draws . The system was named after William Sonneborn and Johann Berger, but it was invented by Oscar Gelbfuhs . 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. 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 . 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 . Average rating of opposition The average rating of the player's opponents . 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. Tardiness 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