Soccermatics — Luck, Structure and Magic (concept review)

Jorge Mendoza Rivilla
3 min readJun 30, 2023

When I started with the football analytical a person that inspired me was David Sumpter through “Friends of Tracking”. David is a professor of applied mathematics, co-founder of Twelve Football, and writer of the amazing book Soccermatics.

The book could not have had a better quote on the cover than “Mathematical Adventures in the Beautiful Game”. In this note, I summarize the first part “On the pitch” which contains five chapters. Each chapter has at least one concept that can help your analytical roadmap.

Histograms

David makes constant use of histograms to explain data distributions and help group numbers into ranges.

The histogram is similar to a bar chart but for continuous data like weight, height, goals, etc.

The X-axis always contains range values and the height of each bar shows how many fall into each range.

source: soccermatics

Poisson Distribution

The Poisson Distribution is a probability distribution that is used to show how many times an event is likely to occur over a specific period. This kind of distribution arises whenever the timing of previous events has no effect on future events. (Sumpter, David).

The histogram of goals during the Premier League season 2012/13 (histogram boxes) compared to the Poisson distribution (solid line). source: soccermatics

Geometry and networks

The chapter “How Slime Moulds Built Barcelona” describes how Pep Guardiola used mathematics and position in the ‘Tiki-taka’.

The FCB 2010/2011 tactic shows a triangle through passes networks. The next picture show as you take any player in the team and rotate them through 360° you can see that they have nearby passing options in all directions. The triangles could solve problems related to connecting points.

FCB formation networks and triangles through passes networks. source: soccermatics

Flow Field

¿How should a defensive player move to intercept a pass? The Flow-field helps us to know how to defender should move. The vector fields in the picture show the defender’s movement depending on her current position.

Two ‘attackers’ stand on opposite sides of a square and pass the ball to each other, while one ‘defender’ in the middle tries to intercept the ball. The arrows show how the defender should move, depending on her current position. If she is near the player with the ball she should try to block. Otherwise, she should run towards the receiver and try to intercept. source: soccermatics

To create opportunities movement and positioning are important in football. Andrea Pirlo through his ability to pass the ball and stay in the perfectly placed to deliver a pass forward is the prime example.

The heat map and flow field of his passes during the game. The shading indicates the place on the pitch where Pirlo made passes from. We can see that Pirlo made a lot of passes from near or just behind the halfway line, usually from the middle of the pitch. The arrows indicate the general direction of Pirlo’s passes made from various positions. These arrows are not the actual passes themselves, which were sometimes long passes from one side of the pitch to the opposite wing, and sometimes short passes to nearby team-mates. The arrows are instead a statistical fit that give a general picture of the direction in which Pirlo tends to move the ball, and from where. source: soccermatics

Extreme value distributions

Extreme value distributions are the limiting distributions for the minimum or the maximum of a very large collection of random observations from the same arbitrary distribution.

Histogram of number of goals scored by the winners of the Pichichi Trophy between 1986/87 and 2013/14 (boxes) compared to the extreme-value distribution (solid line). source: soccermatics

Newton’s equations

The Zlatan goal vs England was a famous shoot for the distance and the acrobatics. Zlatan rotate his body vertically through 180°, meeting the ball in a bicycle kick and lobbing it over Joe Hart’s head from more than 25 metres.

The main force involved is gravity, and the path of the ball can be worked out with the aid of Newton’s equations of motion.

The trajectory of Zlatan Ibrahimovic´’s bicycle lob, according to Newtonian physics. source: soccermatics

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Jorge Mendoza Rivilla

Data Analytics | Management | Football Analytical | AI | I Write to Understand