A Statistical Analysis of the European Soccer Champions League

1. Introduction Pollard and Reep (1997) point out that " soccer coaches, players, fans, and the media are deeply skeptical and often suspicious, to the point of paranoia, at the suggestion that a statistician might have something useful to offer […] ". Statisticians, though, have a different opinion. Statistical interest on the aspects of the game has been steadily rising over the past decades. Although, according to Reep and Benjamin (1968), " chance does dominate the game " , there seem to be several noticeable patterns concerning goal scoring, point accumulation and game strategy. The statistical efforts in their majority treat the issue from the " club viewpoint " , predicting champions, winners and losers. The approach adopted here is the " game viewpoint ". We would like to see, regardless of the team, which aspects of the game influence (and in what way) the performance of the team in a highly competitive tournament such as the U.E.F.A. Champions League. For a detailed account of the literature, see Emonet (2000). The Champions League is a tournament organized yearly by the Union of European Football Associations (U.E.F.A.). It has two league rounds and a knockout round. The competitors are European teams that are either champions at their national championship, or ranked at very high positions, according to the rank of the championship itself (for example, the first four teams of the English Premier League qualify for the Champions League, whereas only the first two teams of the Greek National League qualify for the event). The competitors are considered to be the cream of clubs worldwide, and the competition is fierce. It is considered to be the most important club competition in the world. In the first phase of the tournament, the 32 competitors are divided into 8 groups of four teams. The groups are formed randomly with a " stratification " restriction of randomness, which is that each group must contain four teams from the four different " strength " categories. The " strength " categories are a division of the overall