Table 1 in the appendix presents various sports analytics data sourced from kaggle.com. It contains detailed information on over 10,000 professional football players from various European leagues and seasons. The data include both biographical variables (e.g., height, age) and performance metrics (e.g., goals per 90 minutes, assists, yellow cards, minutes played, injuries, player value).

Before analysis, the dataset was cleaned to ensure accuracy and consistency. Observations with missing values in key variables were removed. Outliers, such as extreme values in player value or minutes played, were examined and excluded if they resulted from data entry errors. All variables were carefully labeled, and some were encoded to enable regression analysis.

The sport analytics variables include the height of a player, the age of a player, number of games played by a player, goals scored by a player per 90 minutes, assists by a player per 90 minutes, number of times a player’s been given a yellow card per 90 minutes, number of times a player’s been given 2 yellow cards per 90 minutes, goals conceded only by a goalkeeper per 90 minutes, number of times a goalkeeper doesn’t concede per 90 minutes, number of minutes played by a player, number of days injured in the player’s career, number of games in which a player didn’t play due to injury, number of awards won by a player, current value of a player according to transfermarkt in Euros, highest valued price of a player in Euros, position of the player (Goalkeeper, 1, Defender, 2, midfield, 3, Attack, 4), dummy variable 1 for winger and 0 for not a winger.

Table 1 provides descriptive statistics for various football analytic variables used in the analysis. The height has 10,754 observations with a mean of 181.24 cm and a standard deviation of 6.97, ranging from a minimum of 156 cm to a maximum of 206.

The age has 10,754 observations with a mean of 26.042 years and a standard deviation of 4.778, ranging from a minimum of 15 years old to a maximum of 43 years old.

The appearance has 10,754 observations with a mean of 36.407 games and a standard deviation of 26.527, ranging from a minimum of 0 to a maximum of 107.

The goals have 10,754 observations with a mean of 0.16 goals per 90 minutes and a standard deviation of 0.236, ranging from a minimum of 0 goals to a maximum of 11.25.

The assists have 10,754 observations with a mean of 0.087 per 90 minutes and a standard deviation of 0.143, ranging from a minimum of 0 to a maximum of 4.

The yellowcards have 10,754 observations with a mean of 0.19 per match and a standard deviation of 0.432, ranging from a minimum of 0 to a maximum of 30.

The scatter plot Figure 1 shows an interesting connection between the number of goals scored and the number of minutes played by each footballer. It is clear that the number of goals scored positively correlates with the number of minutes played, suggesting that the higher number of minutes contributes to more goals.

The scatter plot Figure 2 shows an insightful connection between the number of goals scored and the value of each footballer. It is clear that the number of goals scored positively correlates with the highest market value of players, suggesting that players who score a lot of goals are valued very highly.

The scatter plot Figure 3 shows the link between the number of goals scored and the current value of each footballer. It is clear that the number of goals scored positively correlates with a player’s current value, suggesting that the higher number of goals scored is associated with a higher current value.

The scatter plot Figure 4 shows a connection between the number of games a player is injured for and the number of minutes they have played. It is clear that the number of games where the player is injured correlates positively and strongly with the number of minutes played, suggesting that the higher number of minutes played contributes to more injuries.

The scatter plot Figure 5 shows a link between the number of goals scored and the position played by each footballer. There is a strong positive correlation between the number of goals and where the player plays, illustrating that the higher the player is up the pitch i.e. striker, the more goals they will score.

The scatter plot Figure 6 displays an association between the number of days a player is injured for and the number of minutes played by each footballer. It is clear that the number of days injured positively correlates with the number of minutes played, suggesting that more minutes lead to longer injury time.

The scatter plot Figure 7 shows an interesting relationship between the number of yellow cards received and the number of clean sheets achieved by each goalkeeper. There is a slightly negative correlation between number of yellow cards and clean sheets, suggesting that the more yellow cards the less clean sheets, or in other words more games where a goal is conceded.

The scatter plot Figure 8 shows an interesting connection between the number of clean sheets and the age of a football player. The diagram shows that the number of clean sheets achieved by a goalkeeper positively correlates with their ages. This suggests that the older the player, the more clean sheets they have.

The scatter plot Figure 9 presents a relationship between the number of yellow cards and second yellow cards received by each football player. There is a weakly positive correlation between receiving the yellow card once and again for the second time in a match. This illustrates that one yellow card has a high chance of leading to a second.

Table 2 examines the relationship between the dependent variable, minutes played, and several independent variables, including goals, yellow cards, assists, games injured, and age. Each column represents a different regression model, incorporating various combinations of these independent variables to understand the impact of independent variables on the dependent variables. The p values indicate the statistical significance of coefficients where p < 0.01, p < 0.05, and p < 0.1 (indicating ***, **, and *; respectively). The positive coefficient of the “goals” variable suggests that scoring more goals is associated with more minutes played. The coefficient of goals is significant in all models. For “yellow cards”, the negative and significant coefficient indicates that receiving more yellow cards reduces the minutes played due to the disciplinary actions or performance issues. For the “assists” variable, positive coefficients suggest that players with more assists tend to play significantly more minutes because they are the key to more goals being scored. For the “games injured” variable, positive but small coefficients imply a minor increase in minutes played with more games injured. For the “age” variable, a positive coefficient in model 5 suggests that all the players may play more minutes, perhaps due to more experience or being cheaper to acquire to play for a team.

Robust standard errors in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1.

Table 3 examines the relationship between the dependent variable, highest_value, and several independent variables, including goals, awards, position_encoded, assists, and age. Each column represents a different regression model, incorporating various combinations of these independent variables to understand the impact of independent variables on the dependent variables. The p values indicate the statistical significance of coefficients where p < 0.01, p < 0.05, and p < 0.1 (indicating ***, **, and *; respectively). For the “goals” variable, the coefficients are consistently positively significant, indicating that scoring more goals is associated with a higher value for the player. For the “awards” variable, we can see a positive and highly significant coefficient across all models, therefore suggesting that receiving more awards significantly increases a player’s value. For the “position_encoded” variable, we can see a positive and significant relationship, indicating that higher encoded positions (e.g. 4 being a striker, 3 a midfielder, 2 a defender, and 1 being a goalkeeper) mean a higher value for the player. In other words, a striker is more likely to be worth more than a goalkeeper. For the “assists” variable, we can see positive and significant coefficients in models 4 to 6, showing that achieving more assists enhances the player’s value. The coefficient of the “age” variable, is negative and significant in model 6, implying that all of the player’s values tend to be lower as they get older.

Robust standard errors in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1.

We applied log transformation to the monetary variables (highest_value). The main results remain similar and robust.

Table 4(a) and Table 4(b) examine the relationship between the dependent variable, position_encoded, and several independent variables, including goals, yellowcards, assists, appearance, height, award, highest_value, and current_value. Each column represents a different regression model, incorporating various combinations of these independent variables to understand the impact of independent variables on the dependent variables. The p values indicate the statistical significance of coefficients where p < 0.01, p < 0.05, and p < 0.1 (indicating ***, **, and *; respectively). For the “goals” variable, the coefficients are consistently positively significant, indicating that scoring more goals is associated with a higher value of position encoded (e.g. goals are scored more by strikers than goalkeepers). For the “yellow cards” variable, we can see a slightly positive and significant coefficient across all models, therefore suggesting that receiving more yellow cards correlates with an encoded position of lower values, potentially reflecting more aggressiveness

Robust standard errors in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1.

and fouls closer to the goals by defenders and midfielders. For the “assists” variable, we can see a positive and significant relationship, showing that assists tend to be made by higher encoded positions (e.g. 4 being a striker, 3 a midfielder, 2 a defender, and 1 being a goalkeeper). The coefficient of the “appearance” variable is slightly positive and significant, indicating that more appearances are correlated with lower encoded positions (e.g. a goalkeeper will play more than strikers). The coefficient of the “height” variable is negative and significant, implying that taller players are more likely to occupy lower encoded positions like goalkeepers and defenders. The coefficient of “awards” is negative and significant, suggesting an inverse relationship between awards and encoded positions, which might be a reflection of the distribution of awards amongst different position types. The coefficient of “highest_value” is positive and significant, indicating that higher encoded positions tend to be valued more. For “current_value”, the coefficient is negative and significant, suggesting that players with high current values may occupy positions with lower encoded values.

Although some outcomes (minutes played) are count variables and others (position_encoded) are ordinal, OLS was chosen for simplicity and interpretability. To ensure robustness, we also tested alternative specifications using Poisson and ordered logit models. The results remained consistent in direction and significance.

Future research could expand on this study in several ways. Firstly, additional and more complicated variables, such as Expected Goals and the value of each possession, can be added to see how each performance indicator changes relative to new data. Secondly, Artificial Intelligence based models can be used to help dive deeper into the causes of each event, provide more comprehensive data and refine the data set in order to identify outliers that might not directly impact each performance indicator. Future studies could also explore the psychological factors or other aspects of players that might link to their performance and overall value.

League-mix biases, potential omitted variables (team strength, salary), and correlations do not establish causality.