Natural selection has shaped many different animal groups, from V-like formations of bird flocks 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.
Animal groups have evolved over millions of years, making it difficult for scientists to observe how their formations have changed. We can trace the physical structure of animal bodies back through the fossil record, but the social structure of groups is lost in time.
Fortunately, there are other settings where we can see social evolution in action. One of these is 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.
To help us analyse these formations, we developed a visualisation of the key successful football formations from 1872 to 2012. We start with the first ever official international, a 0-0 draw between Scotland and England. And we end with the World Cup 2010 and Euro 2012 winning Spain team.
There is a rich footballing history to be seen in these formations. The Hungary team of 1956, who showed England that football was about passing beauty and not just strength on the ball. The Italy team of 1982 evolved a defence from Inter Milan’s “net” of 15 years earlier. They used it to beat Brazil 3-2 in a match Zico called “the day football died”. 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 helped stop England qualifying for the 1994 World Cup. And there is, of course, the tika-taka Barcelona side that gave Alex Ferguson’s Manchester United a “hiding” in 2011.
What evolutionary changes can we see in these formations? In his excellent book, Inverting the Pyramid, Jonathan Wilson describes how a top-heavy pyramid has evolved to a stable bottom grounded shape. Overall this is a good analogy. The average position of players has moved steadily backward. In 1872 most players were forwards, but this has declined to reach its current equilibrium somewhere in midfield. At the same time the attacking width of teams has decreased on average, while the width at the back has increased.
I also show the minimum spanning tree connecting all the players together using the shortest possible path (these can be seen in the visualisation by pressing the space bar). 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 some of the most celebrated players in a team, such as Iniesta in Barcelona 2011.
To understand the shape, structure and connections of football teams, I have used a few mathematical tools. These tools were originally developed to study the evolution of animal groups.
Football can act as an inspiration for many of us studying animal groups. Not only can we study how tactics evolve over the years, but modern tracking technology allows us to watch how formations change in real time. The positions and movements of players in the top leagues are automatically tracked to produce heat maps of their positions.
But I believe that football also has something to learn from us. While tracking data is collected and studied by clubs and TV stations, their analysis remains at a rather basic level. Compared to recent aerodynamic analysis of geese flight and the velocity fields of schooling fish, passing statistics and arrows showing the direction of corners seem a bit limited.
This is the reason that research in collective animal behaviour continues to grow: the data analysis techniques we are developing can be useful in everything from the study of cell motion to team sports. It is interdisciplinary research that has genuinely connected many different disciplines. I wouldn’t be surprised if next season Premier League clubs start hiring mathematical biologists to help evolve their tactics.