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Multi-Tier Tournaments: Matching and Scoring Players

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  • Steven J. Brams
  • Mehmet S. Ismail

Abstract

We introduce a novel system of matching and scoring players in tournaments, called Multi-Tier Tournaments, illustrated by chess and based on the following rules: 1. Players are divided into skill-based tiers, based on their Elo ratings. 2. Starting with one or more mini-tournaments of the least skilled players (Tier 1), the winner or winners -- after playing multiple opponents -- move to the next-higher tier. 3. The winners progress to a final tier of the best-performing players from lower tiers as well as players with the highest Elo ratings. 4. Performance in each tier is given by a player's Tournament Score (TS), which depends on his/her wins, losses, and draws (not on his/her Elo rating). Whereas a player's Elo rating determines in which mini-tournament he/she starts play, TS and its associated tie-breaking rules determine whether a player moves up to higher tiers and, in the final mini-tournament, wins the tournament. This combination of players' past Elo ratings and current TS's provides a fair and accurate measure of a player's standing among the players in the tournament. We apply a variation of Multi-Tier Tournaments to the top 20 active chess players in the world (as of February 2024). Using a dataset of 1209 head-to-head games, we illustrate the viability of giving lower-rated players the opportunity to progress and challenge higher-rated players. We also briefly discuss the application of Multi-Tier Tournaments to baseball, soccer, and other sports that emphasize physical rather than mental skills.

Suggested Citation

  • Steven J. Brams & Mehmet S. Ismail, 2024. "Multi-Tier Tournaments: Matching and Scoring Players," Papers 2407.13845, arXiv.org.
    • Handle: RePEc:arx:papers:2407.13845
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    Cited by:

    1. L'aszl'o Csat'o, 2024. "Most Swiss-system tournaments are unfair: Evidence from chess," Papers 2410.19333, arXiv.org.

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