It’s the 2010 FIFA World Cup and chances are your favorite team has played two matches. With one to go, you aren’t sure exactly what has to happen in order for the squad to advance to the next round. Not to worry—MLSsoccer.com has got you covered.
We sat down with Gregory King, a logistics researcher and operations engineer for a renowned think-tank, who gave us some insight into the possible scenarios for the final games of the group stage and a few theoretical ideas concerning strategy for the third matches. Today’s edition: Group A
After two matches, Group A has become a tale of two pairs. At the top of the group sit Mexico and Uruguay, both with four points. At the bottom are France and South Africa with a point a piece. The final day of opening round competition will see the two pairs square off against one another (Mexico v. Uruguay in Rustenburg and South Africa v. France in Bloemfontein) in a set of matches that present some interesting logistical issues.
At the top of the table, a draw in Bloemfontein would send both Uruguay and Mexico through to the knockout stages, no questions asked. Ignoring ethics for a moment, the safest strategy then for both sides would be to simply stand still for 90 minutes after the first whistle is blown.
“There’s an idea in economics called ‘Risk Aversion,’ which states that human beings, when give a choice between a known quantity and an equivalent risk, will always choose the known quantity," King said. "Ethics aside, it would be well within reason for both Mexico and Uruguay to take the known quantity of a draw, rather than risk getting knocked out of the tournament playing for the win.”
Playing for a draw is problematic, however, when one considers goal differential. If Mexico and Uruguay were to indeed play for the draw, then Uruguay would win the group on its +3 goal differential and avoid Group B favorites Argentina in the round of sixteen. Mexico, then, will likely want to play for the win, given that it could help them sidestep Lionel Messi and company.
At the other end of the table, the only hope that either South Africa or France has to get through to the knockout stages is a win, combined with a loss for one of the two top teams. A draw in Rustenburg, then, would be lethal to both sides. With that in mind, the appropriate strategy for both of the bottom teams would be to agree to play their final match with no goalies or to agree beforehand to let one team win.
“It would be strategically irrational for South Africa and France to not agree to flip a coin and let one of them win the game," King said. "Using ideas related to The Nash Equilibrium, a concept in game theory, we can say that it is a better move for both teams to agree to have a winner, rather than accepting the outcome of a draw.”
It’s also the case that if the teams did flip a coin and agree to let one team win, that team should be granted the right to score goals at will. Such a move would allow the winning team to create a highly positive goal differential for itself and increase the chances of moving past the tiebreak with the loser of the Uruguay v. Mexico match.
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