Football is often referred to as o jogo bonito, Portuguese for ‘The beautiful game’ – a nickname popularized by the Brazilian great Pelé. And rightly so. Just like any other beautiful movement, like say dance, it’s got rhythm, coordination and balance. And at the same time, it’s got skill. However, just being a master at dribbling, tackling, shooting or goalkeeping does not necessarily make you a great player.
Some of the best football players on field today are also terrific mathematicians, and believe it or not, they use mathematics in their daily life. They instinctively understand the concepts of geometry, speed-distance-time, calculus which is utilized to the fullest during the game. This is not determined by their ability to solve complex equations on a blackboard, but their intuitive understanding of the power of mathematics which gives them the edge over other players. Here’s the math behind some of the most common goal and defense tactics, which lends a method to the madness in this beautiful game:
A great example of real-time use of geometry to create space and beat defenders is the ‘tiki-taka’. This is a systems approach to football founded upon team unity and a comprehensive understanding in the geometry of space on a football field. The football players try to form triangles all around the pitch to maintain the ball possession, making it difficult for the opponent to obtain the ball and organize their game.
One of the most mathematically sound strategies to distract the striker is to create a larger obstruction to reduce the space available to score, hence lowering the probability of a goal. Often when a striker is in a one-on-one situation with the goalkeeper, the latter charges towards the striker rapidly to close the space thereby reducing the angle and space available to strike the ball.
Beating the goalkeeper’s charge
One of the most beautiful moves in football is chipping a charging goalkeeper. As the space reduces, the cool minded striker notices the increase in space to score. A 3-dimensional view allows the striker to kick over the charging goalkeeper’s head, and into the goal. The chip shot, which is a quite a player and fan favorite among players, doesn’t require power, rather a deft touch which follows a perfect parabola into the net.
Teams these days are aware about past penalties taken by players. Most players follow a pattern in their penalty shots and this analysis of previous shots puts the keeper in a much better situation to predict the next shot.
Square goal posts vs Round posts
The goalposts we see nowadays are circular and have an elliptical cross section. This suggestion was made as the goalposts before 1987 used to have a square cross section. Which invariably meant that most of the shots that hit the posts, came out instead of going in which brought unnecessary disappointment to the team.
Analytics and statistics
While mathematics was initially used for strategizing the buying and selling of players, it is now integrated to what it can also do on the tactical analysis of the game. Believe it or not, almost every football team today has a team of mathematicians or statisticians who help the head coach define strategies based on data. A huge amount of data is collected and analysed to understand opposing teams game-play, strengths and weaknesses of players to define tactics. E.g. if Barcelona’s Messi and Iniesta pass the ball 300 times to each other on an average, what kind of advantage can the opposition gain by reducing their total number of passes to 100?
Football is not just a game but a passion that unites millions of people across the globe. As a famous mathematician and Arsenal fan, Professor Marcus Du Sautoy, once said, “Those players who intuitively have a good sense of geometry and calculus, they’re the ones who will have the edge.” So which player do you think has the edge this World Cup?
(The author of the article is Manan Khurma – Founder & CEO, Cuemath)