# Quantifying Football Shooting Precision: The Expected Shot Impact Timing (xSIT) Approach
## 3 Expected Shot Impact Timing (xSIT) Modeling  
For the development of our model, we utilized and examined various types of data related to factors influencing goal scoring. Prior to proceeding, it is important to clarify that we assumed all players and GKs to be homogeneous. Thus, under identical initial conditions, any player taking a shot would yield the same expected outcome. Based on regulatory standards and the average dimensions of professional football fields, spatial measurements were extracted accordingly. The coordinate system was defined with the origin (0,0,0) located at one corner of the pitch, depending on the data provider's convention. In this system, the x-axis represents the lateral (frontal) width of the field, the y-axis corresponds to the longitudinal (sagittal) depth toward the goal, and the z-axis denotes the vertical height of players and the ball relative to the ground. For our study, the x-coordinate was not necessary to use, as it was not relevant to the analysis (Figure 1). Based on the data described in the table above (Table 1), we can now pose the following questions: _How effective was the shot? Was the player positioned optimally?_ To address these \begin{table}
\begin{tabular}{c c c} \hline \hline
**Features** & **Value** & **Description** \\ \hline Football field & & A 2-element tuple \((\mathrm{x},\mathrm{y})\) where \\ dimension & & \(x\in[0,75\;m],\;y\in[0,120\;m]\) \\ Ball shot location & Numerical & The \(x\) and \(y-\)coordinate of the ball at the \\  & & time of the shot. \\ Ball velocity & Numerical & The average velocity of the ball (km/h). \\ Goalkeeper location & Numerical & The \(x\) and \(y-\)coordinate of the goalkeeper at \\  & & the instant time of the shot. \\ Player’s location & Numerical & The \(x\) and \(y-\)coordinate of all the players at \\  & & the time of the shot. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Variables derived from aligned positional and event data utilized to develop our model. Figure 1: The coordinate system employed to represent the position of the ball or all players was based on two axes: the x-axis (frontal axis), which represents the horizontal distance across the field’s width, and the y-axis (sagittal axis), which denotes the depth or distance toward the goal. questions, we generated an image representing the range of possible player movements. By applying pixel classification techniques to this image, we will assess the quality of the shooting position. In developing this model, the following steps were undertaken:  
**Step 1. Data Extraction. ** Using the aforementioned database, the positions of all players at the moment of each shot were identified. **Step 2. Field Mapping. ** Each player's position was mapped onto a representation of the football field. **Step 3. Role Differentiation. ** Different roles were visually distinguished by color coding:  
- The GK was represented by a green point. - Outfield players were represented by blue points. - The shooter (ball) was represented by a red point. **Step 4. Graphical Representation. ** All players and the GK were modeled as points, following the methodology described in previous studies (Figure 2) [14]. **Step 5. Generation of the Shooting Triangle. ** After obtaining the previous image, we generated a triangle defined by the following vertices (Figure 3):  
- The shooter (the position of the player taking the shot);  
- The left post of the goal;  
- The right post of the goal. This triangle represents the theoretical zone through which the ball could travel toward the goal, assuming no obstacles. Following the creation of the triangle, we incorporated  
Figure 3: Representation of all players on the field with the shooting triangle. Figure 2: Representation of all the players on the field: green point represents the GK; blue point represents the outfield players; and red point represents the shooter (ball). the players who may act as obstacles, and the ball's trajectory was adjusted to account for them.