Just like in our physical world around us, our beautiful game is based on geometry and just like the physical world, the shapes that are created by football are disguised by our inability to see the deep aspect of football, or profundus.
With such a huge amount of our attention invested on the actual ball, we miss the shapes that would seem obvious to a coach or one who is looking for them.
Such shapes are created by the relationship of players to each other, the relation between the ball’s position on the pitch to the position of the players, and of the ball’s movement on the pitch. It is these shapes which occur thousands of times in a single game and are the ones which spectators are oblivious too.
Quite often, the only time a spectator (especially a spectator who is not at the ground) will be prompted to notice these patterns when they are pointed out by the commentator. Even then, the average spectator will soon forget about these patterns and resume their narrow-sighted attention on the ball and not much around it.
So why does it seem so difficult to concentrate on these patterns? It is because they are so complex.
If we have a look at a 4-3-3 formation – the most fantasised of triangulated formations – it is clear to see what’s on offer in terms of the potential passing routes. Graphically, there is a potential to have every player to be part of at least one positional triangle in relation to his teammates.
Since this is the case, it is also possible for the ball to make a triangle on the pitch in three passes with three players. Another option is for only two players to complete the triangle if one of them moves to compensate for the third player not being there.
Furthermore, there are thousands of possible combinations of passes that the players can make and the path that the ball can travel. It is these possibilities which people tend to associate with possession football.
The next question we must ask is whether this association between triangular spacing and possession is in fact a correct one. To answer this question, we can look at the actual geometry to reveal the answer.
Firstly, ask yourself this: can you create a shape on the pitch, other than a triangle, using only three players? The answer is no. The only way you can position three players on the pitch without forming a triangle of some sort is by placing them in a straight line.
In football, straight lines are the enemy of footballers because this is the worst type of spacing that three players can make. The reason is because only one player in this line has the option of passing the ball to both his teammates, assuming that there are no defenders in between.
The players on either side of him can only pass to the teammate in the middle. The only way that a player at the end of the line can pass to the other end of the line is by chipping the ball in the air or curving the ball around the middle player. This is bad for accuracy and requires greater skill to perform, thus reducing the efficiency and probability of a successful pass.
To sum up – only one of the three players has the option to pass to the other two player, while two players can only pass to a single teammate.
This nicely leads to the principle of triangulation, or, spacing players such that they form the triangle shape.
The first thing to note about a triangle is that a triangle cannot, by the law of physics/mathematics/geometry, exist on a flat plane (the playing surface) without having some sort of latitudinal and longitudinal spacing.
In other words, at least one of the points of the triangle must have at least one of either horizontal deviation or vertical deviation. If this does not happen, the three points would essentially be in a straight line.
If you still don’t understand, try thinking of it like this. Imagine that you draw two points on a paper (the paper represents the football field). If you connect these two dots with a line, you will have a straight line between the dots. Now extend this line so that it goes beyond the dot. Now draw another dot on the extended part of the line.
You should now have three dots on a single straight line. Because you drew the last dot on the extended line, you still have a straight line and not a triangle. However, if you drew the third dot off-centre from the extended line, you have created a triangle because you have deviated the last point so that it is no longer directly in line with the first two dots.
Think about it, to deviate the third dot off-centre from the straight line, you either moved the dot left, right, up or down. That, essentially, is what I mean by latitudinal and longitudinal spacing.
Now that we understand a basic property of a triangle, we can now explore how triangles make it easier for a team to keep possession.
Before we do so, we must firstly understand a basic requirement that allows a team to keep possession. This requirement is teammates for the ball possessor to pass to.
If a player with the ball has zero available teammates to pass the ball to, it is virtually impossible to keep possession of the ball. Triangulation helps to solve this problem by utilising a brilliant geometrical property of the triangle- the hypotenuse.
The hypotenuse is a property of the right-angle triangle and it is the key as to why triangles are so effective to keep possession. It has to do with distance.
If we imagine a right-angle triangle, we know that the hypotenuse is the longest of the three sides. If we had three players who formed a right-angle triangle on the pitch, the two players who are stationed on either end of the hypotenuse will have the longest pass to each other in terms of distance. The other two possible passes are both shorter in distance.
This means that a defender would have more distance to run along the hypotenuse and less distance to run along the other two sides.
This has important implications for football, because if we can figure how to manipulate the triangle so that we can make more use of the longer hypotenuse and less use of the shorter sides, possession football will become easier because the opponents would have to cover more ground to reach the player with the ball and his teammates.
This effectively means extra space is created for the team in possession and consequently increases the time they have to make correct passing decisions and makes it easier for his teammates to find space to receive passes.
The way to achieve this is to ensure that no two consecutive players are on the same longitude or latitude as each other – i.e. no player is directly vertical or horizontal to his nearest teammate.
What this does is create triangles, which maximise the distances between each point of the triangle. In effect, it creates triangles entirely made up of hypotenuses. The knock on effect of this is that, since the distances are maximised by utilising both vertical and horizontal spacing, it is harder for the defending team to intercept passes, close down opponents with the ball, and mark the players without it.
The other effect it has is spacing the players of the defending team away from each other so that they cannot keep a compact shape or press in numbers. This reduces more of the game to one on one battles and favours the team who has better technique and tactical organisation to pass the ball and keep possession.
All these favourable outcomes are due to the triangle, and cannot be achieved with any other shape.
As triangles are crucial to the design and construction of real world structures, such as buildings and bridges, so too are they crucial in the design of a football team. When you hear a comment such as “passing in nice triangles” in reference to a nice piece of passing by a team, they are referring to the concept of triangulation.
Even though people tend to ignore the deep analysis of geometry to explain why triangles are so important in football, they are nevertheless correct in making the connection between triangles and effective possession.
Perhaps the team currently most famous for the use of triangles is Barcelona. One term which sums up perfectly this style of play is ‘strangulation by triangulation’. When you have players such as Messi, Xavi and Iniesta playing in triangles across the whole field, it makes for a lethal combination.
In the end, triangles in football are not just something that is thrown around by managers and the media when referring to possession. It is a fundamental geometrical part of football, something which makes football beautiful.
Just like the most famous artists, the brightest mathematicians and the engineers of this world use triangles to create and innovate new methods, styles and discoveries, so too does football.
When we start to truly look for the profundus, the deep side of football, we can truly appreciate how important and fundamental the hidden world of geometry is to football. Perhaps it is only appropriate to label the humble triangle as the the most famous shape in football.
Pavesh
Guest
An article written 6 years ago is coming in handy. I'm an aspiring coach and a Cryuffian. Although I understood the importance of triangulation, this article has given me a better perspective. I also thought it would have been nice if you had also highlighted the importance of a versatile number 6 and their ability to pass and read the game. Anyway, keep up the good work. Cheers!
Feras
Roar Rookie
Thank you. "Thinking" is something which we as a football nation are lacking.
Feras
Roar Rookie
Name a time and a place haha. Thank you.
Feras
Roar Rookie
Once again, I need to clarify. I never said you need a PhD to create a great football team. That's because triangulation occurs naturally in every game. You do not need to tell the players what it is and how to perform it, simply because the players automatically perform it without realising it. The whole point of my article was to explain the geometry behind it, and why it helps a team keep possession of the ball. It's an article for curiosity, not a thesis which you must learn and remember. By the way, if you have more of the ball, you will have more opportunities to score a goal using 3 passess or less. Possession is fundamental.
Feras
Roar Rookie
Of course you could get triangles playing a 442. I am not saying 433 is automatically better than 442. I wrote the article to try and give the reasons why triangles are important in football. I try to explain how correct spacing is acheived. I simply made the comparison between the 442 and 433 to for simplicity. You could use any two formations really, and find weaknesses and strengths in each. Lastly, this fear of going into the deep analysis of movement and pattern is why Australia are lagging behind the top nations. Football is more complicated than you think. Do you think Marcelo Bielsa would say "this is precisely why we shouldn't let people loose on whiteboards to draw diagrams"? No. Neither would Pep, Jose etc. Appreciate your comment nonetheless even if I don't agree with your points.
Ian Whitchurch
Guest
The use of a 'high' defensive line to deny the opposition the space to play triangle games is an entire other article ;)
jbinnie
Guest
dasiva- I think Charlie Hughes may have got his 3 pass idea from a Russian who theorized that if every player in an attacking team did his job properly the ball could travel from the hands of the goalkeepere to the toes of a striker who could have a shot at goal. This sounds speculative but if the first pass goes to the RB. who in turn despatches it first time to his midfielder who sends his fast flank runner on his way, and he cuts the ball back to his striker. the ball has travelled 110 metres in 4 passes ie 25-30 metres a pass,not long by anyones standard. It must be remembered,to be successful, each of the players making a pass must have moved ,received, and sent the ball perfectly. A theory,yes but not impossible.jb
dasilva
Roar Guru
I think I remember reading about Manchester United "4-4-2" in the 90's Is it 4-4-2 or is it 4-2-3-1 or is it 4-4-1-1 it depends on perspective. Manchester United 4-4-2 was asymmetric (with cantona behind the striker) and it resulted in sufficient triangles being created
dasilva
Roar Guru
Actually the stats is 80% i believe However there is this rebuttal "Charles Hughes, who unfortunately was made Technical Director of the Football Association, analysed 100 matches and concluded that 80 percent of goals come from three or less passes. On the surface of it, this appears to support getting the ball forward quickly, but his deeply flawed analysis fails to properly account for another statistic – that 91.5 percent of moves consist of three or less passes, which actually means that there is an 11.5 percent shortfall in the number of goals that should be scored." The idea that when teams implement a multipass moves they are more likely to score than a move with 3 or less pass. It just so happens that teams attempt a 3 or less pass move a lot more often that creates this statistic
TC
Guest
The manager will be concerned with the macro and the micro. Much of his training schedule is dedicated towards the micro: muscle memory. Patterns that can be followed intuitively on the pitch in real game time will emerge from this: a bit of micro and a bit of macro there. Team meetings will substantially be about the macro (although plenty there at the micro level as well, who is standing who at set pieces, etc.) This is one thing I can promise everyone: if those team meetings are going for too much longer than half an hour, most of those players will be asleep. Sir Alex Ferguson famously keeps his team meetings short, if he has them at all. He would usually not invite Becks to them, because he had one simple instruction for him: if you have a free kick inside 35 yards, have a ping. TC
TC
Guest
For mine, it comes down to the reality and practicality of winning the 3 points, versus some idealistic, theoretical pursuit of perfection which seems to have an objective altogether quite different from winning the 3 points. There is no more efficient and productive triangle in the world than the quick interplay between a wide mid and full back that allows the full back to overlap, collect the ball at pace and get behind the defence to plonk that mother on the head of a 6ft 3 centre-forward who plants the ball in the back of the net. Efficient ball use, accurate ball use, outcome: goal and likely 3 points (especially if you can repeat the dose). TC
dasilva
Roar Guru
"pretending that you need a PhD to form a rock band." Good story on that Not A Second Time by The Beatles was praised by Mann "“…so natural is the Aeolian cadence at the end of “Not a second time”" lennon response years after "To this day, I have no idea what [Aeolian cadences] are. They sound like exotic birds." It's like going through the theory of the pentatonic scale. It's nice to know but people have been singing the pentatonic scale throughout every culture before language even been development. People naturally know the pentatonic scale without knowing the theoretical basis behind it. I guess your point is that footballers form triangtles without knowing the theoretical basis behind it. In any case, even if it is something that fans or even players don't need to naturally know or consciously think about It's something essential for managers to know about and devise systems and movements from players to maximise the usage of triangles
Minister for Information for the Democratic People's Republic of Football
Guest
I think we agree this time Cat. Was chuckling while I was reading it. I think the author wears a white coat and owns a Rubick's Cube. Here's my 5 cents worth on shortening this whole article: 1. Players without the ball make runs to entice the player with the ball to pass 2. Player with the ball has composure on the ball to see other players making runs and passes accordingly Alternate option: 1. Skillful player takes opposition player on ,beats him, and thus draws in others trying to stop him. 2. Spaces are created by this for skillful player's teamates. Then skillful player release ball to said teamates. Just a couple of options. Triangle Tiki-Taka only looks good when you have Barca's line-up at your disposal. One touch footballl is getting harder and harder to watch. Bring back the players who want the ball at their feet. While in theory the article may have valid points but spare me the maths lesson!
TC
Guest
Your diagrams are precisely why I thought you were having a laugh with this article. Firstly, for anyone to start equating various formations with or without an increased capacity to create triangles is an extremely naive asssessment of formations. Secondly, (almost to prove point number one above), you have actually offered up an asymmetrical 433 for you to draw in your nice little trangles. Well guess what, every single formation that goes out there in any given game, is going to have at least some component of asymmetry attached to it (otherwise, the manager is not doing his job). So you are comparing an asymmetrical 433 with a flush 442 - a bit of an unfair contest don't you think? For starters, even in the flush 442, there are plenty of additional triangles you could have thrown in, and for someone so enamoured by triangles, it's unusual you didn't draw them in. But the key point is this: make the 442 assymetrical, much as you made the 433 assymetrical (because in the modern game, that's precisely the way it would pan out), and presto, you have as many triangles as you would like. This is precisely why we shouldn't let people loose on whiteboards to draw diagrams. TC
Midfielder
Guest
Feras Great read would love to sit and have a coffee or beer ... have enjoyed reading your article and the posts...
TC
Guest
Titus of course the idea of triangles is fundamental - that's the point!! Kids all over the world are learning to pass in triangles before they can even talk properly - but it's this over-egging the pudding I am talking about. Anyway, I'm big on statistics: over 60% of all goals are scored from sequences involving 3 or less passes, i.e. forget triangles (plural) - but get one triangle right, first time, when it's there and opportunity is knocking - that's the one great skill all players need to develop. But passing it around in triangles as a mantra - that's just kids' stuff. TC
Qantas supports Australian Football
Guest
Really good article and one for the kids to read and try to understand. Who actually plays a straight back four these days? No one! (only the British mentality). I would much prefer for commentators to call a defence as having three at the back with two central defending sweepers; 2 - 3 - and in the attacking midfield to the front line a formation that perfectly illustrates what actually happens when great teams like Barcelona actually take the field. - 2 - 3 or for another description tika-taka (triangle) football..
Titus
Guest
Pick the AFL fan, straight up the guts, put it in the mixer and bang it through the posts. While the article is too much for me to bother reading entirely unless you pay me or give me qualifications at the end, the idea of triangles in football is a fundamental skill, and one of the elements that gives the game its aesthetic qualities. One touch passing working in triangles, moving and stretching the opposition and releasing a man into space with a perfectly weighted and angled through balls is one of the most beautiful things in sport and the basic premise of the article is a good one.
TC
Guest
I'm with Towser here - what a load of gobbledygook. It's a bit like pretending that you need a PhD to form a rock band. This is straight out of the Fos book of mantras: You need multiple masters degrees to understand the game. All evidence is to the contrary. Starving, illiterate people all over the world play the game with aplomb. There are kids in the Brazilan favelas who can run rings round most. Try and talk to them about "triangulation" and they will mistake the tip for "strangulation". The most succesful managers in the world, like Sir Alex Ferguson, keep thinks ultra simple, and it's easy to understand why: more than 60% of all goals are scored from sequences involving 3 passes or less. Cornflakes scrambled the winning goal home the other night, it was because the Sth Koreans may have been thinking a bit too much about triangles, and not enough about basics, like allowing 5 Australians in the 6 yard box, with only 4 Korean defenders. I'll agree with one point - I too would like to hype the hypotenuse. There is no greater efficency and quicker route to goal than lifting that mother over a defensive line that has crept a few metres too far foward, straight along the hypenatuse, and allowing one or two of your players to latch on to it with only the keeper to beat. Like taking candy from a baby. TC
jbinnie
Guest
Towser - 99.9% of football fans are not thick as you describe but it would probably be correct to say that out of that total 90% have no coaching qualifications so have no real interest in picking out patterns, they are in fact "ball watchers".There is nothing derogatory in that description,after all the ball is where most of the action is but if you just refer to our great victory the other night in Korea,we won, but the Koreans were still far ahead of us in first touch control & movement off the ball.Personally I don't expect the normal fan to notice that, for just as a huge crowd roars every time their team wins a corner stats tell us only about 7% of goals come from corner kicks.Let us not lower the fan's excitement by lecturing them on tactics.OK. Cheere jb