Classification of matches played in the last rounds of sports competitions is a well-established tool for evaluating tournament designs. Both deterministic and probabilistic approaches are available for this purpose. Our paper offers the first comparison of them by analysing the most prominent example of four-team round-robin competitions, the group stage of the FIFA World Cup. We show that both methods are highly relevant in practice: all (four) deterministic and (six) probabilistic match types occurred in the 2014 and 2018 FIFA World Cups, respectively. The probabilistic model, which accounts for the relative benefits of attacking and defending, provides deeper insights; for instance, the competitive matches from the deterministic approach can be of any of the six probabilistic types. Finally, the probabilistic framework is used to quantify and decompose the impact of the main reforms introduced for the 2026 FIFA World Cup: the expansion to 48 teams, as well as the modified qualification and tie-breaking rules.

翻译：体育赛事最后一轮比赛分类是评估赛制设计的成熟工具。现有确定性和概率性两种方法可供使用。本文通过分析四队循环赛制中最具代表性的案例——国际足联世界杯小组赛，首次对这两种方法进行了比较。研究表明，两种方法均具有重要实践价值：在2014年和2018年世界杯中，分别出现了全部四种确定性比赛类型和六种概率性比赛类型。考虑攻防相对收益的概率模型能提供更深入见解，例如：确定性方法中的竞技性比赛可能对应六种概率类型中的任意一种。最后，本文利用概率框架量化并分解了2026年世界杯主要改革措施的影响：包括扩军至48支球队、修改晋级规则及平局打破新规。