Lévy Flight: Football teams seem to follow a certain mathematical rule without realizing it

There is a lot to disappoint here. The team from the Okinawa Institute of Science and Technology (Oist) in Japan was interested in Lévy walks and whether they are applying for teams who play a football game. The Lévy Walk or the Lévy flight is a mathematical description of the path of the objects (or in this case, football player), which are characterized by a group of short steps and suddenly long steps in between.

“Lévy Walk is a kind of random walk, although his main feature is that the distribution of the step lengths comes from a scaling-free (performance law) distribution,” explains the team in his paper. “Particles that have Lévy Walk dynamics manifest a super diffuse behavior that spreads faster than Brownscher hikers. The resulting trajectory has fractal properties, with clusters of short steps interspersed with much longer sprints.”

The walks can be seen in a bizarre number of systems, from the microscopic to those of animals that are looking for prey.

“They were seen in the molecular machines that during the intracellular trade, in the movement patterns of T cells within the brain, in DNA, in some mollusks, insects, fishing, birds and mammals, in air, in the Aire flights and in the collective movements of some animal groups, in the air, in which the topic immerse.” Walks are also recognizable in trace fossils (ichnofossils), the stored form of traces made by organisms that occupied about 252-66 million years ago. “

While nobody is really sure what different systems cause to carry out these walks in all areas they absorb, they seem to be advantageous. For example, living organisms can provide the optimal strategy to search for resources such as food, the exploitation of resources nearby (cluster of short steps) and explore potential new resources (the long step).

“Football is a game of resource shortage: to win, a team needs the ball possession of the ball, and there is only one ball in the game,” said Professor Tom Froese, senior author of the study and leader of the embodied cognitive science of Cognitive Science at Oist.

“And so it makes sense for individual players to move so that exploration and exploitation compensate for and ensure that they do not stay in the same place for too long and at the same time increase their chances of bringing the ball at every point. We have found that the teams as a whole act the same way.”

The Lévy Walk was of course seen when they actively searched for the ball. Strangely enough, further analyzes showed that the team seemed to behave like a single unit.

“We found through statistical tests that when hunting the ball Lévy Walk, we showed – similar to animals looking for food. As soon as they got the ball, they from Lévy Walk, possibly due to the restrictions on the interaction with the ball,” added Ivan Shpurov, first author and PhD student in the unit. “We saw the same behavior in the center of the team – the average position of all players – that indicates that the teams act as an individual agent when they have the ball.”

https://www.youtube.com/watch?v=3dyaqi-qarc

^{The player movement was followed in an undressed YouTube video.}

The analysis dealt with teams in the Japanese football league, J-League, and followed the position of each player up to the centimeter and how close they (and the average position of the team) were on the ball. They found that individual players who showed a more pronounced Lévy walk were both closer to both the average team position and the ball themselves.

“Although we cannot conclude that Lévy Walk is the trademark of a good football player, it indicates that players who exhibit Lévy Walk Movement are more active and generally closer to the ball and better contribute to team dynamics,” added Shpurov.

Although the teams such as animals or particles seemed to be behaved in a turbulent liquid, the team emphasizes that football behavior is more complicated. Nevertheless, it is fascinating that they seem to follow this pattern without being aware of this specific mathematical rule.

“A soccer team is a company that has a goal and can pursue it by changing its behavior both during the game and beforehand in the training process,” concludes the team. “Then it is no surprise that the movement strategy that the 'Team Self' adapts to optimize its performance has statistical properties with the movement strategies assumed by individual self, which experience similar environmental prints.”

The study is published in the magazine complexity.