There is more to football than mathematics, and in particular arithmetic and statistics. But at this point there is, without doubt, an irrefutable fact – an obvious and undeniable sign of the closeness of the teams that we are seeing each day at Brasil '14. Five knockout ties required extra time, two of those required penalty shootouts, to decide the ultimate fate of who moves forward and who goes home from the finals of an entire World Cup championship. This, as I see it, adds another competitive aspect – emotion – to an already remarkable event. France, Germany, Argentina and Belgium, three of the four from Europe, the 'old continent',joined the winning teams from the first half of the draw –Brazil, Colombia, the Netherlands and Costa Rica – for a quarter-final line-up that will be balanced four-four between European and American sides. Let us analyse the events that unfolded as these eight sides went through in this World Cup forum.

France, first quarter-finalists

‘Les Bleus' were the first to have their passports to the quarter-finals stamped after winning by a score (2-0) that will have shocked a Nigeria side utilised the strength of their physical attributes. As we had we had seen before in this very stage of the 2014 World Cup, the game got off to a strong start with an interesting range of individual skill on display and, as a result, moments of danger in both penalty areas.

France used its right side to get good crosses in through Valbuena and Debuchy, whilst on the other wing we saw a couple of excellent balls from Matuidi for Benzema. In the middle, Pogba was a constant danger and he moved well to get in an excellent shot. If there was one negative in this first half, it was Benzema’s lack of influence in attack.

For the Africans, the result of one on one with the full-backs and centre-backs allowed quick counter-attacks. There was, as expected, much physical contact, because both teams have very strong players in that respect.

In the second half, Nigeria started to threaten the French goal more and more and Loris was fully utilised in preventing counter attacks. Didier Deschamps reacted by bringing Griezman on for Giroud and moving Benzema to the center forward position. The benefits were seen immediately. A one-two with Griezman put the Real Madrid striker in an ideal position to score but Moses arrived in time to stop the ball before it crossed the goal line.

This signalled the beginning of a period of pressure from the French side, who hit the bar through a shot from Cabaye and went close with a header from Benzema before finally, on 79 minutes, Pogba capitalised on an error from the opposition goalkeeper from a long corner to open the scoring.

Nigeria, inevitably, had to go forward and the defence were caught out by Griezman who managed another attempt on goal that was saved by the goalkeeper and out for a corner.

In added time, France took a corner with the intention of using it to waste some time, but, with the Nigerian defence relaxed, attacked the front post allowing Griezman to beat his man and force an own goal, making the score two-nil and confirming France’squalification, at the same eliminating the last of the African sides from the competition.

Extra-time again

Germany had to go to extra-time to dispose of Algeria. Before kick-off they were clear favourites for most people but after watching the first 18 minutes of the game, in which their opponents had a goal disallowed, a couple more dangerous attempts and a shot from Ghoulam from inside the German area, we were not as confident about this.

The Algerians played compact, sitting back with a 1-4-4-1-1, moving with good coordination and a clear plan, and they were able to recover the ball, utilising their speed against German defence, composed of four centre-backs because its sides are really central, and much slower than their opposition attacking players.

Germany lined up in a 1-4-3-3, with much interchanging of position between all the players, except the previously mentioned back four, playing quite short with remarkable support and mobility. To play that way you have to be very precise and not lose the ball, or you may find what happens is what was happening to Germany, with Algeria more dangerous than Germany with its counter attack quite organized.

The Germans were still playing an attacking game and only the good performance of goalkeeper Neuer ensured they kept a clean sheet. Of course the same could be said of Mbolhi, who made a couple of saves to keep his goal from being breached before the break.

Schurrle, scorer of the opener with his unorthodox kick at the start of extra time, came on at half time in place of Goetze, playing on the right as Germany tried to find a solution, meaning they started the second half with more intensity. But Algeria did not give up its counterattacking approach and still caused a few moments of excitement. The position of the Chelsea player on the right hand side of the German attack gave the German team more breadth and depth while giving more significance to their game.

We have some notes to consider. On sixty-nine minutes the injured Khedira had to be replaced by Mustafi, the latter occupying his natural position in midfield with Lahm moving to right back.

Another good Mbolhi intervention kept his team in the game after 80 minutes. Although Germany had tightened up, Algeria chances came and caused concern quite frequently. The duel was still on and the intensity began to take its toll on some of the notable players’ passing.

Despite the excitement and both teams creating chances throughout the contest, the game was scoreless at the end of regulation time. This was in large part down not only to the great contribution of the Algerian goalkeeper, but also his opposite number Neuer in the German goal,whose advanced position at all times saved his team on more than one occasion and allowed the to play an additional 30 minutes.

At the very beginning of extra time a loose ball in midfield by the Algerian defence allowed a fast counterattack from the German team, culminating in a somewhat fortunate shot from Schurrle, making the score one-nil.

The game opened up after this with Algeria moving forward more looking for the equalizer, leaving more space for the German attackers, who began to have more time to find the right pass and therefore create more danger.

It is only to be expected at the end of the season and in these conditions that fatigue takes its toll on players and that substitutions have to be made for injuries or muscle cramps in every game. Therefore, players who come off the bench, as might be the case with Shürrle and Khedira, give energy, strength and balance to your side and can make a difference.

With Algeria wide open and exhausted Ozil scored the second for Germany and it looked like that would be the final score. Not quite, because a goal in the last minute from Djabou ensured there would be excitement until the last second and kept Algeria’s hopes alive. Once again a team leaves the World but as a credit to all who follow them, Algeria. Congratulations to all the members of this team who have been an example to all.

Argentina, 'in extremis'

More of the same in this knockout. Argentina also needed extra time to settle their tie against a wilful Switzerland, who did not make it exactly easy. Angel Di Maria was worth his weight in gold in extra time, giving 'Albiceleste' options as time was running out and doubts were becoming reality.

There was little to say about the first half to be fair if we are not enthusiastic about everything in football. Just some set pieces with some luster, a corner from Switzerland, passed from Shaqiri to Xhaka whose shot requires a save from Romero, or a sideways pass that looked like it could become an assist. But everything counts.

Even Switzerland’s clearest chance, which fell to Drmic with Romero unsure whether to stay on his line or not, ended with the Swiss player hitting the ball into the goalkeeper's hands when it seemed that the move had much more promise.

Messi played behind the forwards in an area that, logically, must be well populated with players. Furthermore, the lack of breadth of the Argentine attack seemed to facilitate the defence of the central areas by the Swiss midfield. The Argentine system always gives superiority inside but if you have no width that space inside can be simply defended. The first half soon passed into history and, unsurprisingly in view of the above, ended nil-nil.

As we entered the second half we saw something less surprising, more to be expected. A well timed long ball from the South American defence, seeking to make use of Lavezzi’s tremendous pace, ends in an Argentina corner. From there, both teams seem to come to life and we finally see some action that leads to danger at both ends.

Rojo starts to make more moves down the left and sends in some crosses that start to cast doubt in the minds of the Swiss defence, requiring some urgent intervention from their goalkeeper. Another Rojo cross finds Higuaín who finds the space for a dangerous header threatening the Swiss goal. After 65 minutes, Ottmar Hitzfeld reacts and makes his change. Fernandes replaces Xhaka, to protect a right-hand side where the opponents have started to bite.The ‘Albiceleste’ decide to penetrate the other side now and Zabaleta starts getting behind 'enemy lines', creating danger with his crosses.

Palacio comes on for Lavezzi (74mins) and finds Messi’s head in the area with a good cross. Argentina still have the ball, and although they lack some speed of movement they continue to harass the opponent's goal. Both teams tightenup as the end of the match draws near but fatigue starts to appear and does not help the game as errors abound. The consequence of all this is that the game ends goalless leaving us hoping that extra time brings us more.

If it wasn’t easy to work out how Argentina would find the goal, it was even more difficult to guess how the Swiss side could do so. With so few chances being created it seemed inevitable that any goal would be subject to an unexpected defensive mistake or an individual player’s difference. Switzerland were closing well and their opponent was moving the ball around slowly. Fatigue was opening the game up and the counter-attacks were coming more frequently.

Sabella looked to change something and to introduce some energy for the final minutes, bringing Biglia and Basanta on in close succession. Di Maria goes to the right and Messi can be seen between the lines, but that area is congested and not easy to find the way to goal. Switzerland bring Dzemaili into the action, putting him on the left which gives freedom to Shaqiri for a role in the centre.

Just as it seemed we were doomed to another penalty shootout, Argentina win the ball back allowing Messi to face the Swiss defence and pass to Di Maria, who shoots left-footed from the right and to score the only goal of the game. Minutes later Dzemaili's header almost levels the tie but hits the post, making for an exciting final few minutes, with Benaglio playing centre forward and Di Maria trying to score into his empty goal. A free kick on the edge of the area in stoppage time was a last chance for Switzerland to tie the game but Shaqiri’s attempt hit the wall leaving Argentina qualified for the second round. That’s football.

Belgium too

The Belgians and Americans also joined in this fashion of extended matches and added drama. A great kickoff from Belgium saw them regain the ball for a counter attack that ended with a shot from Origi, whilst the Americans also began with intense pressing and ​​quick first touch football.

The European team started with their classic 1-4-2-3-1 and settled on a variant of the same technique, because the three midfielders constantly swapped positions and could be a midfield three in many phases (1-4-3-3). After twenty minutes, the trend remained the same, Belgium taking advantage of its attacking quality to create danger or start their attacks, while the U.S., each time it regained possession, was planted in front of the Belgian defensive line looking for that decisive final pass.

The first half featured one on one plays to the by line, while the entry of Yedlin for USA added more speed and danger to the right-hand side. Ultimately, the game came to a pause at half time in the middle of an entertaining spectacle that could be tilted to either side at any moment.

Perhaps this is why Belgium came out attacking in the second half,making it harder for the Americans to counter-attack, with the US having to defend far more. A Vertonghen cross that Origi fails to finish, a header off the bar from Origi and a De Bruyne shot saved by Howard are the proof. Another opportunity falls to Mertens, in move started by Origi, just before the Napoli winger was replaced by Mirallas, who is also deployed on the right hand side.

When the 'Reds' have to defend, Fellaini plays as a central midfielder with Witsel and as there is the possibility of a cross from the by line, he joins De Bruyne to balance the team. For its part, the American group begins to have trouble keeping pace with the front and Belgium are regularly getting into their area. Zusi leaves the field in place of Wondolowski to give some aerial support to the team, after 71 minutes. For a time it looks like the US can surprise the Belgian defence, but Hazard wins the ball back and launches a counter that almost ends in a goal for Mirallas, stopped by good intervention from Howard.

The game remains open. Hazard counterattacks USA. Belgium recovers and counters, there’s a corner, and a rebound... Then comes a chance for Van Buyten, a header, from a corner kick. The game continues end to end, although the European side creates chances for more often than its opponent.

Then comes a substitution, Origi making way for Lukaku, with a tactical adjustment that sees Hazard moved to the centre and De Bruyne to the left. In his first play Lukaku uses his strength to lose his marker and passes to De Bruyne, who turns very well and shoots to score the opening goal for his team. With the U.S. team focussed on attack, a new counter allows Lukaku himself to make it two-nil and to begin the second period of extra time with a significant advantage. Klinsmann decides to make a change, young Green replacing Bedoya, and the change turns out to be perfect, he scores a goal which motivates his side who now seemed destined to get another goal. Another occasion for Americans and more tension in the Belgian side, then Lukaku could not finish when one-on-one with Howard, who calmly stayed on his feet and prevented the likely third goal Belgium. More changes. Chadlion for Hazard, as Belgium looked for more power for the final minutes. It counted for little, the two teams already camped with the majority in the Belgian area and three or four players in the rest of the field.

A great free kick again tested the Belgian keeper but Courtois again showed his excellence as one of the stars of this World Cup rounding off a huge season.

The US continued to harass the Belgian defence, led by captain Dempsey, their opponents defended 'as they could' keeping men back without much organisation.

Again, a team, in this case Belgium, reaches the quarter-finals after much suffering. They were superior, agreed, but until the end the result was uncertain and everyone who watched the game enjoyed by it. Congratulations to both teams for their parts in a great game.

Having said that and summarise all the above, the eight teams who finished the first phase as champions of their respective groups are vying for the quarter-finals and this is how they will line up: Brazil (Group A) against Colombia (C), Netherlands (B) to Costa Rica (D) France (E) against Germany (G) and Argentina (F) vs. Belgium (H). Interesting, isn’t it? That's it.