# Multi-Tier Tournaments: Matching and Scoring Players

## TL;DR

This paper introduces a new tournament system that allows players of different skill levels to compete and progress through tiers based on performance, not just ratings.

## Contribution

The novel Multi-Tier Tournament system combines Elo ratings and Tournament Scores to fairly assess player progression and tournament outcomes.

## Key findings

- Lower-rated players can progress and challenge higher-rated players in a structured tournament format.
- The system was tested using top 20 active chess players and 1209 games, showing its viability.
- The approach can be adapted to sports like baseball and soccer.

## 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.