Formations: Cartesian Coordinates or Dasein?

Scientific models are not physical representations of reality in the way that flat-pack assembly instructions represent furniture, but are images which assist us to comprehend a highly complex physical world. For example, the molecules that we breathe can be represented as tiny spheres bouncing off one another. Molecules behave as if they were tiny spheres, but this does not mean that they are tiny spheres: a scientific model is a visual aid to the imagination, illuminating processes which exist beyond the limits of our sensory experience.

A football formation could be regarded as a scientific model that helps us to understand a mutable topological arrangement which constantly alters over the temporal course of the game. During a match we do not see the players organized under a neat symmetrical formation. Formations such as 4-4-2 are therefore an aid to the imagination, and should demonstrate players’ approximate positions in relation to one another. To qualify as a scientific model, this representation could be expressed via mathematical equations. Using averaged positions based on where players touch the ball during a game would provide the underpinnings necessary to confirm that formations are scientific models. A Cartesian coordinate system would therefore capture the spatial location of each player: this should tally with formational representations to a meaningful degree.

However, based upon Cartesian coordinates, formations are poor representations of on-pitch reality. We should be able to make predictions from scientific models, but formations do not provide sound predictions of players’ average on-field positioning. Whilst the processual activity of football is more complex and messy than a simple model can express, the model should still have some predictive scope. When we look at the above graphic, we see that the formation could perhaps be expressed as 2-4-2-2. The full-backs push on to be level with the central midfielders, with the centre-backs, based on Cartesian coordinates, essentially the only defenders.

This indicates that we do not apprehend player positioning merely based upon coordinates: we also assess the game with regard to the human significance attached to the use of space. Heidegger’s notion of Dasein shows that our spatial relation with objects is based upon how we define space with regard to the specificity of human activities or being-in-the-world. Closeness and distance therefore only have meaning in relation to aspects of existence relevant to our being: on this basis, the friend I am waving to across the street is closer than the pavement underneath me of which I am unaware. Cartesian ontology is thus an abstraction from our understanding of space as a region of existence inextricably linked to meaningful human activity. Dasein is why we do not view football formations as 2-4-2-2, despite average on-field positions.

Average on-field positions are less vital to us when considering how teams line-up, than the understanding of the value of each position. For example, football fans know that, despite the full-back having licence to push forwards down their flank, their primary responsibility is defence. The key activity for the full-back is that which takes place when they join the centre-backs in defending the goal. On-field positioning suggests that full-backs are midfielders, but defensive work is fundamental to their role, with attacking forays crucial but ancillary. This is why, despite graphical representations to the contrary (as above), we consider that teams usually line up with four defenders.

Formations are ontological and epistemological: they do not simply represent what exists on the pitch, but show us how humans organise their understanding of the game. Rather than reflecting an external physical reality, formations capture a social reality which is more meaningfully expressed when mathematical coordinates are partially eschewed.