1. Introduction
At present, positional data have become a usual tool for performance analysis in football. The main goal of a football match is to score a goal. With this purpose, several players are involved during every phase of the match, assuming different roles. The defending players are continually aiming to reduce the space of the opponents and, consequently, decrease the time available for the attacking squad to move the ball and create threatening situations (e.g., shot at goal), whereas the attacking players are continually exploring the space that was temporarily left available by the defenders to place the ball closer to the goal and as far as possible from the closest opponents or to shoot at the goal in an attempt to score. These paradoxical purposes create restricted possibilities of action for each team, for each moment of the match, and for each player. These opportunities of action can be conceptualized as affordances that emerge due to space–time constraints, which can be depicted by a landscape [
1,
2,
3].
Affordances express an adaptive behaviour between an individual’s capacities and a particular set of properties of the environment [
4,
5,
6]. Hence, it seems relevant to understand how the environment modulates the affordances of each player within a team. For instance, the ball carriers can be a temporary ‘leaders’, providing and creating key affordances to their teammates, orchestrating the offensive movements, and creating relevant information that helps their teammates to progress on the field or score a goal [
7]. However, the behaviour of these ‘leaders’ simultaneously constrains and is constrained by the opponents’ and teammates’ behaviour. They are influenced by a reciprocal compensation that characterizes players co-adaptive behaviour in team sports [
8,
9,
10].
Co-adaptation is a concept based on the perpetual adjustment of individuals to the changes induced by the adaptive actions of other individuals [
11]. Within a competitive environment, co-adaptive behaviours are constrained by a complex combination of tasks and goals (some antagonistic) that characterize players’ interactive behaviours in space and time, supported by emergent local information [
12]. This means that within a competitive match, the landscape of local information is continually changing, influencing players co-adaptive behaviours described by the dynamics of players’ relative positioning, players’ distances to the field boundaries, or the proximity to the scoring area [
13,
14,
15,
16].
Understanding the affordances that emerge during a match may enhance the capacity of a team to recognise the key affordances as well as the players who are able to shape correctly the movement pattern of a team in order to score a goal. Depicting a landscape of affordances (e.g., shooting opportunities) can also help to design specific training sessions to increase the acquisition of skills relative to these specific affordances [
17,
18].
Regarding the opportunities to score created during the course of a match, there is a gap in the literature in terms of depicting variations in shooting opportunities regarding the defending player’s motion. The traditional proxy used to evaluate players or team performance is generally the ratio of shots on goal or even the goal ratio. Neither of these proxies provide information about the qualitative aspect of the shooting opportunity, and they have a binary metric (goal or no goal) that limits the perception of the dangerousness [
19] (or level of threat) of an opportunity. An exception could be the predictive model to estimate the goal scoring chance and the probability of scoring known as the expected goal (xG). This probability for each scoring chance, which ranges from 0 to 1, is calculated on the basis of event-based variables as: (i) shot location; (ii) distance to the goal; (iii) angle to the goal, calculated as the triangle between shot location and the goal posts; (iv) type of shot—part of the body used to score (i.e., feet, head, or other); (v) match sub-phase in which the goal was scored (e.g., open play, direct free-kick, corner kick, or counter-attack); and (vi) various scenarios regarding how a player controlled the ball before taking a shot (direct, volley, two touches, dribbling, or set-piece). Aimed to increase the predictive power of xG model, event data were combined with positional data [
20]. On the basis of this, the goalkeeper positioning or the ‘pressure’ on the player who attempted to score were variables added to the model. The goalkeepers’ positional data were used to check whether they were in the line of shot, which was defined as a triangle between the shot location and the two goal posts. Positional data were also used to calculate the goalkeepers’ distance to the goal. Aiming to assess the level of threat by blocking the shot or the level of pressure over the shooter, the defenders’ positional data were used with this purpose. The number of defenders in the ‘line’ of shot (i.e., triangle between shot location and the goal posts) was counted to assess both the level of threat and the pressure over the shooter [
20]. The defenders’ and goalkeepers’ positional data were captured only in the moment of the shot, which is acceptable for the stated purpose of feeding a machine learning algorithm. However, in this paper, we intended to demonstrate that positional data can be used beyond the quantification of the number of players within the line of shot, and we used players’ current and estimated positions to specify shooting opportunities that locally emerge due to players’ interactive behaviour during the course of a match [
1,
2].
Thus, it seems relevant to understand how specific spatio-temporal constraints (e.g., players co-positioning) influence the landscape of shooting opportunities during a competitive football match. Moreover, we hypothesized that these spatio-temporal constraints create a non-homogeneous distribution of the shooting opportunities, which allow for the identification of where and when the attacking squad creates more threatening situations for the defending team. Therefore, the main goal of this study was to elaborate a two-dimensional model that illustrates a landscape of shooting opportunities which emerge due to the interactive behaviours among the ball carrier, the closest defenders, and the goalkeeper during a competitive football match.
2. Materials and Methods
2.1. Data Acquisition
Data used in this study were captured from a recording of an official competitive football match from the Spanish second division during the season 2017/2018. All players were adult males. Each player position was described with bi-dimensional coordinates (x and y), and both axes were positioned at the level of the field boundaries, representing its length and width. The bi-dimensional coordinates were recorded at 25 fps and represent the main data used to test the capacity of our model to illustrate shooting opportunities. To reduce the noise associated to data collection with tracking systems, each player displacement was calculated with a frequency of 5 Hz.
Events such as passing, ball drives, fouls, exclusions, substitutions, goals, and kick off were defined to provide information allowing the recognition of the ball carrier.
At this stage of model development, simplicity was the rule, which means that other performance details were purposely left out. Similar to previous models regarding landscapes of opportunities of action, we decided to create this model adopting a top-view from the pitch. Thus, the 2D model for illustrating the landscape of shooting opportunities, presented here, was supported by each player’s bi-dimensional positional and events data. This reason supports our decision of not including other types of data, such as technical, tactical, game status (e.g., score), physiological, or psychological variables. These performance variables can be addressed in further stages of development of this model. The study was conducted in accordance with the Declaration of Helsinki, and the protocol was approved by the Ethics Committee of Faculdade de Motricidade Humana, Universidade de Lisboa, under the reference 25/2019. It analyzed performances that did not require identification of individual performers.
2.2. Procedures
First, we selected the plays by visual inspection, using as a criterion the entry of an offensive play within the last 30 m of the field. If the ball carrier or the ball went outside of these last 30 m towards the opponent goal, the offensive play was no longer considered. A total of 75 offensive plays were selected, 9 from the visitors’ team and 66 from the home team.
The second step consisted of defining the multiples events, which allowed our model to recognize the ball carrier at each moment of the match. The attacking team and the ball carrier were both defined using the events mentioned above and additional information over ball position. Based on the literature, we also set an average value of the ball speed during shooting between 25 to 35 m/s, with a mean value of 27.77 m/s or 100 km/h [
21].
To increase the accuracy of our model, the defending players’ estimated positions (which allow or do not allow them to intercept a potential shot) was associated with the ability to change the running line direction. Previous research observed that the capacity to change direction is inversely related to the running speed on a straight line [
22]. Grehaigne and colleagues defined a spherical area where a defender is capable to intervene while running. This area is decreasing in terms of space and in function of the defender’s actual speed. Thus, for each defending player, we defined a potential ‘sphere’ of action as a function of turning ability and speed. The highest turning ability (360°) was established for the lowest recordable speed (0 m/s) [
1].
The potential sphere of action was defined as being the defensive coverage area of each defending player, corresponding to the space occupied even when their running speed is very low or null. The coverage area was defined using a trigonometric rule. First, we defined the angle (αp) in the field of the vector velocity of each defending player and for each position in time. Then, we considered
n = 200 points (allowing the construction the coverage area, see
Figure 1), that went through angles α
t + (α
p/2) and αt-(α
p/2) (
Figure 1). Therefore, we can calculate each one of these points using:
where
yp and
xp represent the position of a defending player at each moment of time, Δ𝑡 = 0.04 s is the time interval, v
tp is the total velocity of the defending player at each moment of time, and one of the 200 angles mentioned above is represented by α
n. Finally,
xn and
yn are the coordinates of the point of each of the
n points of the coverage area [
1]. For velocities below 1.5 m/s, the value of v
t was defined to be equivalent to 1.5 m/s, otherwise a defending player moving at a low or null speed will be considered and measured as covering no space. These vectors provide information regarding direction and velocity in a linear motion and allow our 2D model to recognize the intersection between the potential shooting trajectory and each defending player’s displacement vector.
2.3. Algorithm Description
To illustrate shooting opportunities, 20 separated lines starting from the ball carrier were created towards the goal (see
Figure 1C,D). Furthermore, these hypothetical shooting lines create a reference for the time a defender will take to intercept them. If any defending player may intercept any of these hypothetical shooting lines, they were marked as a blocked shooting opportunity. The defenders’ ability to intercept or block a shooting opportunity was calculated through each defender’s coverage area (see
Figure 1B,D).
As represented in
Figure 1C,D, each shooting opportunity may occur on both sides of the goalkeeper or (dependent on the goalkeeper’s position) on one side only. Hence, to represent each shooting opportunity for the ball carrier, two polygons were created. One outlines the ball carrier, the goalkeeper’s current or estimated position, and the left post of the goal. Another polygon outlines the ball carrier, the goalkeeper’s current or estimated position, and the right post of the goal. The goalkeeper estimated position was calculated on the basis of the direction of the goalkeeper velocity vector (please see
Figure 2). Each polygon allows the depiction of the space available for a shot to happen and was updated every 0.2 s, continuously assessing whether the defenders had the possibility to intercept or block a shooting opportunity.
The overlapping of the created polygons along the match allows the shaping of a heatmap that illustrates a bi-dimensional landscape of the shooting opportunities. The intensity of the colours (from dark blue to red) that were used to build the heatmaps helped to illustrate the superposition and the distribution of the obtained polygons (i.e., the shooting opportunities) in space.
2.4. Distribution of the Shooting Zones and the Level of Threat
According to the area of the field, shooting opportunities may vary the level of threat for the defending team. Thus, we decided to divide the last 30 m of the pitch into 6 zones with different sizes and shapes (please see
Figure 3). This division was made as a function of the penalty area (usually called ‘the box’), which is a rectangular area that extends 16.5 m to each side of the goal (33 m in total) and 16.5 m in front of it. The literature shows evidence that there is a statistical difference in goals scored between shots inside ‘the box’ and outside of ‘the box’ [
23]. Additionally, [
24,
25] identified (i) zones where teams attempted more shots; (ii) zones with more shots towards the goal; and (iii) zones where a greater number of goals were scored. These zones are a simple extension of ‘the box’ line boundaries and an additional line, which marked the 30 m of distance to the goal [
26]. This zone representation provides an accurate identification of the origin of the shooting opportunities and enriches the spatial information obtained from the heatmaps.
2.5. Statistical Procedures
For a better understanding of the dispersion of the results concerning the time that shooting opportunities were available, the following descriptive statistics were calculated for both teams: (i) the mean and the standard deviation of the time that the shooting opportunities were available; (ii) the maximum and the minimum time that shooting opportunities were available; (iii) the quartiles; and (iv) the interquartile range.
Then, the sample (n = 75) was tested to see whether it has a normal distribution. The Shapiro–Wilk and Kolmogorov–Smirnov tests of normality identified that the time that the shooting opportunities were available had a non-normal distribution. Since the normality test showed that results did not have a normal distribution, it was decided to use a non-parametric tests to compare the results of the non-normally distributed sample. Thus, with the help of the software IBM SPSS Statistics, a non-parametric test was applied to compare the time that the shooting opportunities lasted for both teams, as well as regarding the zone location of those shooting opportunities. The independent-sample Kruskal–Wallis test with a p-value of 0.05 was used for this purpose.
5. Conclusions
We may conclude that two-dimensional positional data used to describe players’ interactive behaviour of both teams form a suitable basis to create the heatmaps that illustrate the landscapes of shooting opportunities.
This 2D model can be extended to other levels of performance and to other team sports where space–time constraints bound players’ opportunities of action.
The uniqueness of each heatmap highlights the specificity of the space–time constraints which drive players’ behaviour during the course of a match.
Our 2D model illustrated the shooting opportunities that occur during a football match and provided crucial information over spatial location and time availability of those opportunities. The spatial locations and time lengths of these shooting opportunities were not homogenous over the field; on the contrary, some zones were overused in comparison with others, and the time of their availability was not similar. As expected, the less threatening zones (located far from the goal, with the widest angle to the goal) were areas where more shooting opportunities were created, whereas zones located closest and more in front of the goal, usually considered as high threatening zones, were those with few or no shooting opportunities.
Finally, we may also conclude that the results of this shooting opportunity model provide information that could be appropriate to a post-match report shortening the gap between performance analysts and the coaches’ technical staff.