How to avoid uncompetitive games? The importance of tie-breaking rules
研究揭示平局决胜规则（如净胜球优先）能减少小组赛末轮球队因排名已定而消极比赛的概率，为赛事组织者设计排名系统提供参考。
If the final position of a team is already secured independently of the outcomes of the remaining games in a round-robin tournament, it might play with little enthusiasm. This is detrimental to attendance and can inspire collusion and match-fixing. We demonstrate that tie-breaking rules might affect the occurrence of such a situation. Its probability is quantified via simulations for the four groups of the 2022/23 UEFA Nations League A under two well-established tie-breaking rules, goal difference and head-to-head records. In these home-away round-robin contests with four teams and 12 matches, the competitiveness of the final four games can be promoted by giving priority to goal difference, which reduces the chance of a fixed position in the group ranking by at least two and usually five percentage points in the last round. Our findings, supported by sensitivity analysis in a theoretical model, provide important lessons on how to design ranking systems.