Back to the Classroom

It happens nearly every time we watch a major international tournament. The first four group games are over, the final two remain, and we all run away back to the classroom and a subject many of us hated – numbers, statistics, calculations, probabilities and permutations.

Yes, it’s time for some good old mathematics.

Back to School

After school I’d take a natural turn towards politics and history, but will admit to being rather good at maths when I was at school. Most of it seemed utterly pointless – supported by the fact that I have never found any use for matrices, standard deviation or quadratic equations since then – but I was able to take it all in while many others would find themselves sinking in the painful mire of confusion, the sort of educational boiling oil that scars people for life.

Yet many of us – including those who might have been rubbish at maths – constantly return to the subject whenever we reach the final throes of the group stage in an international football tournament. I’d actually go so far and say that if GCSE maths was only concerned with football-based calculations and permutations and the science of goal difference, we’d have far fewer people flunking their exams.

Sometimes we don’t need to bother with all the complex permutations – for example if you were Dutch or Chilean supporter you would have already known well before the final games that both of your teams were already through to the knockout phase. As Germany supporters we don’t have the same luxury, on account of the two dropped points against Ghana. In Group G, all four teams still have a mathematical chance of making it through to the last sixteen. It matters not whether Germany need to suffer a series of catastrophes and Portugal need a miracle – we will be going into these final matches with a sense of excitement tinged with trepidation.

According to the official regulations, FIFA’s rules should be familiar with those of us used to this familiar charade. 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)

(Source: FIFA Regulations, 2014 FIFA World Cup Brazil)

Germany’s task

The task for Germany is simple, and their fate rests in their own hands. If they win their final game with the United States, they finish top on seven points – leaving the rest to fight for second place. A draw will also guarantee top spot with both teams on five points, with Jogi Löw’s men well ahead of the US on goal difference courtesy of their 4-0 demolition of Portugal. A loss on the other hand will send the US to the top of the table, leaving Germany on four points – a total that can be matched by either the Portuguese or Ghana in their last match-up.

Even in this worst case scenario however, it will take a serious goal swing (said in a Peter Snow voice) to put Jogi’s Jungs out of the competition – another benefit of their thrashing of the Portuguese. With their goal difference of +4, the Mannschaft have a five goal advantage over Ghana (-1) and an massive eight goal advantage over Portugal (-4).

In simply layman’s terms, it means that if Germany are to be eliminated, they will need to lose by a significant margin with either one of Ghana or Portugal racking up enough goals to overhaul them on goal difference and then, should that be equal, goals scored. To provide one of the many permutations, if Germany were to repeat their result against the US of last May and lose 4-3, the Ghanaians would need to beat Portugal by five clear goals to edge in front of Löw’s side. Of course, should Germany beat the US Ghana would not have to score as many goals themselves to make up what is only a -2 deficit compared to the US.

Portugal meanwhile will be hoping for a miracle. In addition to a convincing win over Ghana, with the -8 deficit far too much to make up on the Germans they will be hoping for an equally resounding win for the Mannschaft against the team now coached by former Nationaltrainer Jürgen Klinsmann.

Ein Nichtangriffspakt von Recife?

That both Germany and United States only need a draw from their final match to ensure the progression of both sides has naturally drawn some comparisons with West Germany’s infamous 1-0 win over Austria in the 1982 World Cup, known as Der Nichtangriffspakt von Gijón – the non-aggression pact of Gijón. The Germans would take the lead early on, but for the rest of the game both teams would just stroll around the pitch until the final whistle – knocking out Algeria in the process.

With German Nationaltrainer Löw up against Klinsmann – his friend and former boss during the 2006 World Cup campaign – there will be plenty of talk about a plot being hatched in Recife between the Mannschaft and a US side containing a number of former German youth players, but as far as I can see there will be no quarter given. Both sides will surely be looking to build some momentum ahead of the knock-out phase, and there’s no way Jogi Löw will tolerate anything less than a win.