If the United States and Germany tie on Thursday, they both advance to the Round of 16. This is 100% guaranteed, as they would both have 5 points, which is more than the possible 4 points that Ghana or Portugal could have at the end of the day. In a world where advancing is the only thing that mattered, the USA and Germany would likely be conspiring for a tie, whether publicly or behind closed doors. Fortunately for FIFA, the order of those advancing in the group affects placement in the round of 16, so the team in first place gets to face a second place team of another group, a team that is usually weaker than a first place team.
Still, however, there are merits to guaranteed advancement. To Germany, a guaranteed tie has absolutely no downsides, as they would advance as the top team in the group. We want to focus on the merits of conspiracy from the U.S. perspective. First of all, the scenario where both teams kick the ball around and refuse to score for 90 minutes isn’t feasible, at least from a game theory perspective. The Germans would be wary that the United States could “defect” on their agreement and try to go for the win by scoring themselves, so straight conspiracy to not score would not work because of the easy potential of defection.
There is a theoretical scenario in which conspiracy could work without defection. The way to work this would be to allow Germany to score immediately. Having done this, the Germans would know that they do not have to worry about U.S. defection, as a 1-0 victory would be equivalent to a 1-1 tie in that Germany still gets first place. As a response to getting a free goal, Germany would not score anymore (the difference between 1-0 and 2-0 not mattering to them), and the U.S. would also refuse to score until the very end of the game. Germany, indifferent between the win and the tie, would let America score in stoppage time of the second half, leaving almost no time on the clock for any further scores and allowing both teams to advance with a tie. If agreed upon, this conspiracy is absolutely possible and can be setup so that both teams do not have to have any fear of defection from the other team.
Realistically this will never happen, and there are some obvious obstacles in the way of conspiracy. The first is the matter of gamesmanship. Nobody wants to see two teams conspire and not give any effort. The world cup only comes around once every four years, so making a mockery of one of the few games a team gets would absolutely be frowned upon. The second matter is the sentimentality associated with accepting second place in the group for the United States. Does the U.S. really not want to even try to win the supposed “Group of Death”? How can we expect soccer to be recognized as up and coming in America if, given the opportunity to defeat a strong German power, the U.S. rather decided to fold and conservatively take second place? A decision like that would ruin the legitimacy of the sport in the eyes of soccer fans.
For the moment, lets remove the implications of reality and examine the USA’s mathematical incentive to conspire. To do this we can look at a breakeven equation, looking at the value of finishing first or second in the group, given both the conspiracy and non-conspiracy scenarios.
V1(pfirst)+V2(psecond) + 0(peliminated) = V2
To fill in these probabilities, we can use the estimates put forth on fivethirtyeight.com, for the USA’s finish in group G:
.153(V1)+.606(V2) = V2
V1 = 2.575(V2)
Basically this is saying that if you value finishing in first 2.575 times more than finishing in second, then you are indifferent between the choice of whether to play the match out, or to conspire. If you value finishing first more than 2.575 times the value of finishing second, you would rather play the match out. If you value finishing first less than 2.575 times the value of finishing second, you would want to conspire. Obviously, it’s a little hard to evaluate intuitively how much value first place brings compared to second place. One way we can look at it is by assessing the percent chance, given a round of 16 placement, that the U.S. would advance to the round of 8. If the U.S. makes it to the round of 16, they would play one of the teams that advanced from Group H.
The probabilities for Group H finishes, again from fivethirtyeight, are as follows:
|1st. Place||2nd. Place|
Using each teams ELO rankings, compared to the ELO ranking of the United States, we can calculate the percent chance that the U.S. would beat each team. Then, by multiplying that chance by the probability that the U.S. would face each team, we can calculate another breakeven to see if it is more or less than the 2.575 we found.
U.S.(1858) vs. Belgium(1867): 48.71%
U.S.(1858) vs. Algeria(1660): 75.76%
U.S.(1858) vs. Russia (1783): 60.63%
U.S.(1858) vs. South Korea (1616): 80.11%
V1(.964*.4871+.036*(.7576)) = V2(.036*.4871+.591*.7576+.367*.6063+.006*.801)
V1 = 1.394(V2)
As we can see, the 1.394 is much less than the 2.575 that we calculated earlier, indicating that the potential value of obtaining first is not worth risking by playing the game out instead of conspiring to win. Obviously, there are a couple assumptions we made here in that the perceived value of a round of 16 spot is measured by the probability of advancing to the round of 8, but mathematically, it does appear advantageous for the United States to attempt to conspire for a tie on Thursday.
There is no way that the United States and Germany will completely conspire for guaranteed advancement, even in the manner that I described earlier. But just because the two teams are extremely unlikely to conspire doesn’t mean that the point situation in the group won’t affect the teams’ style of play. I expect a conservative matchup played at a slow pace, and if it remains tied late in the game, don’t be too surprised if both teams appear to pack it in.
Image courtesy of Soccer Lens
Georgetown University Class of 2016