Spatial relations between the field of play for team sports and the target. Case study: football

The objective of this research paper is to establish the relationship between a randomly selected point of the field of play and the target. The analysis has been based on an exemplary pitch and the rules of football. A decision to desist from the field gain and to take a shot must take into account the relationship between the possible angle of dispersion and the angle at which the goal can be seen. The latter one (denoted as γ) has been devoted special attention here. Then, we have paid special attention to the fact that the view of the goal decreases as the player moves away from the longitudinal axis of the pitch. By turning the direction of the goal line b to the direction that is perpendicular to the line of shot, we obtain a decreased projection of the goal t. The indicators such as angle γ, projection t and its quotient version N aptly define various spatial situations that occur in the field of play. However, in order to add better illustration to the assessment, another indicator (V) has been proposed. It treats the changing view of the goal as an “aiming target” observed from varying distances. The comparability of the opportunities has also been demonstrated in the form of circle-shaped isolines, based on the chord of the goal. The performed analyses have legitimised the standard rule and aim of football which involves favourable field gain along the wings and finally crossing the ball into the middle field.