tied for second place. Norway Chess 2015 took place in mid-June 2015 and was a part of the inaugural Grand Chess Tour. The tournament has since decided to withdraw from the Grand Chess Tour.

<span class="mw-page-title-main">Candidates Tournament 2018</span> Chess tournament in Berlin

The Candidates Tournament 2018 was an eight-player double round-robin chess tournament, which was held in Berlin, Germany, between 10–28 March 2018. The winner, Fabiano Caruana, earned the right to challenge the defending world champion, Magnus Carlsen of Norway, in the World Chess Championship 2018 match.

<span class="mw-page-title-main">Candidates Tournament 2022</span> Chess tournament

The 2022 Candidates Tournament was an eight-player chess tournament to decide the challenger for the World Chess Championship 2023. The tournament took place at the Palacio de Santoña in Madrid, Spain, from June 16 to July 5, 2022, with the World Championship finishing in April 2023. As with every Candidates tournament since 2013, it was a double round-robin tournament.

<span class="mw-page-title-main">FIDE Grand Swiss Tournament 2021</span> Chess tournament in Riga, Latvia

The FIDE Grand Swiss Tournament 2021 was a chess tournament that formed part of the qualification cycle for the World Chess Championship 2022. It was an 11-round Swiss-system tournament, with 108 players competing, running from 25 October to 8 November 2021 in Riga, Latvia, in parallel with the FIDE Women's Grand Swiss Tournament 2021. The tournaments were held while Latvia was in a COVID-19 lockdown, which led to a number of players withdrawing before the tournament began.

The Champions Chess Tour 2022, known for sponsorship reasons as the Meltwater Champions Chess Tour, was a 9-month series of nine online chess tournaments featuring some of the world's top players, who played for a prize money pool of US$1.6 million. The tour started on February 19, 2022 and lasted until November 20, 2022.

<span class="mw-page-title-main">World Blitz Chess Championship 2022</span> Global chess tournament

The 2022 World Blitz Chess Championship was the 2022 edition of the annual chess tournament held by FIDE to determine the world champion in chess played under blitz time controls. Since 2012, FIDE has held the World Rapid and Blitz Championships at a joint tournament. The tournament was held in Almaty, Kazakhstan from 29–30 December 2022, using a Swiss-system with 21 rounds for the open tournament and 17 rounds for the women's tournament. Players eligible to participate were to either be rated at least 2550 Elo in a FIDE rating list during 2022, or be a reigning national champion. Time controls for the tournament were 3+2, meaning each player initially starts with 3 minutes and gains 2 additional seconds following each move.