The United States is in a group with Germany, Portugal, and Ghana. The two of four teams with the most points after a round robin will advance to the second round. I am giving the US about 25% to advance out of the group stage and this seemed high to some of my readers. This initial reaction is not surprising when you consider that Germany and Portugal are ranked two and three respectively in the FIFA World Rankings and Ghana beat the US in two straight World Cups. But, the numbers make sense.
This 25% is actually a very complicated calculation and it starts with the six individual games that will be played in Group G’s round robin. A win gets a team 3 points and a draw 1 point.
Germany and Portugal are heavy favorites in their games, but this is not American football or best of seven series in baseball, hockey, or basketball; single low scoring games leave open reasonable probabilities of upsets or draws. Thinking about these games independently, Germany is between 65 and 75% to beat Ghana and the US. While Portugal is between 55 and 60% to beat Ghana and the US. But, this is soccer where draws happen and Germany is about 20% to draw Ghana and the US. While Portugal is also between 20 and 25% to draw Ghana and the US.
There are six games with three possible outcomes each, leaving a total of 729 possible overall outcomes after the games are played. Knowing the independent likelihood of any of these three outcomes for the six games, I can compute the probability of any of the 729 overall outcomes and which teams would qualify in any of them. With this independence assumption, the US and Ghana are both a little over 25% to qualify with Portugal at about 65% and Germany at about 85%.
Thinking about the progression of games, the first set of games is the US versus Ghana and Portugal versus Germany. Germany is about 50% likely to win, Portugal is about 20% to win, and there is a 30% likelihood of a draw. The US is about 33% likely to win versus Ghana.
1) If the US loses against Ghana they have a negligible chance of advancing.
2) If the US draws against Ghana they are less about 15% to advance.
2) But, there is a 33% likelihood they beat Ghana and if they do, they are about 50% likely to advance! Two more points will guarantee they advance and one more point puts them at just over 50% to advance. No team with five or more points has failed to advance (think about it; that means they are either 3-0-0, 2-0-1, or 1-0-2) and a little over half the teams with four points advance (they are 1-1-1). The US will play Portugal then Germany. Let’s do the math:
Guaranteed to Advance (36%): win and win (2.7%), win and draw (4.7%), draw and win (2.7%), draw and draw (4.7%), win and loss (13.9%), or loss and win (7.4%). A win and win, win and draw, and draw and win would also be enough to advance if they tied Ghana. A win and loss and loss and win would give them about 50% likelihood of advancing if they tied Ghana.
Over 50% to Advance (26.5%): draw and loss (13.8%) or loss and draw (12.7%).
Guaranteed to not-Advance (37.5%): loss and loss (37.5%).
I will talk more about possible deviation from independence in future blog posts (i.e., how I expect my game-by-game predictions to shift as the earlier games unfold).
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