 "Game theories")
SOCCERMATICS
MATHEMATICAL ADVENTURES IN THE BEAUTIFUL GAME
Author: David Sumpter
Publisher: Bloomsbury
Price: Rs 499
The author is a Professor of Applied Mathematics at Uppsala University, Sweden. He is an Englishman brought up in Scotland, a Liverpool fan, and self-confessedly a poor football player. His previous book was a treatise on Collective Animal Behaviour. It was well-received in academic circles. His wife, also a mathematician, is one of the few people to have won a football pool.
None of this explains why Soccermatics is the most fascinating book on football that I have read since the late Sir Terry Pratchett's Unseen Academicals (which wasn't quite about football). Sumpter says, "Mathematics can be used to understand football and football can help in understanding maths", which is true, of course.
This book demonstrates that it can be done in such a way as to keep both football fans and maths geeks happy. Each chapter takes some aspect of football, dissects it, and explains the mathematics involved in the dissection. It then zooms out to describe other real-life situations where similar thinking and maths models can apply. It is done with rigour and clarity but with a leavening of humour and a touch of the personal. Discussing tribalism for instance, he describes interactions between him (Liverpool fan) and his granddad (Everton fan) in a way that will resonate with East Bengal- Mohun Bagan families.
The "pure" football fans (who cannot count beyond 22) will relate to the diagrams. The ones who do enjoy maths will be impressed by the insights. Soccermatics makes few assumptions about prior knowledge. You need not understand or computational geometry or the offside rule - in fact, Sumpter avoids discussing the latter.
The book has brilliant graphics and diagrams but Steven Hawking's famous rule about every equation halving book sales has been ignored. While some equations are incorporated into the text, there is more in the footnotes (which are excellent).
There is a lovely chapter on formations. Back in 1872, England played a 1-2-7 formation against Scotland that played 2-2-6. This hyper-aggression (partly driven by the offside rule of the time) resulted in a goalless draw. Hungary played 5-1-4 in the 1950s, with the legendary Nandor Hidegkuti as a withdrawn centre-forward, who linked defence to attack and scored goals too. Brazil used to play 4-2-4, Barcelona plays 4-3-3, and Inter Milan, in the 1960s, was best described as 1-1-4-1-3.
The key to making any formation work is the "triangle of passes". Every player forms a triangle with the two others to whom he can pass to most easily. Those triangles and the interlinks between different triangles dictate how teams creates chances and how they must create space, and the zones players should occupy relative to each other.
One strength of tiki-taka for example, lay in the fact that Barca (and Spain) could equally, easily create triangles to left or right. The Catenaccio "net" started with those two Inter deep defenders creating triangles with the four midfielders. City-planners use graph theory to similarly link nodes on metro lines and bus routes. Incidentally, slime mould also grows in similar ways to exploit food sources.
The shutting down of space, or "zone minimisation", is of course, as important. There are elegant explanations of bow effective defence works, and of the optimal locations and movements of defenders. Bayern Munich successfully broke Barca's triangles in the 2013 Champions League semi-final by using "herding and hunting" methods reminiscent of lionesses working together to corral prey.
Readers may remember school experiments using iron filings to chart magnetic fields. Similar-looking flow fields can be charted (using high-speed GPS data) to discern passing styles and player movements, on/off ball. Some players have a left to left/right-right passing bias; others play across from right-to left. Those biases translate into team styles.
A playmaker like Andrea Pirlo is relatively static and passes from midfield, Bastian Schweinsteiger runs all over. A decentralised passing style like tiki-taka involves three or four players (Xabi Alonso, Xavi, Sergio Busquets, Andres Iniesta). It is less vulnerable to disruption than highly centralised Italy with its reliance on Pirlo.
The last few sections look at betting and offer a simple introduction to probability theory, odds and risk-reward. There is also a look at the incentives of the 3-point system ( teams attack more) and evolutionary "survival of the fittest" pressures on managers.
There is a brief section on extreme value distribution (EVD): Where do you place Messi's 50 goals in one La Liga season, or Usain Bolt's insane sprint records? EVD measuring methods are used in climate change. Crowd management is another field that has relevance well beyond football. Here, the author draws on his experience at understanding collective animal behaviour to compare how a school of fish responds to a predator, or how pigeons formations fly. Tribalism, and its ugly cousin, racism, are also examined.
The author points out that new technology ensures that every move of every player can be, and is now routinely mapped and recorded at higher levels. This means huge new data, which can yield new insights. For example, intriguingly, an analysis of split-second leads and lags in player movements off the ball may indicate which players are inspirational and which play "follow-the-leader" .
Better data collection now enables soccer to use maths modelling for scouting players. The 2014 Danish champions, FC Midtjlland (which is owned by a bookmaker!), has done this successfully. As "moneyballing" catches on in soccer, Sumpter is likely to be among those tapped. I'm sure he'll do a good job but let's hope his voice is never throttled by non-disclosure agreements. We need more intersectional books like this.
MATHEMATICAL ADVENTURES IN THE BEAUTIFUL GAME
Author: David Sumpter
Publisher: Bloomsbury
Price: Rs 499
The author is a Professor of Applied Mathematics at Uppsala University, Sweden. He is an Englishman brought up in Scotland, a Liverpool fan, and self-confessedly a poor football player. His previous book was a treatise on Collective Animal Behaviour. It was well-received in academic circles. His wife, also a mathematician, is one of the few people to have won a football pool.
None of this explains why Soccermatics is the most fascinating book on football that I have read since the late Sir Terry Pratchett's Unseen Academicals (which wasn't quite about football). Sumpter says, "Mathematics can be used to understand football and football can help in understanding maths", which is true, of course.
This book demonstrates that it can be done in such a way as to keep both football fans and maths geeks happy. Each chapter takes some aspect of football, dissects it, and explains the mathematics involved in the dissection. It then zooms out to describe other real-life situations where similar thinking and maths models can apply. It is done with rigour and clarity but with a leavening of humour and a touch of the personal. Discussing tribalism for instance, he describes interactions between him (Liverpool fan) and his granddad (Everton fan) in a way that will resonate with East Bengal- Mohun Bagan families.
The "pure" football fans (who cannot count beyond 22) will relate to the diagrams. The ones who do enjoy maths will be impressed by the insights. Soccermatics makes few assumptions about prior knowledge. You need not understand or computational geometry or the offside rule - in fact, Sumpter avoids discussing the latter.
The book has brilliant graphics and diagrams but Steven Hawking's famous rule about every equation halving book sales has been ignored. While some equations are incorporated into the text, there is more in the footnotes (which are excellent).
There is a lovely chapter on formations. Back in 1872, England played a 1-2-7 formation against Scotland that played 2-2-6. This hyper-aggression (partly driven by the offside rule of the time) resulted in a goalless draw. Hungary played 5-1-4 in the 1950s, with the legendary Nandor Hidegkuti as a withdrawn centre-forward, who linked defence to attack and scored goals too. Brazil used to play 4-2-4, Barcelona plays 4-3-3, and Inter Milan, in the 1960s, was best described as 1-1-4-1-3.
The key to making any formation work is the "triangle of passes". Every player forms a triangle with the two others to whom he can pass to most easily. Those triangles and the interlinks between different triangles dictate how teams creates chances and how they must create space, and the zones players should occupy relative to each other.
One strength of tiki-taka for example, lay in the fact that Barca (and Spain) could equally, easily create triangles to left or right. The Catenaccio "net" started with those two Inter deep defenders creating triangles with the four midfielders. City-planners use graph theory to similarly link nodes on metro lines and bus routes. Incidentally, slime mould also grows in similar ways to exploit food sources.
The shutting down of space, or "zone minimisation", is of course, as important. There are elegant explanations of bow effective defence works, and of the optimal locations and movements of defenders. Bayern Munich successfully broke Barca's triangles in the 2013 Champions League semi-final by using "herding and hunting" methods reminiscent of lionesses working together to corral prey.
Readers may remember school experiments using iron filings to chart magnetic fields. Similar-looking flow fields can be charted (using high-speed GPS data) to discern passing styles and player movements, on/off ball. Some players have a left to left/right-right passing bias; others play across from right-to left. Those biases translate into team styles.
A playmaker like Andrea Pirlo is relatively static and passes from midfield, Bastian Schweinsteiger runs all over. A decentralised passing style like tiki-taka involves three or four players (Xabi Alonso, Xavi, Sergio Busquets, Andres Iniesta). It is less vulnerable to disruption than highly centralised Italy with its reliance on Pirlo.
The last few sections look at betting and offer a simple introduction to probability theory, odds and risk-reward. There is also a look at the incentives of the 3-point system ( teams attack more) and evolutionary "survival of the fittest" pressures on managers.
There is a brief section on extreme value distribution (EVD): Where do you place Messi's 50 goals in one La Liga season, or Usain Bolt's insane sprint records? EVD measuring methods are used in climate change. Crowd management is another field that has relevance well beyond football. Here, the author draws on his experience at understanding collective animal behaviour to compare how a school of fish responds to a predator, or how pigeons formations fly. Tribalism, and its ugly cousin, racism, are also examined.
The author points out that new technology ensures that every move of every player can be, and is now routinely mapped and recorded at higher levels. This means huge new data, which can yield new insights. For example, intriguingly, an analysis of split-second leads and lags in player movements off the ball may indicate which players are inspirational and which play "follow-the-leader" .
Better data collection now enables soccer to use maths modelling for scouting players. The 2014 Danish champions, FC Midtjlland (which is owned by a bookmaker!), has done this successfully. As "moneyballing" catches on in soccer, Sumpter is likely to be among those tapped. I'm sure he'll do a good job but let's hope his voice is never throttled by non-disclosure agreements. We need more intersectional books like this.