An application of integer programming to playoff elimination in football championships

Football is the most followed and practised sport in Brazil, with a major economic importance. Thousands of jobs depend directly on the activity of the football teams. The Brazilian national football championship is followed by millions of people, who attend the games in the stadiums, follow radio and TV transmissions, and check newspapers, radio, TV, and, more recently, the Internet in search of information about the performance and chances of their favorite teams. Teams which do not qualify for the playoffs lose a lot of money and are even forced to dismantle their structure. We comment and compare the complexity of playoff elimination in football and baseball championships. We present two integer-programming models which are able to detect in advance when a team has already qualified for or been eliminated from the playoffs. Results from these models can be used not only to guide teams and fans, but are also very useful to identify and correct wrong statements made by the press and team administrators. The application and the use of both models in the context of the 2002 edition of the Brazilian national football championship are discussed.