What question did this study set out to answer?

The study aims to determine conditions under which the largest and lowest scores in a round-robin tournament are distinct.

April 10, 2026Open Access

On the Size of the Largest Distinct Extreme Score Set in Random Round-Robin Tournaments

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Key Points

The study aims to determine conditions under which the largest and lowest scores in a round-robin tournament are distinct.
Modeling a round-robin tournament with equally strong players
Analyzing scores represented as values in a countable subset of [0,1]
Proving conditions for distinct extreme scores through mathematical limits
As the number of players increases, the largest scores are likely to be distinct with high probability
Similar results apply to the lowest scores due to symmetric properties of the model
Condition with k(n) growing indefinitely is critical for the findings

Abstract

We consider a general round-robin tournament model with equally strong players in which X₈₉ denotes the score of player i against player j. We assume that X₈₉ takes values in a countable subset of 0, 1 and satisfies X₈₉+X₉₈=1. We prove that if k (n) as n and k (n) ²\! (n/k (n) ) n 0, then with probability tending to one, the largest k (n) scores are all distinct. By symmetry, the same conclusion holds for the lowest k (n) scores.

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Authors

Yaakov Malinovsky

University of Maryland, Baltimore County

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On the Size of the Largest Distinct Extreme Score Set in Random Round-Robin Tournaments

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Abstract

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