Soccer is Harder Than Football

Abstract

It is known that deciding whether or not a team in a soccer tournament in progress can still win or, more generally, can obtain a certain position is NP-complete. We show that deciding whether or not a team is guaranteed a certain minimum position is coNP-complete. We also show that deciding with regards to goal difference, the standard tie-breaker for teams having the same number of points, whether or not a team can reach a certain position is NP-complete.