Mathematical Thinking

# FIFA World Cup 2018: How math gives players an edge over opponents

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FIFA World Cup 2018 mania has certainly gripped the nation and the world – from cafeteria discussions to weekend catch ups. However, this article is bound to give you a perspective you’ve probably never read before!

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, itrequiresrhythm, coordination and balance. And at the same time, it also requires 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 lives. They instinctively understand the concepts of geometry, speed-distance-time, calculus which they utilizeto 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, givingthem 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:

Spain’s tiki-taka

A great example of real-time use of geometry to create space and beat defenders is the ‘tiki-taka’. This is a systematicapproach 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.

Goalkeeper’s charge

One of the most mathematically sound strategies used in distracting a 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 goalpost. The chip shot, which is a quite a player and fanfavorite among players, doesn’t require power, rather a deft touch which follows a perfect parabola into the net.

Saving penalties

Teams these days are aware about the past penalties taken by players. Most players follow a pattern in their penalty shots and this analysis of theprevious shots puts the keeper in a much better situation to predict the next shot.

Square goal posts vs Round posts

The goalposts we see noware circular and have an elliptical cross section. The goalposts before 1987 had the square cross section. Thisinvariably meant that most of the shots that hit the posts, came out instead of going in which brought unnecessary disappointment to the teams.

Analytics and statistics

While mathematics was initially used for strategizing the buying and theselling 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 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?