What are the Odds at the Russia 2018 FIFA World Cup?

Abstract

In this note we explore the group stage competition format in a standard FIFA World Cup Soccer Championship group phase. The group stage involves thirty-two teams divided into eight groups of four teams each, based on a draw that takes the national teams' seeding and geographical location into consideration. Each of the four teams in a given group is scheduled to play one match against every other team in the same group. Upon the completion of six games in each of the eight groups (for a total of 48 games), the top two highest scoring teams (the winner and the runner-up) advance to the knockout stage. In this note we focus on the forty different ways (sequential configurations or states) that a group stage in an arbitrary group can result at the end of the group stage upon the completion of the six games in a typical World Cup Championship. We generate simulations for these configurations on spreadsheets. We use the Russia 2018 FIFA World Cup as an example, along with other relevant historical data, to compare and contrast theoretical versus actual configurations and their probabilities.