Executive Summary

Vitória Viana Limonge Goeking; Juliano Domingues da Silva

Summary prepared by the ResumeAI tool, an artificial intelligence solution developed by Instituto Pecege focused on synthesis and writing.

This study aimed to identify and analyze the main statistical and tactical factors that influence the performance of Clube Atlético Mineiro, based on data from the 2023 and 2024 seasons. The investigation sought, through regression models, to understand which game variables correlate with performance metrics such as goal difference, wins, pass accuracy, and shots, providing a quantitative overview for the team’s strategic evaluation.

Football in Brazil is a relevant economic pillar, moving R$ 52.9 billion, the equivalent of 0.72% of the national GDP (CBF & EY, 2021). This magnitude is reflected in the complexification of club management, which has evolved into business models such as the Football Corporation (SAF). The sector’s resilience, with a 20% growth in the main clubs’ revenues in 2016 even during a crisis (Sousa et al., 2022), reinforces the need for data-driven strategies to ensure sustainability and competitive success.

In this context, the pursuit of competitive advantages has driven the use of data analysis in technical and tactical planning. Understanding the reasons for superior performance is a primary objective for coaches and scholars (Vendite, Vendite and Moraes, 2003). Statistical analysis has become a pillar for intelligence teams to optimize performance, dissecting information about their own team and opponents. Modern football demands high performance, making the scientific study of the sport indispensable for success (Cunha, Binotto and Barros, 2001).

The relevance of data analysis is recognized by organizations such as FIFA, which developed the FIFA Football Language tool for performance analysis. In the academic field, the application of statistical and machine learning techniques to predict results has gained prominence (Silva, Barros, and de Albuquerque, 2020), with authors like YU (2022) affirming the central role of data in the evolution of sports. However, despite global advancements, there is a gap in studies applying robust statistical models to specifically analyze the performance of Brazilian clubs.

This work addresses this gap, proposing an analysis focused on Clube Atlético Mineiro to identify the factors that enhance its performance. Unlike generic analyses, the study seeks to unveil the team’s particularities, offering applicable insights for the technical committee and management. The research is justified by the need to translate the volume of data from each match into strategic knowledge, contributing to the club’s advancement and to the literature on performance analysis in Brazilian football.

The research is quantitative and applied. A database was built from public sources, covering 139 matches of Clube Atlético Mineiro in the 2023 and 2024 seasons, in all championships played. The original dataset contained 25 attributes per match, including numerical (shots, ball possession, passes, fouls) and categorical (home team, stadium, championship, tactical formations) variables.

The data were processed for suitability for statistical modeling. The tactical schemes (of Atlético and the opponent) were reclassified into offensive, defensive, and balanced. Textual variables, such as lineup, were transformed into quantitative metrics, creating the indicators “lineup variation” and “substitution variation” to measure the proportion of different players compared to the previous match and assess the impact of rotation. Relevant categorical variables, such as championship and tactical scheme, were dummified for inclusion in the regression models.

The methodological premise is that “good performance” is a multifaceted concept, not measurable by a single metric. Therefore, the research was structured into four analysis scenarios, each with a different response variable: Scenario 1 (goal difference), Scenario 2 (binary win variable), Scenario 3 (pass accuracy), and Scenario 4 (number of shots on goal). This approach allows for a more complete understanding of the team’s performance.

To analyze the data, supervised regression models were applied. In Scenarios 1, 3, and 4 (continuous responses), multiple linear regression was used. In Scenario 2 (binary response), binary logistic regression was applied. Variable selection for the final models was enhanced by the Stepwise method, which iteratively tests the inclusion and exclusion of variables to find the model with the best fit and statistical significance. Model robustness was assessed by diagnostic tests, such as the Variance Inflation Factor (VIF) for multicollinearity, Shapiro-Francia tests for residual normality, and Breusch-Pagan and White tests for heteroscedasticity, ensuring the validity of the results (Gujarati, 2004).

Exploratory analysis revealed expected correlations, such as the positive one between ball possession and number of passes, and between total shots and shots on goal. The correlation matrix also pointed to a significant association between corners and number of shots, suggesting that set pieces are a relevant source of finishing. The distribution of results from the 139 matches showed a balance between wins and losses, with a predominance of draws, a pattern accentuated in the Brazilian Championship. The temporal analysis of lineup and substitution variation indicated that player rotation remained stable, close to the average.

In Scenario 1 (goal difference), the linear regression model, refined by the Stepwise method, identified six significant variables. The number of shots on goal and participation in the Campeonato Mineiro positively influenced the goal difference. In contrast, facing opponents with balanced or offensive tactical schemes, the number of yellow cards received, and the number of corner kicks in favor correlated negatively with the goal difference. This latter result suggests that, although corner kicks generate shots, their conversion into goals may be inefficient or the team becomes vulnerable to counter-attacks.

The analysis of Scenario 2 (probability of victory) used a logistic regression model. The results indicated that playing as the home team, the number of shots on goal, and the number of substitutions increase the chance of victory. On the other hand, ball possession showed a negative and significant correlation with the probability of winning. This is one of the most counterintuitive findings of the study, suggesting that a playing style with less possession, possibly more vertical and focused on quick transitions, is more effective for Atlético Mineiro than a control game. Facing opponents with balanced or offensive formations also decreased the probability of victory.

Scenario 3 (passing accuracy) presented methodological challenges. The initial model, after Stepwise, indicated that passes, variation in substitutions, and quantity of substitutions positively influence accuracy. However, the diagnosis revealed problems with non-adherence to the normality of residuals. The application of the Box-Cox transformation improved the model fit (adjusted R² rose from 0.193 to 0.533), indicating that participation in the Campeonato Mineiro, variation in the lineup, and the number of passes positively impact accuracy. Nevertheless, even after the transformation, the residuals did not follow a normal distribution and the model exhibited heteroscedasticity (White test). Such violations of the assumptions indicate that the results of this scenario should be interpreted with caution, as the validity of the significance tests may be compromised.

For Scenario 4 (number of shots on goal), the linear regression model identified two variables with a positive and significant impact: the number of passes and the number of corners. This result reinforces that a higher volume of passes creates more finishing opportunities and that corners are a fundamental mechanism for the team to generate danger. The diagnosis of this model was satisfactory, not presenting significant heteroscedasticity problems (White test), which gives greater reliability to its conclusions.

The performance of the models was evaluated comparatively. In the linear regression models, the Stepwise method improved the fit indicators (AIC, BIC) and increased the adjusted R², indicating that more parsimonious models were more efficient. In the logistic model of Scenario 2, the ROC curve resulted in an area under the curve (AUC) of 0.7691, indicating good discriminatory capacity to predict wins. The analysis of different cutoff points demonstrated the model’s flexibility: a cutoff of 0.5 maximized accuracy (69.8%), while lower values increased sensitivity and higher values, specificity.

The discussion of the results was enriched by comparison with the literature. The findings partially corroborate Santos et al. (2024), who also identified finishing on goal as a determining factor in Brazilian football. However, the discovery of the negative impact of ball possession on Atlético Mineiro’s victories contrasts with the general view that game control is always beneficial, revealing a tactical particularity. The negative relationship between yellow cards and goal difference aligns with the findings of Villa and Lozano (2016) in the Spanish league. Compared to Socin et al. (2021), who analyzed the 2013 Brazilian Championship, there was agreement on the positive relationship between corners and shots on goal, but divergence on the factors influencing passing accuracy, reinforcing that performance dynamics are specific to each club and context.

In summary, the analysis of the four scenarios allowed for a detailed understanding of the performance factors of Clube Atlético Mineiro. To increase the goal difference (Scenario 1), the team must focus on finishing efficiency, especially in the Campeonato Mineiro, and minimize yellow cards. To increase the probability of victory (Scenario 2), the results suggest a more direct and vertical playing style, with less possession, leveraging the home advantage and using substitutions strategically. To improve passing accuracy (Scenario 3), the volume of passes and lineup stability seem important, although conclusions are limited by statistical issues. To generate more shots on goal (Scenario 4), the strategy should focus on increasing the volume of passes and optimizing corner kicks. The main limitation of the study lies in the problems of adherence to statistical assumptions in the Scenario 3 model, which indicate the need for alternative modeling approaches.

For future research, it is suggested to deepen the investigation into non-normality and heteroscedasticity in the pass accuracy model, exploring nonlinear models or the inclusion of other variables. The incorporation of defensive variables (disarms, interceptions) as explanatory or as new response variables could provide a more complete panorama, balancing the analysis between offensive and defensive aspects. It is concluded that the objective was achieved: the main factors influencing the performance of Clube Atlético Mineiro in the 2023 and 2024 seasons were demonstrated through statistical modeling, revealing tactical and statistical particularities of the team.

This study aimed to identify and analyze the main statistical and tactical factors that influence the performance of Clube Atlético Mineiro, based on data from the 2023 and 2024 seasons. The investigation sought, through regression models, to understand which game variables correlate with performance metrics such as goal difference, wins, pass accuracy, and shots, providing a quantitative overview for the team’s strategic evaluation.

Football in Brazil is a relevant economic pillar, moving R$ 52.9 billion, the equivalent of 0.72% of the national GDP (CBF & EY, 2021). This magnitude is reflected in the complexification of club management, which has evolved into business models such as the Football Corporation (SAF). The sector’s resilience, with a 20% growth in the main clubs’ revenues in 2016 even during a crisis (Sousa et al., 2022), reinforces the need for data-driven strategies to ensure sustainability and competitive success.

In this context, the pursuit of competitive advantages has driven the use of data analysis in technical and tactical planning. Understanding the reasons for superior performance is a primary objective for coaches and scholars (Vendite, Vendite and Moraes, 2003). Statistical analysis has become a pillar for intelligence teams to optimize performance, dissecting information about their own team and opponents. Modern football demands high performance, making the scientific study of the sport indispensable for success (Cunha, Binotto and Barros, 2001).

The relevance of data analysis is recognized by organizations such as FIFA, which developed the FIFA Football Language tool for performance analysis. In the academic field, the application of statistical and machine learning techniques to predict results has gained prominence (Silva, Barros, and de Albuquerque, 2020), with authors like YU (2022) affirming the central role of data in the evolution of sports. However, despite global advancements, there is a gap in studies applying robust statistical models to specifically analyze the performance of Brazilian clubs.

This work addresses this gap, proposing an analysis focused on Clube Atlético Mineiro to identify the factors that enhance its performance. Unlike generic analyses, the study seeks to unveil the team’s particularities, offering applicable insights for the technical committee and management. The research is justified by the need to translate the volume of data from each match into strategic knowledge, contributing to the club’s advancement and to the literature on performance analysis in Brazilian football.

The research is quantitative and applied. A database was built from public sources, covering 139 matches of Clube Atlético Mineiro in the 2023 and 2024 seasons, in all championships played. The original dataset contained 25 attributes per match, including numerical (shots, ball possession, passes, fouls) and categorical (home team, stadium, championship, tactical formations) variables.

The data were processed for suitability for statistical modeling. The tactical schemes (of Atlético and the opponent) were reclassified into offensive, defensive, and balanced. Textual variables, such as lineup, were transformed into quantitative metrics, creating the indicators “lineup variation” and “substitution variation” to measure the proportion of different players compared to the previous match and assess the impact of rotation. Relevant categorical variables, such as championship and tactical scheme, were dummified for inclusion in the regression models.

The methodological premise is that “good performance” is a multifaceted concept, not measurable by a single metric. Therefore, the research was structured into four analysis scenarios, each with a different response variable: Scenario 1 (goal difference), Scenario 2 (binary win variable), Scenario 3 (pass accuracy), and Scenario 4 (number of shots on goal). This approach allows for a more complete understanding of the team’s performance.

To analyze the data, supervised regression models were applied. In Scenarios 1, 3, and 4 (continuous responses), multiple linear regression was used. In Scenario 2 (binary response), binary logistic regression was applied. Variable selection for the final models was enhanced by the Stepwise method, which iteratively tests the inclusion and exclusion of variables to find the model with the best fit and statistical significance. Model robustness was assessed by diagnostic tests, such as the Variance Inflation Factor (VIF) for multicollinearity, Shapiro-Francia tests for residual normality, and Breusch-Pagan and White tests for heteroscedasticity, ensuring the validity of the results (Gujarati, 2004).

Exploratory analysis revealed expected correlations, such as the positive one between ball possession and number of passes, and between total shots and shots on goal. The correlation matrix also pointed to a significant association between corners and number of shots, suggesting that set pieces are a relevant source of finishing. The distribution of results from the 139 matches showed a balance between wins and losses, with a predominance of draws, a pattern accentuated in the Brazilian Championship. The temporal analysis of lineup and substitution variation indicated that player rotation remained stable, close to the average.

In Scenario 1 (goal difference), the linear regression model, refined by the Stepwise method, identified six significant variables. The number of shots on goal and participation in the Campeonato Mineiro positively influenced the goal difference. In contrast, facing opponents with balanced or offensive tactical schemes, the number of yellow cards received, and the number of corner kicks in favor correlated negatively with the goal difference. This latter result suggests that, although corner kicks generate shots, their conversion into goals may be inefficient or the team becomes vulnerable to counter-attacks.

The analysis of Scenario 2 (probability of victory) used a logistic regression model. The results indicated that playing as the home team, the number of shots on goal, and the number of substitutions increase the chance of victory. On the other hand, ball possession showed a negative and significant correlation with the probability of winning. This is one of the most counterintuitive findings of the study, suggesting that a playing style with less possession, possibly more vertical and focused on quick transitions, is more effective for Atlético Mineiro than a control game. Facing opponents with balanced or offensive formations also decreased the probability of victory.

Scenario 3 (passing accuracy) presented methodological challenges. The initial model, after Stepwise, indicated that passes, variation in substitutions, and quantity of substitutions positively influence accuracy. However, the diagnosis revealed problems with non-adherence to the normality of residuals. The application of the Box-Cox transformation improved the model fit (adjusted R² rose from 0.193 to 0.533), indicating that participation in the Campeonato Mineiro, variation in the lineup, and the number of passes positively impact accuracy. Nevertheless, even after the transformation, the residuals did not follow a normal distribution and the model exhibited heteroscedasticity (White test). Such violations of the assumptions indicate that the results of this scenario should be interpreted with caution, as the validity of the significance tests may be compromised.

For Scenario 4 (number of shots on goal), the linear regression model identified two variables with a positive and significant impact: the number of passes and the number of corners. This result reinforces that a higher volume of passes creates more finishing opportunities and that corners are a fundamental mechanism for the team to generate danger. The diagnosis of this model was satisfactory, not presenting significant heteroscedasticity problems (White test), which gives greater reliability to its conclusions.

The performance of the models was evaluated comparatively. In the linear regression models, the Stepwise method improved the fit indicators (AIC, BIC) and increased the adjusted R², indicating that more parsimonious models were more efficient. In the logistic model of Scenario 2, the ROC curve resulted in an area under the curve (AUC) of 0.7691, indicating good discriminatory capacity to predict wins. The analysis of different cutoff points demonstrated the model’s flexibility: a cutoff of 0.5 maximized accuracy (69.8%), while lower values increased sensitivity and higher values, specificity.

The discussion of the results was enriched by comparison with the literature. The findings partially corroborate Santos et al. (2024), who also identified finishing on goal as a determining factor in Brazilian football. However, the discovery of the negative impact of ball possession on Atlético Mineiro’s victories contrasts with the general view that game control is always beneficial, revealing a tactical particularity. The negative relationship between yellow cards and goal difference aligns with the findings of Villa and Lozano (2016) in the Spanish league. Compared to Socin et al. (2021), who analyzed the 2013 Brazilian Championship, there was agreement on the positive relationship between corners and shots on goal, but divergence on the factors influencing passing accuracy, reinforcing that performance dynamics are specific to each club and context.

In summary, the analysis of the four scenarios allowed for a detailed understanding of the performance factors of Clube Atlético Mineiro. To increase the goal difference (Scenario 1), the team must focus on finishing efficiency, especially in the Campeonato Mineiro, and minimize yellow cards. To increase the probability of victory (Scenario 2), the results suggest a more direct and vertical playing style, with less possession, leveraging the home advantage and using substitutions strategically. To improve passing accuracy (Scenario 3), the volume of passes and lineup stability seem important, although conclusions are limited by statistical issues. To generate more shots on goal (Scenario 4), the strategy should focus on increasing the volume of passes and optimizing corner kicks. The main limitation of the study lies in the problems of adherence to statistical assumptions in the Scenario 3 model, which indicate the need for alternative modeling approaches.

For future research, it is suggested to deepen the investigation into non-normality and heteroscedasticity in the pass accuracy model, exploring nonlinear models or the inclusion of other variables. The incorporation of defensive variables (disarms, interceptions) as explanatory or as new response variables could provide a more complete panorama, balancing the analysis between offensive and defensive aspects. It is concluded that the objective was achieved: the main factors influencing the performance of Clube Atlético Mineiro in the 2023 and 2024 seasons were demonstrated through statistical modeling, revealing tactical and statistical particularities of the team.

References:
Caldas, R. I. da S. (2019). Sociedade anônima do futebol: o novo paradigma do futebol brasileiro. Trabalho de Conclusão de Curso (Graduação em Direito), Faculdade Dom Helder Câmera, Belo Horizonte.
Confederação Brasileira de Futebol (CBF) & EY. (2021). Relatório de Impacto do Futebol Brasileiro na Economia. Rio de Janeiro: CBF.
Cunha, S. A., Binotto, M. R., & Barros, R. M. L. (2001). Análise da variabilidade na medição de posicionamento tático no futebol. Revista Paulista de Educação Física, 15(2), 111-116.
Gujarati, D. N. (2004). Basic econometrics. McGraw-Hill.
Santos, J. F. de S., De Araújo Jr, W. L., Leonel, D. F., & Lopes, F. J. G. (2024). Quais variáveis de desempenho técnico e tático diferenciam as equipes de futebol do campeonato brasileiro masculino série A?. Revista Brasileira de Futsal e Futebol, 16(64), 97-102.
Silva, A. B. L., Barros, K. N. N de O. B., & De Albuquerque, M. A. (2020). Modelagem via árvore de decisão para previsão de jogos de futebol. Research, Society and Development, 9(9).
Soncin, R., Lima, W. P., Lopes, R., Diniz, R., Amadio, A. C., Serrão, J. C., & Mezêncio, B. (2021). Análise do scout do campeonato brasileiro de futebol 2013. Revista Brasileira de Futsal e Futebol, 13(56), 717-725.
Sousa, R. B. (2019). A influência da limitação de toques na bola no comportamento tático e na rede de interações de jogadores de futebol durante pequenos jogos. Escola de Educação Física, Fisioterapia e Terapia Ocupacional da UFMG.
Vendite, L. L., De Moraes, A. C., & Vendite, C. C. (2003). Scout no futebol: uma análise estatística. CONEXÕES: Campinas, 1(2), 115-224.
Villa, G., & Lozano, S. (2016). Assessing the scoring efficiency of a football match. Escuela Superior de Ingenieros, University of Seville, Camino de los Descubrimientos, s/n, 41092 Seville, Spain.
YU, W. (2022). Football Result Prediction Based on Machine Learning. Faculty of Science and Technology, Beijing Normal University-Hong Kong Baptist University United International College, China.
Caldas, R. I. da S. (2019). Sociedade anônima do futebol: o novo paradigma do futebol brasileiro. Trabalho de Conclusão de Curso (Graduação em Direito), Faculdade Dom Helder Câmera, Belo Horizonte.
Confederação Brasileira de Futebol (CBF) & EY. (2021). Relatório de Impacto do Futebol Brasileiro na Economia. Rio de Janeiro: CBF.
Cunha, S. A., Binotto, M. R., & Barros, R. M. L. (2001). Análise da variabilidade na medição de posicionamento tático no futebol. Revista Paulista de Educação Física, 15(2), 111-116.
Gujarati, D. N. (2004). Basic econometrics. McGraw-Hill.
Santos, J. F. de S., De Araújo Jr, W. L., Leonel, D. F., & Lopes, F. J. G. (2024). Quais variáveis de desempenho técnico e tático diferenciam as equipes de futebol do campeonato brasileiro masculino série A?. Revista Brasileira de Futsal e Futebol, 16(64), 97-102.
Silva, A. B. L., Barros, K. N. N de O. B., & De Albuquerque, M. A. (2020). Modelagem via árvore de decisão para previsão de jogos de futebol. Research, Society and Development, 9(9).
Soncin, R., Lima, W. P., Lopes, R., Diniz, R., Amadio, A. C., Serrão, J. C., & Mezêncio, B. (2021). Análise do scout do campeonato brasileiro de futebol 2013. Revista Brasileira de Futsal e Futebol, 13(56), 717-725.
Sousa, R. B. (2019). A influência da limitação de toques na bola no comportamento tático e na rede de interações de jogadores de futebol durante pequenos jogos. Escola de Educação Física, Fisioterapia e Terapia Ocupacional da UFMG.
Vendite, L. L., De Moraes, A. C., & Vendite, C. C. (2003). Scout no futebol: uma análise estatística. CONEXÕES: Campinas, 1(2), 115-224.
Villa, G., & Lozano, S. (2016). Assessing the scoring efficiency of a football match. Escuela Superior de Ingenieros, University of Seville, Camino de los Descubrimientos, s/n, 41092 Seville, Spain.
YU, W. (2022). Football Result Prediction Based on Machine Learning. Faculty of Science and Technology, Beijing Normal University-Hong Kong Baptist University United International College, China.

---

Executive summary from the Final Course Work of the Specialization in Data Science and Analytics of the MBA USP/Esalq

_{Learn more about the course; click here:}