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.
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.
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).
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.
¿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.
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.
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.
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.