Multi-Tier Tournaments: Matching and Scoring Players
Steven J. Brams, Mehmet S. Ismail

TL;DR
This paper proposes Multi-Tier Tournaments, a new system combining Elo ratings and tournament scores to fairly rank players across skill tiers, demonstrated with chess data and adaptable to other sports.
Contribution
It introduces a novel multi-tier tournament structure that integrates Elo ratings and performance-based scores for fairer player progression and ranking.
Findings
Effective in ranking top chess players using real game data
Allows lower-rated players to advance and challenge higher-rated players
Applicable to various sports beyond chess
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…
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Taxonomy
TopicsAuction Theory and Applications · Game Theory and Applications · Game Theory and Voting Systems
MethodsSpatio-temporal stability analysis
