Abstract
We propose a simple method of undoing tiebreaks in sport competitions with a large number of competitors and relatively small number of rounds of competition. Such methods are common in many games including Chess, Go, Bridge or Scrabble, among others. Tie-breaking methods decide in strict order the prizes to be received. One of the most commonly used methods is the well-known Buchholz method, based on the arithmetic mean of the scores obtained by the opponents. The alternative method that we propose in this paper, which is quite close to the median of the scores obtained by the opponents, is also a weighted average of the opponents’ scores, whose weights are based on the binomial distribution. The main objective of the article is to compare the proposed method with that of Buchholz, highlighting the many advantages over it.
Unfortunately, even today Buchholz’s method and its variants are routinely used as the first and second tiebreaker criteria. It is the used as a first and second criteria in the rapid and blitz chess world championships that took place in December 2021. We believe that Buchholz’s method should be replaced by the one proposed here as soon as possible.
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Acknowledgements
This research is part of the I+D+i project PID2019-104987GB-I00 supported by MCIN/AEI/10.13039/501100011033/
The author greatly appreciates the detailed comments of the two referees that have contributed to improve the revised version of this article. He also acknowledges the comments made on this article by Jordi Magem, Chess Grandmaster and FIDE Senior Trainer; Vladimir Zaiats, Mathematician and International Chess Arbiter; Josep M. Barón, Mathematician and FIDE Chess Master; and Juli Pérez, Mathematician and National Chess Master.
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Freixas, J. (2022). The Decline of the Buchholz Tiebreaker System: A Preferable Alternative. In: Nguyen, N.T., Kowalczyk, R., Mercik, J., Motylska-Kuźma, A. (eds) Transactions on Computational Collective Intelligence XXXVII. Lecture Notes in Computer Science(), vol 13750. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-66597-8_1
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