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<p>We propose procedures for draws in sports tournaments that will achieve balanced groups of size 3. We start by developing an efficient algorithm that finds all possible balanced groupings; that is, allocations of teams to groups such that the strength of all groups lies between two bounds. The algorithm uses comparison results to discard large sets of unfeasible allocations and backtracking. We then define pot-and-ball draws that randomly pick one of the balanced groupings. Our draw procedures ensure that all groups are of (virtually) identical competitive levels, thereby enhancing the overall fairness and interest of the tournament.</p>

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Draw procedures for balanced 3-team group rounds in sports competitions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月6日

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  • Pablo Laliena,
  • F. Javier López

摘要

We propose procedures for draws in sports tournaments that will achieve balanced groups of size 3. We start by developing an efficient algorithm that finds all possible balanced groupings; that is, allocations of teams to groups such that the strength of all groups lies between two bounds. The algorithm uses comparison results to discard large sets of unfeasible allocations and backtracking. We then define pot-and-ball draws that randomly pick one of the balanced groupings. Our draw procedures ensure that all groups are of (virtually) identical competitive levels, thereby enhancing the overall fairness and interest of the tournament.