Natural selection has shaped a whole range of different animal groups, from V-like formations of geese to circular mills of schooling fish. These shapes are the result of millions of years of evolution. Animals that hold their formation survive and those that don’t follow the group die out, either left behind or picked off by predators.
The same type of selection acts on formations in team sports. Over the years, if a formation works and the players win, then other teams adopt it. If the formation fails and the team loses then the manager is sacked and new tactics are used. This type of selection occurs much more rapidly in sport than in nature. In football, we can trace it over the last 100 years. And the changes have been dramatic.
In the visualisation below you can step through some of the key successful football formations from 1872 to 2012 (Click here to see the visualisation in its own window). We start with the first ever International, a 1-1 draw between England and Scotland. And we end with the World Cup and Euro 2012 winning Spain team.
There is a rich footballing history to be seen here. There is the Hungary team of 1956, who showed England that football was about passing beauty and not just strength on the ball. There is the Italy team of 1982 who, by adopting the defence that evolved from the Inter Milan 'net' of 15 years earlier, beat Brazil 3-2. Zico called this match “the day football died”, and it certainly was the death of their 4-2-2-2 formation. We can also see the famous total football structure of Ajax, and the 4-2-4 and 4-4-2 of European champions, Celtic and Liverpool. There is the defensive, “long ball” football of Norway, which stopped England qualifying for the World Cup in 1992. And there is, of course, the Tika-Taka Barcelona side that gave Alex Ferguson’s team a “hiding” in 2011.
The formations displayed above are adapted from Jonathon Wilson’s excellent book, ‘Inverting the Pyramid’. He gives a detailed account of the background and development of tactics over these years and it is a wonderful read for anyone who wants to know more about how football has changed over the years.
The question I look at now is how the overall structure has changed over time. Wilson’s idea is that a top-heavy pyramid has evolved to a stable bottom grounded shape. Overall this is a good analogy. Below I plot how the average position of players has changed over the years. In 1872 most players were forwards, but this has declined over the years, to reach its current equilibrium in midfield.
At the same time the attacking width ofteams has decreased on average, while the width at the back has increased. There is however quite a lot of variation, with some teams using wide attacking players, with others relying on the defenders to provide width.
There is probably no single stable formation. If one team adopts wide forwards, it can benefit the other team to play down the middle. Many of the great tactical battles over the last 50 years have pitted different formations against each other. No single formation is always better.
Finally, in the visualisation I calculate the minimum spanning tree connecting all the players. This tree connects all players together using the shortest possible path. In the 1870s the players were connected in one long loop. But since the Uruguay team of the 1930s key defenders and midfielders provide connecting junctions that link between defence and attack. These are often the most celebrated players in a team, like Iniesta and Mascherano in Barcelona 2011, and Viera and Zidane in France 2000.
There is a lot more to a successful football team than how its formation is drawn out on a chalkboard. Now that the positions and movements of players in the top leagues are automatically tracked to produce heat maps of their positions, it is possible to measure how formations change in response to the opposition in real time. This tracking data is collected and studied by clubs, but I do wonder whether they really are exploiting the rich mathematical tools that could be used to look at football tactics? There is a lot more that could be done in football analytics.
Much of the recent research by our group has looked at dynamic formations in fish and birds, and revealed rich patterns in how individuals interact. It would be interesting to do the same to football teams. Premier league clubs (as long as you are Liverpool!) are welcome to contact me to find out what we can do to help your team's formation.
Text and visualisation: David Sumpter
Artistic design: Elise Sumpter
Data source: Inverting the Pyramid by Jonathon Wilson