An expected goals on target (xGOT) model: accounting for goalkeeper performance in football

Academic Editor: Carson K. Leung Received: 29 January 2025 Revised: 3 March 2025 Accepted: 5 March 2025 Published: 10 March 2025 Citation: De-la-Cruz-Torres, B.; Navarro-Castro, M.; Ruiz-de-Alarcón-Quintero, A. An Expected Goals On Target (xGOT) Model: Accounting for Goalkeeper Performance in Football. Big Data Cogn. Comput. 2025,9, 64. https://doi.org/10.3390/ bdcc9030064 Copyright: © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/). Article An Expected Goals On Target (xGOT) Model: Accounting for Goalkeeper Performance in Football Blanca De-la-Cruz-Torres 1,* , Miguel Navarro-Castro 2,* and Anselmo Ruiz-de-Alarcón-Quintero 3 1Department of Physiotherapy, University of Seville, c/Avicena s/n, 41009 Seville, Spain 2Department of Applied Mathematics I, Higher Technical School of Architecture, University of Seville, Avd. Reina Mercedes s/n, 41012 Seville, Spain 3Football and Handball Academy, Street nº 12B, Office 6, 41960 Seville, Spain; [email protected] *Correspondence: [email protected] (B.D.-l.-C.-T.); [email protected] (M.N.-C.) Abstract: A key challenge in utilizing the expected goals on target (xGOT) metric is the limited public access to detailed football event and positional data, alongside other advanced metrics. This study aims to develop an xGOT model to evaluate goalkeeper (GK) performance based on the probability of successful actions, considering not only the outcomes (saves or goals conceded) but also the difficulty of each shot faced. Formal definitions were established for the following: (i) the initial distance between the ball and the GK at the moment of the shot, (ii) the distance between the ball and the GK over time post-shot, and (iii) the distance between the GK’s initial position and the goal, with respect to the y-coordinate. An xGOT model incorporating geometric parameters was designed to optimize performance based on the ball position, trajectory, and GK positioning. The model was tested using shots on target from the 2022 FIFA World Cup. Statistical evaluation using k-fold cross-validation yielded an AUC-ROC score of 0.67 and an 85% accuracy, confirming the model’s ability to differentiate successful GK performances. This approach enables a more precise evaluation of GK decision-making by analyzing a representative dataset of shots to estimate the probability of success. Keywords: generative model; shot on target trajectory; goalkeeper evaluation; ball position; data analysis 1. Introduction In professional football (soccer), the proportion of attacking plays that culminate in a goal is exceedingly low, with only 1% of such sequences and approximately 10% of all shots resulting in a successful outcome [ 1 – 3 ]. Despite this, goals remain the fundamental determinant of match outcomes and are widely regarded as the principal metric for evaluating the performance of both teams and individual players. Relying exclusively on this metric, however, fails to capture the complexity of player and team contributions. This approach emphasizes outcomes while neglecting the processes that underpin them. To address this limitation, the field of football performance analysis has increasingly adopted more complex, process-oriented metrics. These advanced metrics provide a comprehensive framework for assessing performance beyond the evaluation of goals, enabling a deeper and more nuanced understanding of the game. Therefore, the use of shot characteristics as a proxy for success has been increasingly validated in numerous football studies [ 4 ]. Among these metrics, the expected goals on target (xGOT) stands out as particularly noteworthy [ 5 ]. The xGOT is an advanced metric in football analytics that refines the standard expected goals (xG) model by incorporating additional factors related Big Data Cogn. Comput. 2025,9, 64 https://doi.org/10.3390/bdcc9030064 Big Data Cogn. Comput. 2025,9, 64 2 of 13 to the quality and placement of shots on target [ 6 – 9 ]. While xG estimates the likelihood of a shot resulting in a goal by evaluating the shot’s quality before it is taken based on factors such as shot location, shot type, and build-up play, xGOT adjusts this probability after the shot is executed. It takes into account the actual shot placement and the difficulty for the goalkeeper (GK) to save it. Key elements considered in xGOT include shot placement (the precise location within the goal frame where the shot is aimed, such as the top corner versus the center), GK influence (the positioning and reaction of the GK at the time of the shot), and shot characteristics like power and trajectory (which affect the shot’s speed and movement and, consequently, its save difficulty) [ 10 , 11 ]. By integrating these factors, xGOT provides a more accurate assessment of both shot quality and GK performance, making it a valuable tool for understanding match outcomes and evaluating player contributions. The primary challenge in utilizing the xGOT metric lies in the limited public availability of detailed football event and positional data, as well as other advanced metrics. To the best of the authors’ knowledge, such datasets remain largely inaccessible [ 12 , 13 ]. Companies like Opta and STATSBOMB collect these data independently and disseminate the results directly via their platforms. This lack of transparency and the opacity surrounding the algorithms used to calculate these metrics—commonly referred to as “black-boxing”— hinders the understanding and interpretation of how specific metric values are derived. This underscores the necessity of developing an xGOT model that explicitly identifies the influencing variables and quantifies their respective impacts, thereby enhancing interpretability and analytical utility [12,13]. In the existing literature, efforts to create interpretable xGOT models have primarily focused on leveraging publicly available datasets, such as those from platforms like Wyscout [ 14 ] or open-source initiatives (e.g., STATSBOMB’s free datasets) [ 15 ]. Indeed, Gottini GA [ 16 ] performed a thesis in which they emphasized xGOT as a key metric for evaluating goalkeeper performance within specific models, yet without offering the technical or mathematical foundations behind its computation (i.e., a “black box”). The authors referenced studies and organizations such as STATSBOMB that employ xGOT, but treated this metric as an external resource rather than one that was developed or replicated within the scope of their study. Despite these efforts, existing studies have yet to develop an xGOT model that both identifies the influencing variables and quantifies their respective impacts [ 12 , 13 , 16 ]. This aspect is crucial for enhancing coaches’ understanding and for the development of training strategies aimed at improving match performance. Therefore, this study aims to bridge this gap by presenting a shot prediction model developed using event and positional data. The accuracy of the model is evaluated through statistical analysis and validated through consultations with professional match analysts, each with over 25 years of experience across all levels of competition. Expert input is also incorporated into the feature selection process and the interpretation of their impact on predictions. Furthermore, practical applications are demonstrated using data from the 2022 FIFA World Cup matches, highlighting use cases relevant to coaching staff and decision-makers in football analytics. The structure of this paper is organized as follows: Section 2provides an overview of the data and key definitions used in the study. Section 3outlines the methodology for constructing the xGOT model. In Section 4, we present the practical applications of the model. In Section 5, we compare the xGOT values between our own model and the output from the STATSBOMB model. Finally, Section 6discusses the implementation of our approach using data from the 2022 FIFA World CUP, accompanied by a critical analysis of the results. Big Data Cogn. Comput. 2025,9, 64 3 of 13 2. Data and Definitions In this study, we analyzed 1536 shots from the 2022 FIFA World Cup. From the total number of shots, we selected only those taken from the ground for our model, resulting in a final dataset of 344 shots. This international tournament featured 32 men’s teams from five confederations, competing across 64 matches. The event data were sourced from an openly accessible website [ 17 ]. Below, Table 1provides a detailed overview of the different values observed for each shot. Table 1. Features extracted from synchronized positional and event data that we used to train our model. Features Value Definitions Football field dimension Numerical A 3-element tuple (x, y, z)where x∈[0, 68 m],y∈[0, 105 m],z∈[0, ∞m). Ball diameter Numerical 0.225 m Ball shot location Numerical The x-, y-, and the z-coordinate of the ball at the instant time of the shot. Goalkeeper location Numerical The x-, y-, and the z-coordinate of the goalkeeper at the instant time of the shot. Speed of ball Numerical The speed of the ball. We will assume it to be constant. Type of shot Categorical Two types: straight line shot and parabolic shot. 3. Expected Goals On Target (xGOT) Modeling For the development of our model, we have analyzed and considered various types of data that influence goal scoring. At the outset, it is important to clarify that we have assumed all players and GKs to be identical. Therefore, our variable assumes that any individual taking a shot under the same initial conditions will achieve the same outcome. Table 1provides the definitions of the variables required for the development of the model. All the variables mentioned above can be calculated using various existing tools. Following the regulations and the average dimensions of football fields, we have extracted the measurements. The coordinate origin (0, 0, 0) will be set at one of the corners, depending on the website from which the data were sourced. The x-coordinate represents the horizontal distance across the width of the field (frontal axis); the y-coordinate indicates the depth or distance toward the goal (sagittal axis); and the z-coordinate represents the height of the players and the ball relative to the ground (vertical axis). Consequently, the z-value is generally 0, except for when a shot is taken or a player jumps (Figure 1). Big Data Cogn. Comput. 2025, 9, x FOR PEER REVIEW 3 of 14 2. Data and Definitions In this study, we analyzed 1536 shots from the 2022 FIFA World Cup. From the total number of shots, we selected only those taken from the ground for our model, resulting in a final dataset of 344 shots. This international tournament featured 32 men’s teams from five confederations, competing across 64 matches. The event data were sourced from an openly accessible website [17]. Below, Table 1 provides a detailed overview of the different values observed for each shot. Table 1. Features extracted from synchronized positional and event data that we used to train our model. Features Value Definitions Football field dimension Numerical A 3-element tuple 󰇛x, y ,z󰇜 where 𝑥∈ 󰇟0,68 m󰇠,𝑦∈󰇟0,105 m󰇠,𝑧∈󰇟0,∞ m󰇜. Ball diameter Numerical 0.225 𝑚 Ball shot location Numerical The 𝑥-, 𝑦-, and the 𝑧-coordinate of the ball at the instant time of the shot. Goalkeeper location Numerical The 𝑥-, 𝑦-, and the 𝑧-coordinate of the goalkeeper at the instant time of the shot. Speed of ball Numerical The speed of the ball. We will assume it to be constant. Type of shot Categorical Two types: straight line shot and parabolic shot. 3. Expected Goals On Target (xGOT) Modeling For the development of our model, we have analyzed and considered various types of data that influence goal scoring. At the outset, it is important to clarify that we have assumed all players and GKs to be identical. Therefore, our variable assumes that any individual taking a shot under the same initial conditions will achieve the same outcome. Table 1 provides the definitions of the variables required for the development of the model. All the variables mentioned above can be calculated using various existing tools. Following the regulations and the average dimensions of football fields, we have extracted the measurements. The coordinate origin (0, 0, 0) will be set at one of the corners, depending on the website from which the data were sourced. The x-coordinate represents the horizontal distance across the width of the field (frontal axis); the y-coordinate i ndicates the depth or distance toward the goal (sagittal axis); and the z-coordinate represents the height of the players and the ball relative to the ground (vertical axis). Consequently, the z-value is generally 0, except for when a shot is taken or a player jumps (Figure 1). Figure 1. The coordinate system used to represent the position of the ball or a player consists of three axes: the x-axis (frontal axis), which represents the horizontal distance across the width of the field; the y-axis (sagittal axis), which indicates the depth or distance toward the goal; and the z-axis Figure 1. The coordinate system used to represent the position of the ball or a player consists of three axes: the x-axis (frontal axis), which represents the horizontal distance across the width of the field; the y-axis (sagittal axis), which indicates the depth or distance toward the goal; and the z-axis (vertical axis), which represents height relative to the ground, with a value of 0 when the ball or player is on the ground and which increases when the ball is airborne or a player jumps. Based on the variables presented in the table, we can now pose the following question: Can we model the movement of the ball and the GK? The answer is yes. To address this, Big Data Cogn. Comput. 2025,9, 64 4 of 13 we will use differential equations. For simplicity and to ensure accessibility for sports professionals, we have chosen to employ simplified equations in this study. As indicated in the table of variables and given that football involves two distinct types of shots on goal, each type will be analyzed and discussed in detail in separate subsections. 3.1. Straight-Line Shot Equations We have made use of the differential equations to calculate the movement in each of the coordinates, i.e., our shot will appear as follows (Figure 2): Big Data Cogn. Comput. 2025, 9, x FOR PEER REVIEW 4 of 14 (vertical axis), which represents height relative to the ground, with a value of 0 when the ball or player is on the ground and which increases when the ball is airborne or a player jumps. Based on the variables presented in the table, we can now pose the following question: Can we model the movement of the ball and the GK? The answer is yes. To address this, we will use differential equations. For simplicity and to ensure accessibility for sports professionals, we have chosen to employ simplified equations in this study. As indicated in the table of variables and given that football involves two distinct types of shots on goal, each type will be analyzed and discussed in detail in separate subsections. 3.1. Straight-Line Shot Equations We have made use of the differential equations to calculate the movement in each of the coordinates, i.e., our shot will appear as follows (Figure 2): Figure 2. Graphic of straight-line shot on target. Thanks to our previous considerations, the motion of the ball will be described by the equations: 𝑥󰇛𝑡󰇜𝑥𝑣𝑡𝑐𝑡 𝑦󰇛𝑡󰇜𝑦𝑣𝑡𝑐𝑡 𝑧󰇛𝑡󰇜0.225 where the variable t represents time; the values x 0 and y 0 denote the initial position of the ball on the field; v 0x and v 0y correspond to the initial velocity components of the ball at the moment it is kicked; and 𝑐 is the coefficient of friction, which, being the friction between rubber and dry earth, will be between 󰇟0.4,0.6󰇠. To see this coefficient, we have accessed where they give a list of friction coefficients [18], among which is the coefficient between grass and plastic. Additionally, the function z(t) is a constant function, independent of time. In this type of shot, the ball remains on the ground. This value represents the height of the ball relative to the ground; however, some datasets assign values within the range [0, 0.4], despite the ball staying on the ground in all cases [19]. Nonetheless, z(t) remains constant. 3.2. Parabolic Shot Equations We used the differential equations to calculate the movement in each of the coordinates, i.e., our shot will appear as follows: Thanks to our previous considerations, the motion of the ball will be described by the equations (Figure 3): 𝑥󰇛𝑡󰇜𝑥𝑣𝑡󰇛sinψcosα󰇜 𝑦󰇛𝑡󰇜𝑦𝑣𝑡󰇛sinψsinα󰇜 𝑧󰇛𝑡󰇜𝑧𝑣𝑡cosψ𝑔𝑡 2 Figure 2. Graphic of straight-line shot on target. Thanks to our previous considerations, the motion of the ball will be described by the equations: x(t)=x0+v0xt−ct2 y(t)=y0+v0yt−ct2 z(t)=0.225 where the variable trepresents time; the values x0and y0denote the initial position of the ball on the field; v 0x and v 0y correspond to the initial velocity components of the ball at the moment it is kicked; and c is the coefficient of friction, which, being the friction between rubber and dry earth, will be between [0.4, 0.6] . To see this coefficient, we have accessed where they give a list of friction coefficients [ 18 ], among which is the coefficient between grass and plastic. Additionally, the function z(t) is a constant function, independent of time. In this type of shot, the ball remains on the ground. This value represents the height of the ball relative to the ground; however, some datasets assign values within the range [0, 0.4], despite the ball staying on the ground in all cases [19]. Nonetheless, z(t) remains constant. 3.2. Parabolic Shot Equations We used the differential equations to calculate the movement in each of the coordinates, i.e., our shot will appear as follows: Thanks to our previous considerations, the motion of the ball will be described by the equations (Figure 3): x(t)=x0+v0xt(sin ψcos α) y(t)=y0+v0yt(sin ψsin α) z(t)=z0+v0ztcos ψ−gt2 2 where ψ∈0, π 2 represents the shot angle with respect to the XZ plane, and α∈[0, 2π] represents the shot angle with respect to the XZ plane. If α = 0 or 2 π , the shot does not affect the y-coordinate, and the shadow of the ball will describe a linear trajectory. Similarly, when ψ=π 2for any value of α, the ball will follow a purely vertical motion. Big Data Cogn. Comput. 2025,9, 64 5 of 13 Big Data Cogn. Comput. 2025, 9, x FOR PEER REVIEW 5 of 14 where ψ∈󰇣0, 󰇤 represents the shot angle with respect to the 𝑋𝑍 plane, and α∈󰇟0,2π󰇠 represents the shot angle with respect to the 𝑋𝑍 plane. If α = 0 or 2π, the shot does not affect the y-coordinate, and the shadow of the ball will describe a linear trajectory. Similarly, when 𝜓  for any value of α, the ball will follow a purely vertical motion. Figure 3. Graphic of parabolic shot on target. Conversely, when 𝜓0, the shot describes a parabolic trajectory along the ground. This type of shot is rare in football. A study by Howard Masur [20] derived the equations for such a trajectory in the context of billiards. When both angles are zero, the shot follows a linear trajectory in its ground projection. Moreover, since ψ = 0, the ball remains on the ground, meaning its actual motion coincides with its projection. In this case, we apply the equations from the previous section. Consequently, we assume that both angles are nonzero in our analysis. In this section, we employ a simplified model, previously published in an earlier study [21], where angular velocity is not considered. The values x 0 and y 0 denote the initial position of the ball on the field, while v 0x and v 0y represent the initial velocity components at the moment of the kick. The parameter g denotes the gravitational constant. 3.3. Goalkeeper Equations Based on the data analyst specializing in football with over 25 years of experience across all levels of competition, and because we aim to develop a simple algorithm, we have decided that the GK’s movement will follow a rectilinear trajectory. Thus, the equations are as follows: 𝑥󰇛𝑡󰇜𝑥 𝑣 𝑡 𝑦󰇛𝑡󰇜𝑦 𝑣 𝑡 𝑧󰇛𝑡󰇜𝑧 𝑣  𝑡 The values x , y , and z  represent the GK’s initial position on the field. Similarly, 𝑣 , 𝑣 , and 𝑣  denote the GK’s initial velocity at the moment the player kicks the ball. 3.4. Build of xGOT Through the construction of the differential equations and the way we modeled the field, we are able to calculate the time instances for both the ball and the GK. However, to achieve our objective, we need to determine when both coincide, which only occurs under specific conditions. To simplify this, we will consider only the instances when they lie within the same 𝑋𝑍 plane at a given value of 𝑦. This allows us to focus on solving the following problem: 𝑦 𝑣 𝑡𝑦𝑣𝑡󰇛sinψsinα󰇜 This leads to the following: 𝑡 𝑦 𝑦 𝑣󰇛sinψsinα󰇜𝑣  Figure 3. Graphic of parabolic shot on target. Conversely, when ψ= 0, the shot describes a parabolic trajectory along the ground. This type of shot is rare in football. A study by Howard Masur [ 20 ] derived the equations for such a trajectory in the context of billiards. When both angles are zero, the shot follows a linear trajectory in its ground projection. Moreover, since ψ = 0, the ball remains on the ground, meaning its actual motion coincides with its projection. In this case, we apply the equations from the previous section. Consequently, we assume that both angles are nonzero in our analysis. In this section, we employ a simplified model, previously published in an earlier study [ 21 ], where angular velocity is not considered. The values x 0 and y 0 denote the initial position of the ball on the field, while v 0x and v 0y represent the initial velocity components at the moment of the kick. The parameter gdenotes the gravitational constant. 3.3. Goalkeeper Equations Based on the data analyst specializing in football with over 25 years of experience across all levels of competition, and because we aim to develop a simple algorithm, we have decided that the GK’s movement will follow a rectilinear trajectory. Thus, the equations are as follows: ˆ x(t)=ˆ x0+ˆ v0xt ˆ y(t)=ˆ y0+ˆ v0yt ˆ z(t)=ˆ z0+ˆ v0zt The values ˆ x0 , ˆy0 , and ˆz0 represent the GK’s initial position on the field. Similarly, ˆ v0x , ˆ v0y, and ˆ v0zdenote the GK’s initial velocity at the moment the player kicks the ball. 3.4. Build of xGOT Through the construction of the differential equations and the way we modeled the field, we are able to calculate the time instances for both the ball and the GK. However, to achieve our objective, we need to determine when both coincide, which only occurs under specific conditions. To simplify this, we will consider only the instances when they lie within the same XZ plane at a given value of y . This allows us to focus on solving the following problem: ˆ y0+ˆ v0t=y0+v0yt(sin ψsin α) This leads to the following: t=ˆ y0−y0 v0y(sin ψsin α)−ˆ v0y In this manner, we can calculate: - The initial distance between the ball and the GK, denoted as d0. - The distance between the ball and the GK when both share the same y-coordinate value, denoted as dgb. - The distance between the initial position of the GK and the goal, with respect to the y-coordinate, denoted as dg. Big Data Cogn. Comput. 2025,9, 64 6 of 13 With these definitions, we will define our value of xGOT as: xGOT =min1,  dg+dgb d0 The value obtained from the xGOT metric represents the probability of scoring a goal after the shot has been taken and is on target. This value is expressed on a scale from 0 to 1, where a higher xGOT value indicates a greater probability of scoring, while a lower xGOT value reflects a reduced likelihood of scoring. 4. Practical Applications of the Model This model evaluates the decision-making processes of GKs by analyzing their positioning and movement during critical game situations. The framework combines spatial, temporal, and event-based data to quantitatively assess a GK’s performance. Key variables include shot location, trajectory, ball speed, and the GK positioning at both the initiation and conclusion of the play. To further clarify these ideas, the authors present two examples of shots on goal to illustrate the final xGOT values obtained (Table 2, Figure 4). The first example (A) is a shot on goal that is saved by the goalkeeper, resulting in an xGOT value of 0.07. This indicates that the shot has a 7% chance of becoming a goal, which may be attributed to the low quality of the shot or the GK’s good performance. The second example (B) is a shot on goal that is not saved by the goalkeeper, resulting in an xGOT value of 0.82. This indicates that the shot has an 82% chance of becoming a goal, which may be due to the high quality of the shot or the GK’s poor performance. Table 2. An example of calculating the xGOT value for two types of shots on goal. Example Ball’s Initial Position Ball’s Final Position GK’s Initial Position GK’s Final Position A. Shot on goal stopped x = 89.0 m y = 34.7 m z=0m x = 104.5 m y = 38.0 m z = 0.7 m x = 103.9 m y = 38.9 m z=0m x = 104.5 m y = 38.0 m z = 0.7 m d0: 15.48 m; dgb: 0 m; dg: 1.10 m xGOT value = 0.07 (7%) B. Shot on goal scored x = 95.2 m y = 39.1 m z=0m x = 105.0 m y = 32.5 m z = 1.1 m x = 102.6 m y = 37.0 m z=0m x = 102.6 m y = 35.4 m z=0m d0: 7.69 m; dgb: 3.92 m; dg: 2.4 m xGOT value = 0.82 (82%) Abbreviations: d 0 , the initial distance between the ball and the GK; d gb , the distance between the ball and the GK at a given instant time; and d g , the distance between the initial position of the GK and the goal, with respect to the y-coordinate. Big Data Cogn. Comput. 2025, 9, x FOR PEER REVIEW 6 of 14 In this manner, we can calculate: - The initial distance between the ball and the GK, denoted as 𝑑. - The distance between the ball and the GK when both share the same y-coordinate value, denoted as 𝑑. - The distance between the initial position of the GK and the goal, with respect to the y-coordinate, denoted as 𝑑. With these definitions, we will define our value of xGOT as: 𝑥𝐺𝑂𝑇min󰇧1,𝑑𝑑 𝑑󰇨 The value obtained from the xGOT metric represents the probability of scoring a goal after the shot has been taken and is on target. This value is expressed on a scale from 0 to 1, where a higher xGOT value indicates a greater probability of scoring, while a lower xGOT value reflects a reduced likelihood of scoring. 4. Practical Applications of the Model This model evaluates the decision-making processes of GKs by analyzing their positioning and movement during critical game situations. The framework combines spatial, temporal, and event-based data to quantitatively assess a GK’s performance. Key variables include shot location, trajectory, ball speed, and the GK positioning at both the initiation and conclusion of the play. To further clarify these ideas, the authors present two examples of shots on goal to illustrate the final xGOT values obtained (Table 2, Figure 4). The first example (A) is a shot on goal that is saved by the goalkeeper, resulting in an xGOT value of 0.07. This indicates that the shot has a 7% chance of becoming a goal, which may be attributed to the low quality of the shot or the GK’s good performance. The second example (B) is a shot on goal that is not saved by the goalkeeper, resulting in an xGOT value of 0.82. This indicates that the shot has an 82% chance of becoming a goal, which may be due to the high quality of the shot or the GK’s poor performance. Figure 4. Expected goal on target (xGOT) model: d 0 , the initial distance between the ball and the GK; d gb , the distance between the ball and the GK at a given instant time; and d g , the distance between the initial position of the GK and the goal, with respect to the y-axis. Figure 4. Expected goal on target (xGOT) model: d 0 , the initial distance between the ball and the GK; d gb , the distance between the ball and the GK at a given instant time; and d g , the distance between the initial position of the GK and the goal, with respect to the y-axis. Big Data Cogn. Comput. 2025,9, 64 7 of 13 The model computes a ‘decision efficiency’ score. Using this score, a heatmap (Figure 5) can be generated to assist coaches in analyzing optimal decisions across various shot types. Figure 5illustrates the probability of scoring a goal as a function of the ball’s final position of the shot, based on the xGOT metric, for both straight-line and parabolic shots on target. The axis limits correspond to the actual dimensions of a professional football goal. The color bar on the right indicates the probability values associated with different colors, where a goal probability of 1.0 signifies that the shot on target always resulted in a goal. No recorded shots had a goal probability of zero. Areas of the goal represented by the corresponding blue color (goal probability of 0.0) indicate regions where no shots on target entered. Figure 5clearly demonstrates a positive relationship between the position of the shot on target, regardless of the shot type, and the probability of scoring. In this way, the model produces outputs such as maps of the optimal positioning zones, movement success probabilities, and comparative benchmarks against peers. This approach enables coaches to pinpoint areas for improvement and supports GKs in refining their anticipatory decision-making. Ultimately, it enhances their ability to prevent goals through effective positioning. To further clarify these concepts, the authors present four examples of shots on goal with varying final positions of the ball to illustrate the xGOT value spectrum (Figure 6). Heatmaps were generated from these examples to visualize high-risk goal zones (red areas), emphasizing the regions where GKs should position themselves to minimize the xGOT (blue areas). (A) is a heatmap of a foot shot with the GK positioned at the center of the goal (ball position: x = 34 m, y = 11 m, z = 0 m); (B) is a heatmap of a foot shot with the GK moving to the left (ball position: x = 34 m, y = 11 m, z = 0 m); (C) is a heatmap of a foot shot on target with the GK jumping to the right (ball position: x = 34 m, y = 11 m, z = 0 m); and (D) is a heatmap of a header shot from at the left side of the goal (ball position: x = 23 m, y = 5.50 m, z = 1.80 m). To simplify the examples, all shots were considered to have been conceded by the GK. Big Data Cogn. Comput. 2025, 9, x FOR PEER REVIEW 8 of 14 Figure 5. This heatmap illustrates the xand y-coordinates of the goal and the probability of scoring a goal after the shot has been taken and is on target. The x-axis represents the width of the goal (7.32 m), while the y-axis represents the height of the goal (2.44 m), corresponding to the dimensions of a real football goal. The GK is assumed to be positioned at the center of the goal. The color spectrum reflects the xGOT values of the shots on target that resulted in a goal, ranging from red to blue. Areas where the ball is more likely to arrive are shown in red (indicating high xGOT values), whereas areas where the ball is less likely to arrive are depicted in blue (indicating low xGOT values). Taking these calculations into account, the main practical application of this model is that GK coaches and analysts could use it to assess the strengths and weaknesses of both their own team’s GKs and opposing GKs, allowing for a more targeted and personalized approach to training and tactics. By understanding specific GKs’ tendencies, such as preferred positioning, reaction times, and areas of vulnerability, coaches can tailor their training sessions to address weaknesses and build on strengths. Additionally, this insight helps in developing tactical plans, such as determining which areas of the goal to target or when to adjust shooting techniques to exploit an opponent’s GK behavior. Moreover, this model goes beyond just tactical preparation. It can be extended to enhance player decision-making during critical moments in a match. For example, players can be trained to recognize when a GK is more likely to make a save based on the GK’s habits and positioning tendencies, allowing them to make better decisions about shot placement in real-time. This integration of GK analysis into player decision-making fosters a more strategic approach to both attacking and defending, ultimately improving the overall team performance. By leveraging these data, teams gain a competitive edge not only in game preparation but also in adapting to in-match dynamics for more effective play. Figure 5. This heatmap illustrates the xand y-coordinates of the goal and the probability of scoring a goal after the shot has been taken and is on target. The x-axis represents the width of the goal (7.32 m), while the y-axis represents the height of the goal (2.44 m), corresponding to the dimensions of a real football goal. The GK is assumed to be positioned at the center of the goal. The color spectrum reflects the xGOT values of the shots on target that resulted in a goal, ranging from red to blue. Areas where the ball is more likely to arrive are shown in red (indicating high xGOT values), whereas areas where the ball is less likely to arrive are depicted in blue (indicating low xGOT values). Big Data Cogn. Comput. 2025,9, 64 8 of 13 Big Data Cogn. Comput. 2025, 9, x FOR PEER REVIEW 9 of 14 Figure 6. Heatmap of xGOT based on the ball’s final position. Heatmap illustrating different examples of shots on goal: (A) A foot shot on target with the GK positioned at the center of the goal (ball position: x = 34 m, y = 11 m, z = 0 m); (B) a foot shot on target with the GK moving to the left (ball position: x = 34 m, y = 11 m, z = 0 m); (C) a foot shot on target with the GK jumping to the right (ball position: x = 34 m, y = 11 m, z = 0 m); and (D) a header shot from the left side of the goal (ball position: x = 23 m, y = 5.50 m, z = 1.80 m). To simplify the examples, all shots were considered to have been conceded by the GK. Figure 6. Heatmap of xGOT based on the ball’s final position. Heatmap illustrating different examples of shots on goal: (A) A foot shot on target with the GK positioned at the center of the goal (ball position: x = 34 m, y = 11 m, z = 0 m); (B) a foot shot on target with the GK moving to the left (ball position: x = 34 m, y = 11 m, z = 0 m); (C) a foot shot on target with the GK jumping to the right (ball position: x = 34 m, y = 11 m, z = 0 m); and (D) a header shot from the left side of the goal (ball position: x = 23 m, y = 5.50 m, z = 1.80 m). To simplify the examples, all shots were considered to have been conceded by the GK. Taking these calculations into account, the main practical application of this model is that GK coaches and analysts could use it to assess the strengths and weaknesses of both their own team’s GKs and opposing GKs, allowing for a more targeted and personalized Big Data Cogn. Comput. 2025,9, 64 9 of 13 approach to training and tactics. By understanding specific GKs’ tendencies, such as preferred positioning, reaction times, and areas of vulnerability, coaches can tailor their training sessions to address weaknesses and build on strengths. Additionally, this insight helps in developing tactical plans, such as determining which areas of the goal to target or when to adjust shooting techniques to exploit an opponent’s GK behavior. Moreover, this model goes beyond just tactical preparation. It can be extended to enhance player decision-making during critical moments in a match. For example, players can be trained to recognize when a GK is more likely to make a save based on the GK’s habits and positioning tendencies, allowing them to make better decisions about shot placement in real-time. This integration of GK analysis into player decision-making fosters a more strategic approach to both attacking and defending, ultimately improving the overall team performance. By leveraging these data, teams gain a competitive edge not only in game preparation but also in adapting to in-match dynamics for more effective play. Statistical Evaluation of the Shot Prediction Model The shot prediction model estimates the likelihood of a shot resulting in a goal based on spatial and temporal variables, including ball trajectory, ball velocity, and GK positioning. The primary objective of this algorithm was to evaluate GK performance and decisionmaking. To assess its efficacy, we employed k-fold cross-validation, achieving an Area Under the Curve–Receiver Operating Characteristic (AUC-ROC) score of 0.67 and an accuracy of 85%. These metrics were computed using the FIFA World Cup 2022 database described in Section 2. We used Python 3.11.9 code to read the data and classify shots as either saves or goals. To evaluate all the properties of our model, we used the R library within Python. The model validation is presented in Table 3below, where we compare the values of our model with those of the STATSBOMB model. Table 3. Comparison between own model and output from STATSBOMB model. Own Model (Mean ±DS) STATSBOMB Model (Mean ±DS) pValue d Cohen xGOT (total shots on goal) 0.38 ±0.12 0.33 ±0.09 0.05 - xGOT (goal shots) 0.73 ±0.08 0.55 ±0.09 <0.001 2.11 xGOT (shots saved) 0.19 ±0.03 0.20 ±0.04 0.48 - Abbreviations: xGOT, expected goals on target. Building on this framework [ 22 ], decision-making can be modeled as a game theory problem, where the GK must evaluate their positioning within the penalty area to identify the most advantageous position. As illustrated in the heatmap above, by knowing the initial positions of the ball and the GK, simulations can generate the optimal areas for the GK to position themselves prior to the shot. This ensures that, regardless of ball speed, the GK minimizes the required movement distance to make a save. 5. Comparation of xGOT Values Between Our Own Model and Outputs of STATSBOMB Model Table 3presents the results of a comparative analysis of the xGOT data generated using our proposed model and the model developed by STATSBOMB. For this analysis, the following variables were considered: the xGOT of total shots on goal, the xGOT of shots resulting in goals, and the xGOT of shots saved. A descriptive analysis was conducted by calculating the mean and standard deviation, while a comparative analysis was performed using an independent Student’s t-test. Statistical significance was established at p< 0.05. Additionally, effect sizes (Cohen’s d) were calculated to determine the practical significance of the findings, with thresholds defined as small (<0.2), medium (0.5), and large (>0.8). All