Even though the most tracked part of a football match is where the ball is, the most interesting things often happen off the ball. The ball is only in play for 50-60 minutes of a 90-minute match, and each individual player is only on the ball a minimal part of that time. The majority of the game is played off the ball by all players, they need to move about the pitch in relation to their teammates, the opposition and the ball. A forward can move off the ball to find space between defenders to receive a pass, whilst the defenders need to keep an eye on the forwards and track these attempts.
For a specific player, at a given point of the game, there are locations on the pitch that would be considered worse positions to be in than others. For example, if the opposition had the ball on the edge of your penalty area, you would consider your central defender to be at a worse position if they were standing by the opposition’s corner flag than if they were marking the opposition’s forward. Since there is a concept of better or worse positions, that leads to the possibility of there being an optimal position for a specific player at a given point of the game. You could also think of it such as if you were to remove a single player from the game, where would you want to replace them in the game such that you couldn’t move them to a better place.
Several factors could affect the perception of a position at a given time being better or worse. These could be physical states of the game, such as locations of teammates, opposition or the ball. They could also be non-physical, such as score, the aim of the tactics or time on the clock. Considering where the ball is and who is in control of the ball will dictate the general area where your teammates and opposition will set up. Considering the tactics and formation that you and the opposition are looking to play will dictate the general areas of where individual players will set up.
Different tactical styles, scores and time remaining will affect what the aims of a team are. Some teams, such as Manchester City, want to control the largest surface area of the pitch possible. Control of the pitch can be determined by which team is likely to get possession of the ball if the ball was located in that area. Whilst other teams are aware that they can’t afford to try to control the largest surface area of the pitch, but rather look to control the areas of high interest such as around their own penalty area. Individual players need to position themselves with appropriate distances between each other to reflect their tactical style and goal. Certain distances between certain players would be better or worse than others, so again there must be an optimal distance with respect to tactical aim. When each player achieves this optimal distance, the collective team would appear to perform optimally.
A geometric way of viewing the areas of control on a pitch would be to look at Voronoi diagrams.
If we look at Figure 1 with team red against team blue, each of the polygons surrounding each player would correspond to the areas on the pitch that they control. If the ball happened to be within their boundaries, they would most likely get to the ball first (considering each player has the same speed). This concept has been around for a while and has been made possible due to the technology available to football clubs, player tracking is everywhere nowadays and is crucial to understanding how your team is performing.
Voronoi diagrams can be used at a team level to understand structure and how well a team can transition between situations, but also is useful at the player level as you can identify which players find the most space or which players are the best at denying space.
In terms of quantifying better or worse positions of an individual player, the surface area of a player’s Voronoi region can be indicative of how well positioned they are. It is important to note that not all spaces on the football pitch are equal, controlling the areas closer to the goals area more beneficial than controlling the centre of the pitch. Perhaps a weighted surface area would be a better quantifier of control of the pitch and would be another contributor to identifying optimal positioning.
Special mention to below for their work already on Football Geometry and Voronoi Diagrams:
@Soccermatics – https://medium.com/@Soccermatics/the-geometry-of-attacking-football-bee87e7a749
@UTVilla – http://durtal.github.io/interactives/Football-Voronoi/