The World Cup starts tomorrow and I just filled out my bracket.  In academia Americans are a minority and people are intensely nationalistic.  So the optimal bracket strategy is to have USA advance as far as I can before even I burst out laughing  (it turns out that’s the semi-finals this year) and also give preference for under-represented countries.  Based on a cursory survey of our department’s demographics, the team that maximizes quality per department representative is Spain.  So Spain is my team to win it all this year.

The World Cup is paradoxical because the group stage is exciting and the elimination stage is extremely boring.  There are probably many reasons for this but often people focus on the penalty shootout.  You hear arguments like this.  Playing it safe gives you essentially a coin flip.  And if the other team is playing it safe, taking risks and playing offensively can actually be worse than waiting for the coin flip.

I have heard proposals to hold the penalty shootout before extra time.  The winner of the shootout will be the winner of the match if it remains tied after extra time.  The uncertainty is resolved first, then they play.

The rule would have ambiguous effects on the quality of play.  For sure, the team that won the shootout would play defensively and the disadvantaged team would be forced to play an attacking game.  There would be exactly one team attacking.

But that would be less exciting than a game in which both are attacking so the rule change would be a net improvement only if most extra-time games would otherwise have neither team attacking.

Here is a theoretical analysis of the question by Juan Carillo.  I am not sure I can summarize his conclusions so help would be appreciated.  Here is an empirical analysis.