The Buchholz system (also spelled Buchholtz) is a ranking or scoring system in chess developed by Bruno Buchholz (died ca. 1958) in 1932, for Swiss system tournaments (Hooper & Whyld 1992). 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 (Hooper & Whyld 1992).
The method is to give each player a raw score of one point for each win and a half point for each draw. When used as an alternate scoring system, each player's Buchholz score is calculated by adding the raw scores of each opponent and multiplying by the player's raw score (Hooper & Whyld 1992). When used for tie-breaking among players with the same raw score, no multiplying is done, and the sum of the opponent's raw score is used to break ties (Golombek 1977). When used as a tie-break system, it is equivalent to the Solkoff system.
The major criticism of this system is that tie-break scores can be distorted by the set of opponents that each player plays (especially in early rounds). To avoid this problem a version of Buchholz, the Median-Buchholz System is sometimes used. In the Median-Buchholz System the best and worst scores of a player's opponents are discarded, and the remaining scores summed.