There are many numbers used in the analysis of most sports, and the World Cup football games are no exception. For example, in 2010, mathematicians from the University of London collected ball-passing data from all of the FIFA World Cup games, and then predicted which teams would win the matches. They put together a network of passes between players throughout the tournament, then analyzed how the networks compared between the teams. This was a straight use of graph theory, the same mathematical ideas used to analyze different types of networks, such as the Internet computer network, modeling what would happen if parts of the network were suddenly removed.

With the football game, each player in the network was given a score called the “centrality,” which measured how useful they were to the entire network (team). The higher the centrality score, the bigger the impact if the player were to be removed. From this, the researchers determined that the Spanish players made the highest number of passes in that year’s tournament—almost 40 percent more than the German team—giving them a higher centrality score. In contrast, the Dutch team was more on the offensive side, with a very low number of passes between players, and thus a low centrality score. The Germans seemed more balanced, with a higher number of passes; and the English team seemed almost even, with no single player more important than another.

Overall, the mathematical formula was right on the money: In 2010, Germany beat England and Spain beat the Netherlands in semifinal play, and the Spanish won the FIFA World Cup final against Germany.