On the decisiveness of a game in a tournament

• We suggest a measure of how decisive a particular game is in a sport tournament.
• We use entropy-related concepts to assess the uncertainty around the final winner.
• We study the decisiveness of the 2012 UEFA European Football Championship games.
• We analyze the recent UEFA decision to expand the Euro from 16 to 24 teams.
• We show that the 16-teams format has to be favored over the 24-teams format.

In sport tournaments in which teams are matched two at a time, it is useful for a variety of reasons to be able to quantify how important a particular game is. The need for such quantitative information has been addressed in the literature by several more or less simple measures of game importance. In this paper, we point out some of the drawbacks of those measures and we propose a different approach, which rather targets how decisive a game is with respect to the final victory. We give a definition of this idea of game decisiveness in terms of the uncertainty about the eventual winner prevailing in the tournament at the time of the game. As this uncertainty is strongly related to the notion of entropy of a probability distribution, our decisiveness measure is based on entropy-related concepts. We study the suggested decisiveness measure on two real tournaments, the 1988 NBA Championship Series and the UEFA 2012 European Football Championship (Euro 2012), and we show how well it agrees with what intuition suggests. Finally, we also use our decisiveness measure to objectively analyse the recent UEFA decision to expand the European Football Championship from 16 to 24 nations in the future, in terms of the overall attractiveness of the competition.