World Cup Tiebreaker Sudoku

All my life, I have loved trying to figure out sports tiebreakers. They are like sports sudoku puzzles or the impossibly addictive 2048 game which now takes up roughly 18 hour a day for me. Tiebreakers. Magic numbers. NFL playoff possibilities. This stuff has always been fun, and in this way (and in only this way) the shocking (and, grrr, brilliant) last second goal by Portugal Sunday is a gift. Had the U.S. held on for just 30 more seconds, they would be through to the knockout round of the World Cup.

As it stands, the Portugal draw offers the opportunity to unlock the tiebreakers.

Here is the United States group as things currently stand:

Team Wins Draws Losses Goals Goals Against Points Germany 1 1 0 6 2 4 USA 1 1 0 4 3 4 Ghana 0 1 1 3 4 1 Portugal 0 1 1 2 6 1 OK, that seems pretty simple. Each team only plays three matches so there are not too many possibilities here. Here is how FIFA determines what two teams advance out of each group.

1. Most points (three points for a win, one point for a draw). 2. Goal differential. 3. Most goals scored. 4. Goal difference in game(s) played between the tied teams. There are a couple of other tiebreakers including the organizing committee “drawing lots,” which is a lot like the coin flip at the bottom of the NFL tiebreaker system. It has never come to that and, you would hope, never will. In the U.S. case, these four tiebreakers shouldl be enough to determine their fate.

We only care about the U.S. chances here but it should be noted that Germany is not quite in yet. It would take the U.S. beating Germany, probably by several goals, to put the Germans at risk, and the chances of that are so small that there’s really no point in discussing it. Germany is almost certainly in. With a draw or better, the Germans will advance as the top team in the group

The United States is about three-quarters of the way in which is more than just about anyone could have expected after the first two games of the Group of Death. Incidentally, I’ve already written this -- that whole “Group of Death” thing was pretty ridiculous overkill. The U.S. found itself in a good group, but this was no Group of Death. Group D -- with Costa Rica playing absurdly well, and with former World Cup winners Italy, Uruguay and England -- THAT is what a Group of Death looks like. Italy, Uruguay and Italy are ALL Top 10 teams in the FIFA World rankings and only one will advance. England, one of the most soccer-loving countries on planet earth, is at risk of losing all three of its matches and sending that great nation into another self-loathing pub crawl. Group D is the Group of Death. The U.S. group is more like the Group of Fairly Severe Back Pain.

OK, to the tiebreakers. First three scenarios are easy.

-- With a win, the United States advances as the top team out of the group.

-- With a draw, the United States advances as the the second team out of the group.

-- If Ghana and Portugal draw, the United States advances no matter what they do against Germany.

So, those are the sure things. The United States has four points, Ghana and Portugal have only one point each. The only way either Ghana or Portugal can match the U.S. point total is to win their game and have the U.S. lose. I appreciate that I’m writing obvious things here but this is the fun of tiebreakers. Some of it is obvious. Some isn’t.

So, now, what if the U.S. loses and Ghana and Portugal do not tie? Well, let’s deal first with the less-likely threat, Portugal.

-- If the U.S. loses by one goal, Portugal must win by four goals just to even up the goal differential -- that’s what happens when you lose a match 4-0 as Portugal did to Germany. This is obviously very unlikely but to give an example, let’s say the U.S. loses 1-0 to Germany. If Portugal won its match 4-0, I believe Portugal would advance. I’ve seen it written in various places that Portugal would actually need to win by FIVE goals, but I don’t think that’s right.

If U.S. loses 1-0, it will have scored four goals and given up four goals.

If Portugal wins 4-0, it will have scored six goals and given up six goals.

So they would be tied on goal differential. Portugal would then advance on the next tiebreaker, which is most goals scored.

This is highly unlikely. The U.S. could make it harder on itself and lose by two or three goals. That would make the Portugal job a little easier but still not easy. There is actually a scenario that is kind of frightening. Let’s say the U.S. lost 3-0 and Portugal won 2-0. This isn’t going to happen (please!) but if it it did, there would be some madness.

In that scenario:

The U.S. would have 4 points, 4 goals, 6 goals against.

Portugal would have 4 points, 4 goals, 6 goals against.

They tied in their game so that wouldn’t make the difference. Best I can tell from the tiebreaker system I have seen, this would force FIFA to draw lots, as mentioned earlier. But it’s not going to happen so let’s not worry about it.

Bottom line: The goal DIFFERENCE between a U.S. loss to Germany and a Portuguese win over Ghana would need to be five goals to give Portugal a chance -- and even that isn’t a sure thing. I have spent too much time going over a very remote possibility.

-- Ghana is a whole other matter. The U.S. advantage over Portugal is a massive lead in goal differential. The U.S. advantage over Ghana is their win over Ghana.

So, if the U.S. loses to Germany 1-0, and Ghana wins 1-0, the U.S. still advances. They will have the same number of points, and their goal differential will be the same. But the U.S. victory over Ghana would be the decisive tiebreaker.

For Ghana to win on goal differential, there needs to be a three-goal difference. That part is fairly easy to follow. But what’s tricky -- especially in our American mindset where head-to-head play is always the decisive tiebreaker -- is that goals scored comes BEFORE head-to-head play in the World Cup. So (as brilliant reader Sean points out) if the U.S. loses 1-0 and Ghana wins 2-1, Ghana will advance NOT the United States.

If U.S. loses 1-0, they will have scored four goals and given up four goals.

If Ghana wins 2-1, they will have scored FIVE goals and given up five goals.

That means Ghana advances even though the U.S. beat Ghana.

To put it another way, for Ghana to advance over the U.S.

1. Ghana must win. 2. The U.S. must lose. 3. The goal differential in the two games needs to be three OR Ghana simply needs to score two more goals than the U.S. scores.

Anyway, I THINK that’s how it goes.