Developing winning football tactics with Game Theory
I must confess that I am passionate football lover. When I mean football, I am not referring to American football — however, the methodology explained is applicable to American football.
My love for football started precisely in the year 2006. Prior to that time, my peers always made fun of me as I spent most of my TV time with cartoons. They laughed at me saying, I couldn’t comment on their conversations because I was too childish to understand how football works and they were not talking about cartoons. My TV time with cartoons was because it helped me build my imaginative prowess, as cartoons sometimes showed what was impossible in real world as possible. However, I gradually replaced cartoons with football in my TV time.
In December 2006, I saw the game Manchester United vs Chelsea — a game Manchester United defeated Chelsea by a goal to nil scored by Darren Fletcher. What baffled me about that game was that Chelsea had 81% ball possession but lost the game. I have since that time seen a lot games, but this particular brings memories — this was when I began supporting Manchester United (and I know Man U is not playing well already).
Recently, I began learning product strategy in my role as a PM. I realized that product in “Product Strategy” is only a qualifier, and to better understand it, I had to look into the etymology of the phrase. Thus, the study of strategy begun. It turns out the application of strategy transcends products, it goes into every aspect of our daily lives — from choosing what and how we eat to stay healthy, to who we choose to spend the rest of our lives with in marriage, to schools we decide our children to go to (I will not spend much time on the nuances in the application of strategy, I list some books on that below). In my search, I encountered the mathematics of Strategy, Game Theory.
Game Theory, as defined by Wikipedia:
is the study of mathematical models of strategic interaction in between rational decision-makers… Originally, it addressed zero-sum games, in which each participant’s gains or losses are exactly balanced by those of the other participants.
We could go into further explanation but I would you to personal study for the sake of this post. One keyword in the definition is zero-sum games, which one participant’s loss is the other participant’s gain. This is the typical football game. Games can also be of two types, Simultaneous and Sequential games. Wikipedia definition below:
Simultaneous games are games where both players move simultaneously, or if they do not move simultaneously, the later players are unaware of the earlier players’ actions (making them effectively simultaneous). Sequential games (or dynamic games) are games where later players have some knowledge about earlier actions. This need not be perfect information about every action of earlier players; it might be very little knowledge. For instance, a player may know that an earlier player did not perform one particular action, while s/he does not know which of the other available actions the first player actually performed.
So, can we apply game theory techniques for winning sequential games to developing winning football tactics?
Sequential Game Technique and Football Tactics
I played chess in high school. I remember studying chess moves from top players in my high school first year (2000). Chess by definition is a sequential game. Moves are made based on knowledge earlier actions. This theory has helped in developing computer programs that defeated the best chess players — even in Go, AlphaGo.
One technique in modeling sequential games so as to develop winning strategies is Game Tree:
In game theory, a game tree is a directed graph whose nodes are positions in a game and whose edges are moves. The complete game tree for a game is the game tree starting at the initial position and containing all possible moves from each position; the complete tree is the same tree as that obtained from the extensive-form game representation.
Below is an image a simplified game tree for chess
By establishing the premise of sequential games, we can draw a logical conclusion of its application in developing football tactics if the assumption below holds true:
A football match can be classified as a sequential game if actions of football managers in training sessions and match tactics on game day are based on previous actions of the football team and its opponent.
If the lemma above holds true, then we can model a football game tactic as a game tree. In this regard, we should be able anticipate an opponent’s play and as such develop winning tactics. Implementing the modeled tactics is a different conversation due to human factors involved — players that would follow and execute this strategy are needed. See simplified image below of football game tactics as game tree:
Is this even possible?
If it can be achieved with AlphaGo, it can definitely be achieved. With compute power doubling almost every two years — Moore’s law and storage cost reducing to almost nothing, we can leverage data to build complex game trees for football tactics that can win games. Data points feeding into this are already available in unstructured, textual formats as documented text live match updates from SkySports, Goal.com. I am also absolutely certain that football teams already have these data available to them in structured formats.
Would this always guarantee a win?
Definitely not! This is only a technique. There are several other approaches football teams can leverage to develop winning tactics. However, using game trees should be mixed with different strategies — even in game theory. Example: Seeing football matches as both Simultaneous and Sequential games and developing strategies from a mixture of both.
Wrap Up
Thank you for following thoughts. Applications of game theory in developing strategies is beyond football. I chose football due to my love for the sport and because ManUtd is playing badly now (😊).
I hope you learned something new. I would love to hear your comments and feedback on this. Feel free to reach out to me via:
Twitter: @elesinOlalekan
LinkedIn: https://www.linkedin.com/in/elesinolalekan
Resources
Good Strategy, Bad Strategy — Richard P. Rumelt
Competitive Strategy — Michael E. Porter
Art of Strategy — Avinash K. Dixit, Barry J. Nalebuff
Thinking Strategically — Avinash K. Dixit, Barry J. Nalebuff
What is Strategy — Michael E. Porter
