Topics in Tournament Ranking

Ranking rules are a crucial component of every tournament design. This chapter argues for a better consideration of theoretical results in the construction of ranking criteria. Our axiomatic approach provides insight into three fields: points scoring systems applied to determine the outcome of championships including multiple competitions, ranking in Swiss-system tournaments where the strength of opponents has to be taken into account, and tie-breaking criteria in round-robin tournaments. A method is proposed to decide the final ranking in a round-robin league if the season is stopped and cannot resume. The previous FIFA World Ranking, used between 2006 and 2018, illustrates how many ways a rating formula can go awry.