Multi-Tier Tournaments: Matching and Scoring Players
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910534982434816 |
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| author | Brams, Steven J. Ismail, Mehmet S. |
| author_facet | Brams, Steven J. Ismail, Mehmet S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13845 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multi-Tier Tournaments: Matching and Scoring Players Brams, Steven J. Ismail, Mehmet S. Theoretical Economics 90C10, 91A80, 91A20 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. |
| title | Multi-Tier Tournaments: Matching and Scoring Players |
| topic | Theoretical Economics 90C10, 91A80, 91A20 |
| url | https://arxiv.org/abs/2407.13845 |