With so many variables at play, does anybody ever know anything?
In football, narrative is everything; from intricate statistical analysis to romanticised headlines, the concept of linear progression – completed stories with beginnings and ends, with heroes and villains – fuels our obsession. Every season is the next novel, with new plot lines and twists, and every match is the next set-piece, anticipated and adored for its function in the narrative arc.
Where art ricochets through the crisis of post-modernism, sport continues to offer us the comforting illusion of linearity and progression, a cause-and-effect safety net. And as spectators and humans, we crave the world that we create; it is a world in which all variables can be harnessed and understood, where ascent and decline can be analysed and accounted for, and where coaches and players control their own destiny. We may at times enjoy the “unpredictability”, but for the most part, sport conforms to a deeply instinctive human yearning for a version of reality that, after 200 years of existential angst in art and philosophy, is consistently denied: concrete meaning and the rejection of chaos.
In truth, the deeper we dig in our analysis of the game, the more this simplified model of causality is called into question. Is it time to re-think the way in which we structure commentary and analysis, and in doing so, radically re-evaluate our understanding of football?
All football commentary, from the Sun to The Blizzard, works on the basis that football is, to some extent, predictable and explainable; the signings, tactics, and performances are constantly analysed, in order to project future outcomes or justify results. The quality of the journalism may change the extent to which this idea is believed (many do recognise the complexity of variables and the chaos of sporting outcome), but nevertheless most of us believe, to some extent, that in-depth tactical analysis can tell us how and why a given result was reached.
However, this idea is difficult to accept when we consider the impact of chaos theory.
In a close match entering extra time at 0-0, we can accept that a number of minor incidents could have changed the name on the World Cup trophy. The BBC’s commentary team focused on Martin Demichelis being caught between tracking Thomas Müller and dropping onto Mario Götze for that vital goal. Others focused on Ezequiel Garay’s slowness to cover, Jogi Löw’s substitutions or Rodrigo Palacio’s miscontrol when clean through on goal moments before. But the truth is, all of these things affected the outcome, as did every other moment in this match, every other moment in the World Cup and every other moment in the history of world football.
Like a sentient chessboard, football – as a humanly contained space of fixed boundaries and variables – perfectly displays the frightening reality of chaos theory. Chaos theory describes a world of non-linear dynamics, in which each microscopic element of reality is chaotically entangled with its surroundings. The archetypal example – a butterfly flapping its wings in Brazil causing a tornado in Texas – may help illuminate the idea of chain reactions, but to conceptualise chaos theory fully we must realise that the web of interconnectivity is virtually infinite; as a microcosm of reality, football cannot escape the clutches of determinism.
On a pitch, every movement of the ball affects the positioning of multiple players. The match shifts with every touch and therefore the potential pathways for the future also shift, irreversibly. If player A passes the ball 10 yards to his or her left, players all over the pitch will move to accommodate the play. Even if the ball is instantly switched back to player A, countless variables have changed with the passage of time – from runs made to weather conditions — and all future action in the match has been affected by that initial decision. If we accept that the positioning of any single player on the pitch affects the passing and movement options of the player on the ball, it is self-evident that the number of variables affecting the next millisecond of a match are uncountable. Each decision creates a ripple effect of variables, expanding into a Cantorian infinity of responses, and responses to responses, until it becomes clear that the events of a football match can unfold in an infinite number of ways and that every minuscule action has a dramatic, irreversible effect on this outcome.
In simpler terms, if André Schürrle had turned back and passed the ball inside to Müller, rather than crossing for Götze in that decisive moment in the 118th minute, the action would have been affected and countless players would have repositioned themselves (not least the two ‘caught out’ Argentina centre-backs). Müller could have been tackled and Argentina could have broken away to score the winning goal, or he could have reworked the attack so that it was still Philipp Lahm lifting the trophy. This part is easy to accept.
But in truth, there are thousands of different touches and movements Schürrle could have made, each affecting the potential decisions of other players on and off the ball, over the five seconds that followed. The chain reaction of decision-making continues to inflate exponentially over the following two minutes: considering that each decision will shift the match slightly, it quickly becomes evident that there are tens of trillions of potential outcomes to this football match. In any given game, each microscopic movement or decision – anywhere on the pitch – permanently denies trillions of potential pathways, whilst simultaneously opening up trillions of new ones.
We tend to trace the route of a goal back to the opening of the move – or at most, the breakdown of the previous one – when in truth its foundations stretch back to kick-off and the first decisions made by every player on the pitch. The reason Götze scored that goal was no more because of Schürrle’s trickery or Götze’s skill, as it was an Argentinian player’s decision to make a back-pass rather than a clearance in the second minute.
Of course, the variables that we traditionally consider important in determining results could be seen to counteract the butterfly effect; in a 90-minute match, the stronger side will win and the cream will rise, regardless of the countless potential changes in player and ball position. After all, a player reacts in real time to situations and a consistently high performing team should still create a victorious scenario. Still a very thorny issue for chaos theorists, one could argue that the individual is still free to choose their next decision, regardless of the complex tapestry of variables that carried them to that point. These arguments will inevitably lead us towards contemplation of the nature of free will itself, which will be discussed later.
But leaving the free will debate to one side for a moment, we can still see that the cream does not always rise and that those tiny decisions within a game really can have a butterfly-effect impact. We all know how unpredictable football can be, how fine the margins between victory and defeat are, and how the team that performed worse can emerge victorious. Football is not a stable system. Considering the role of psychology – impetus, confidence and determination – on the performances of teams and the outcomes of matches, it is reasonable to assume that results, then entire tournaments, seasons, and careers, could be twisted and shaped by any single fragile and seemingly innocuous moment on a pitch.
Consider a two-footed tackle in a Premier League match that is punished by a red card. In most cases, this rush-of-blood moment could only occur given an exact intertwining of variables; the opportunity for this rash action to take place relies on the position of the players involved, the ball movement prior to it and the emotional condition of the offender (which itself is dependent upon time, status of the match, etc). It is highly unlikely that factors would have converged to this moment – and surely they would not have – had any of the variables been changed slightly. The combined effect of these variables would have fallen apart if a single player had made a single different decision between kick-off and that moment. The match could be swung by it and then the players’ performances in the next few matches – defining a season and careers and so on.
It would seem, then, that chaos theory seriously undermines traditional football analysis. TR Young, in his seminal essay “Chaos Theory and the Knowledge Process”, states that “the findings of chaos theory inform us that the task of the social scientist is not, cannot be, the discovery of the immutable laws of society; it is not, cannot be, to build grand theory by means of value-free research designed to approach objective reality through the method of successive approximations… For all social groups, their geometry is fractal.” The complexity of the trillions of variables that affect both the individual events within a football match and the final outcome makes objective analysis of a non-linear system impossible. Does that mean all football commentary is useless?
Unfortunately, this is not the worst of it. In popular culture, chaos theory’s effects are represented as pendulum moments on which our fate swings; answering a phone call, missing a train. But what is overlooked is that every single moment of our lives represents a shift in our fate and, perversely, every single moment of everybody else’s lives. The football field is an excellent analogy for the world at large; the minutest changes in variables, through a knock-on effect, completely re-shape the future.
Our world can be considered as one complexly unstable system in which each of its components, in both action and inaction, affect a multitude of variables around it. Since the butterfly effect dictates that one variable has a dramatic ripple effect on future events, then, if the theory is accepted as true, clearly this is also true of every other event that has ever happened. Every motion in the universe, therefore, is inextricably intertwined with every other, by trillions of little causal threads that expand exponentially into the future, in an intricate web too complex to understand. Every event on the planet directly results from an incalculable number of variables over the past 14.7 billion years, and every event in the future will be the result of an unfathomable amount of variables all effecting quadrillions upon quadrillions more.
Consequently, our complex cause-and-effect system is mathematically predictable, even if such an equation is light years beyond the realm of possible human comprehension. Theoretically, one could analyse all of the events and variables of a given moment in time and predict exactly what would happen one second later. Since this information is now known, we could predict the next second and so on. If predicting the future is possible, then what does that say about free will? Do we live in a deterministic universe?
If this theory is to be accepted as true, then we must also accept that our attempts to predict the future based on a narrow selection of variables – such as form, ability, tactics, etc – are far too simplistic. The factors that appear to us as important, from in-game player performance to weather conditions and stadium capacity, are not a complete list. It may conform to our idealisation of sport as solid, simplistically causal and gratifyingly anti-post-modern, but it cannot be considered true.
An uncountable volume of variables, from the breakfast choice of a coach to the decisions of a person on the other side of the world, affect the future, and trillions and trillions of factors have an equal right to claim causal effect on the outcome of a match. As Young writes, “Instead of discrete object, bounded and self contained, the geometry of natural systems is more like Cantor dust, Koch curves, a Sierpenski carpet, a Menger sponge or the lovely patterns of a Mandelbrot set; such forms are riddled with holes and open to the passage of other systems… If we think of a person in fractal terms, we find a discrete object answering to the concept of the ‘individual’ hard to find in nature… Self and society are twin born; where a mother ends and a father starts is difficult to know. Where a mind starts and stops or meets another mind is hard to know.”
Can we state with certainty that the Germany and Argentina players had any actual freedom to choose their actions on the pitch, considering the extent of the deterministically causal web they were trapped in? The reasons for receiving the ball, and the option available to them, depended upon such an intricate system of expansive chaos, one could argue that no other options could have been chosen.
Many people will argue that, in the moment, we freely choose our next decision, regardless of the fact that our scenario is conjured via an exact convergence of variables. If one believes this, then clearly the coach and analyst, dissecting a phase of play, are at least partially redeemed.
We will never be able to settle this point, although it is worth mentioning that a deeper discussion of free will in a chaos-based system would ultimately lead to questions regarding the neural pathways of the brain, the extent to which our actions are influenced by reason or impulse and the extent to which our neurological activity can itself be seen as another intricate web of cause-and-effect.
If we decide to believe in the model of determinism, as many chaos theorists do, then we would have to accept that not only is it futile to attempt to analyse the reasons for a result or predict the outcome of others, but it is also impossible to know, given the number of variables stretching back through millennia, whether or not the action could have taken place in any other way.
And, crucially, we would find ourselves asking the question: if gazillions of interconnected phenomena led up to the moment the first ball was kicked in the World Cup final, were we incorrect to assume that either team could have won?
Of course if the result is essentially pre-determined, then we are no longer simply questioning the value of analysis, but the value of spectating altogether. Perhaps all that is left is an empty spectacle of pre-ordained moves, as sport becomes less like a battle and more like a play, a scripted performance. But would this really be problematic? Does football not already, in its grace and its artistry, resemble a theatre or a ballet performance? These are surely all questions that require serious attention.
In truth, even if free will can exist within chaos theory, we are still faced with difficult questions about the integrity of football analysis, for journalists and coaches alike. To return to Young: “[The chaos theory] view holds that nature is a seamless totality and that selection of only part of it to study necessarily results in partial knowledge. If we want to know how a particle or a system will behave, we must expand our research design to measure everything; to record more and more of reality until we have it all on paper.”
It does not make sense to predict a result based on tactical suppositions, just as it does not hold true that a goal was the result of the brilliance or incompetence of an individual. On some level we may like to celebrate the unpredictability of football, but ultimately we enjoy the notion that teams and players and coaches succeed or fail for a reason. As uncomfortable as it is to accept, football – and football journalism – do not conform to the simplistic narratives we place upon them.
Perhaps what it really comes down to, when we consider the artistry and beauty of the matches themselves, is whether or not we believe this possible truth to be important.
This article appeared on Episode Sixty Five of the Blizzard Podcast. You can see which other articles we have featured by searching the Podcast tag, but we'd really like you to subscribe which you can do through iTunes, Soundcloud, our RSS feed or wherever you usually get your podcasts of choice.