How to avoid uncompetitive games? The importance of tie-breaking rules

In a round-robin tournament, if the final position of a team is already secured independently of the outcomes of the remaining games, 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, each of them being a home-away round-robin with four teams and 12 matches. The competitiveness of the last two games can be promoted by preferring goal difference over head-to-head results: the priority of goal difference reduces the chance of a fixed position in the group ranking by at least two and usually five percentage points. Our findings provide important lessons on how to design ranking systems.