Deutsche Wertungszahl
The Deutsche Wertungszahl (abbreviation: DWZ, ger. German Evaluation Number) is an evaluation number in chess to compare the playing performance of individual players. It is a chess rating system used in Germany. A higher rating number corresponds to a stronger player. A beginner is rated around 500 and a world champion about 2800.
The DWZ was introduced by the DSB (Deutscher Schachbund, ger. German Chess Association) after the German reunification in 1990. On January 1, 1993, the DWZ was introduced nationwide and replaced the Ingo-System of the DSB in the Federal Republic of Germany and the NWZ-System of the German Chess Association in East Germany. The DWZ is similar to the Elo rating system of the FIDE, but was enhanced further over the years. In development, the experiences of the Ingo-System and the NWZ-System were respected. The scale goes from about 500 (beginners) to over 2800 (world champions), but is, in theory, open at the top and bottom. The evaluation of the tournaments is done by DWZ-abstractors who transfer the tournament results to the headquarters of the DOSB (Deutscher Olympischer Sportbund, ger. German Olympic Sports Confederation), where the ZDB (Zentrale Wertungsdatenbank, ger. Central Evaluation Database) is administrated. There, a chronological subsequent billing is accomplished according to the finish date of the tournament.
In contrast to the Ingo System, a higher DWZ represents a better playing ability. The DWZ consists of an evaluation number as a measurement of the playing ability and an index number which is separated from that by a "-" sign. For players who do not have a DWZ, but have a FIDE-ELO, the FIDE-ELO is used, marked with the index 6 and resumed as DWZ. For players who neither have a DWZ nor a FIDE-ELO, but have a national evaluation number, this number is used and translated if necessary. In this case the index is set to zero.
The basic curve for calculation is the Gauss error distribution curve. For calculation, an integral is necessary to determine the expectation of winnings. Only chess results against competitors with a DWZ are taken into account.
The DWZ is calculated in the following way:
The achieved points W are the sum of the game results in which a win counts 1 point, a draw counts ½ point, and a defeat 0 points. The expected points We are calculated with the following approximation:
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