With World Cup Group G standings being the way they are, I decided to read up on tiebreaks.

Here are the FIFA rules (PDF)

The relevant sections are:

18.4.a: … with three points for a win, one point for a draw and no points for a defeat (league format)

…

18.6: In the league format, the ranking in each group is determined as follows:

a) greatest number of points obtained in all group matches;

b) goal difference in all group matches;

c) greatest number of goals scored in all group matches.

If two or more teams are equal on the basis of the above three criteria, their rankings shall be determined as follows:

d) greatest number of points obtained in the group matches between the teams concerned;

e) goal difference resulting from the group matches between the teams concerned;

f) greater number of goals scored in all group matches between the teams concerned;

g) the goals scored away from home count double between the teams concerned (if the tie is only between two teams).

18.7 discusses play-off matches between teams that are *still* tied after all of 18.6.a-g are applied. As we’ll see, there is no possibility of the United States being involved in a play-off.

Let’s start with 18.6.a. The current point standings in Group G are:

- Germany
- Four points, with a win and a tie
- United States
- Four points, with a win and a tie
- Ghana
- One point, with a tie and a defeat
- Portugal
- One point, with a tie and a defeat

The remaining games are United States-Germany and Portugal-Ghana.

If the United States-Germany game results in a tie, then the United States and Germany will have five points apiece, with a win and two ties. They will be the top two teams in the group, regardless of the outcome of the Portugal-Ghana game.

If the Portugal-Ghana game results in a tie, then Ghana and Portugal will have two points apiece, with two ties and a defeat. Regardless of the results of the United States-Germany game, the United States and Germany will be the top two teams in the group.

So we need only consider what happens if both games are decisive.

The winner of the United States-Germany game will have seven points, with two wins and a tie. They are in on points.

The loser of the Portugal-Ghana game will have one point, with one tie and two defeats. They are out on points.

The remaining two teams (the loser of the United States-Germany game, and the winner of the Portugal-Ghana game) will have four points apiece, with a win, a tie, and a defeat.

So in this scenario, 18.6.b will be invoked. At this point we have to look at the goal difference for the teams. (The goal difference for, say, Germany is just the number of goals Germany scored, minus the number of goals Germany allowed.) These are currently:

- Germany
- +4
- United States
- +1
- Ghana
- -1
- Portugal
- -4

The raw numbers look good for Germany and the United States, and bad for Ghana and Portugal. But let’s bear in mind that we are considering the scenario where Germany or the United States has just lost, and Ghana or Portugal has just won. How do you win? By scoring more goals than you allow! So the goal differential of the loser of the United States-Germany game will be lower than it is now, and the goal differential of the winner of the Portugal-Ghana game will be higher than it is now.

So as a United States fan:

- Beat Germany and we’re in on points.
- If we can’t beat Germany, tie Germany and we’re in on points.
- If Germany beats us, root for a Portugal-Ghana tie and we’re in points.
- If Germany beats us, and the Portugal-Ghana game is also decisive, root for Portugal to win, and for the margin of victory for both games to add up to no higher than four, and we’re in on goal differential.

More explicitly:- If Germany wins by one goal, our GD will be zero; Portugal can win by as many as three goals and we will be in on goal differential. If Portugal wins by five or more, we’re out on goal differential. If Portugal wins by precisely four, see below.
- If Germany wins by two goals, our GD will be -1; Portugal can win by as many as two goals and we will be in on goal differential. If Portugal wins by four or more, we’re out on goal differential. If Portugal wins by precisely three, see below.
- If Germany wins by three goals, our GD will be -2; Portugal can win by one goal and we will be in on goal differential. If Portugal wins by three or more, we’re out on goal differential. If Portugal wins by precisely two, see below.
- If Germany wins by four goals, our GD will be -3. If Portugal wins by two or more, we’re out on goal differential. If Portugal wins by precisely one, see below.
- If Germany wins by five goals or more, we’re out on goal differential.

- If Germany beats us, and Ghana beats Portugal, root for the margin of victory in both games to add up to two.
- If Germany wins by one goal, our GD will be zero; if Ghana wins by one goal, their GD will also be zero. See below.
- If Germany wins by two goals or more, we’re out on goal differential.

What if Germany beats us, and Portugal beats Ghana, but the margin of victory of both games adds up to exactly four? Or what if Germany beats us and Ghana beats Portugal, and the margin of victory of both games adds up to precisely two – that is, each game is decided by a single goal?

We can still get in on 18.6.c. At this point we have to look at the number of goals scored by each team. These are currently:

- Germany
- 6
- United States
- 4
- Ghana
- 3
- Portugal
- 2

Note that the United States has one more goal than Ghana, and two more goals than Portugal. This is good. In the “goal differential” case, there was a strong relationship between winning and changing your goal differential. But there is only a weak relationship between winning and changing your raw goal count.

For example, if Germany beats the United States 3-2, and Ghana beats Portugal 1-0, the United States will actually have pulled even farther ahead in the 18.6.c race!

So:

- If Germany beats us, and Portugal beats Ghana, and the margin of victory of both games adds up to exactly four, root for Portugal’s winning score to be no more than one goal higher than our losing score, and we’re in on goals scored.
- If Portugal’s winning score is three or more goals higher than our losing score, we’re out on goals scored.
- If Portugal’s winning score is precisely two goal higher than our losing score, see below.

- If Germany beats us, and Ghana beats Portugal, and the margin of victory of both games adds up to exactly two, root for Ghana’s winning score to be no more than our losing score, and we’re in on goals scored.
- If Ghana’s winning score is two or more goals than our losing score, we’re out on goals scored.
- If Ghana’s winning score is precisely one goal higher than our losing score, see below.

What if Germany beats us, and Portugal beats Ghana, and the margin of victory of the two games adds up to exactly four, and Portugal’s winning score is precisely two goals more than our losing score? Or what if Germany beats us and Ghana beats Portugal, and the margin of victory of both games adds up to precisely two, and Ghana’s winning score is precisely one goal higher than our losing score?

Then we are in or out on 18.6.d-g. At this point we have to look at the results of the Ghana-United States and United States-Portugal matches. In each match, the first team is the home team and the second team is the away team.

- Ghana-United States
- 1-2
- United States-Portugal
- 2-2

So:

- If Germany beats us, and Portugal beats Ghana, and the margin of victory of both games adds up to exactly four, and Portugal’s winning score is precisely two goals higher than our losing score, we’re out:
- We’re still tied on direct match points (18.6.d)
- We’re still tied on direct match goal differential (18.6.e)
- We’re still tied on direct match goals scored (18.6.f)
- We’re out on direct match goals scored with away goals counting double (18.6.g)

- If Germany beats us, and Ghana beats Portugal, and the margin of victory of both games adds up to exactly two, and Ghana’s winning score is precisely one more than our losing score, then we’re in on direct match points (18.6.d)

Note there is no possibility of a playoff. Had the United States-Portugal game been a 0-0 tie instead of a 2-2 tie, that would have been a possibility, since double 0 is still 0.

I didn't know the rules were this complete/complicated.

Luckily for us Dutch folks there is an easier way to win! :-)

For the record, what actually happened was:

Germany beat the US by one goal (1-0). Portugal beat Ghana by one goal (2-1).

The points are:

Germany has two wins and a tie: 7 points.

The US has one win, one tie, and one defeat: 4 points.

Portugal has one win, one tie, and one defeats: 4 points.

Ghana has one tie and two defeats: 1 point.

So Germany is in on points, Ghana is out on points, and the US and Portugal go to 8.17.b: goal differential.

The United States scored four goals (two against Ghana, and two against Portugal), and had four goals scored on them (one by Ghana, two by Portugal, and one by Germany), so our goal differential is 0. Portugal scored four goals (two against the United States, and two against Ghana), and had seven goals scored on them (four by Germany, two by the United States, and one by Ghana), so their goal differential is -3.

So the US is in on goal differential, and Portugal is out.