From groups to a single league: evaluating competitiveness in the UEFA Champions League

Recently, UEFA changed the group stage of its international soccer competitions to an incomplete round robin tournament. Previously, teams were divided into groups, each playing a double round robin tournament with a resulting ranking table. In contrast, the new format has all teams competing in one league, producing a single ranking. We investigate the effect of the new format on the probability of competitive matches in the UEFA Champions League. A match is non-competitive if the prize for at least one opponent does not depend on the match outcome, or if there exists an opportunity for both opponents to collude; otherwise, we call a match competitive. Using Monte Carlo simulations and integer programming, we show that the new format results in proportionally more competitive matches than the old format, although it also results in a noticeable increase in the risk of collusion.