## 2 Materials and Methods
### Statistical Analysis  
The statistical analysis in this study focuses on identifying and classifying new dimensions in high-level women's basketball positions based on data from the last three seasons of the Women's Euroleague. Several steps and statistical methods were employed to achieve this objective.  
A descriptive analysis was conducted to examine the average performance of players based on their listed positions. While the traditional classification includes five positions (PG, SG, SF, PF, and C), teams often report hybrid roles (e.g., G or F). Therefore, seven positional categories were included in the analysis.  
Firstly, variables were normalized per minute played. This step was crucial to ensure comparability among players and to minimize the effect of differences in playing time. Normalization adjusted all performance statistics proportionally, providing a more accurate basis for subsequent analysis [35].  
Next, a descriptive analysis of traditional positions was conducted, offering an overview of the average characteristics and performance of the five classic basketball positions: point guard, shooting guard, small forward, power forward, and center [38]. This initial approach identified trends and variations within each position, providing contextual insights for more advanced analyses.  
A one-way ANOVA with Games-Howell post hoc tests was then used to identify variables with significant differences (\(p<0.05\)) among traditional positions. The Games-Howell tests were selected for their ability to handle variations in variances and unequal sample sizes, ensuring a robust evaluation of significant group differences.  
\begin{table}
\begin{tabular}{l l} \hline
**Variable** & **Definition** \\ \hline RT & Total number of rebounds grabbed by a player \\ AS & Number of assists made by a player \\ FP & Total number of fouls committed by a player \\ BP & Total number of turnovers a player has made against the defense \\ BR & Number of steals made by a player in defense \\ TP & Number of blocks made by a player against the opponent’s offensive shots \\ \hline \end{tabular} Note.: Description of the game variables used in the statistical analysis of player performance in the Women’s Euroleague.  
\end{table}
Table 4: _Cont._Principal component analysis (PCA) was applied to reduce the dimensionality of the game-related statistics dataset. This technique transformed a set of potentially correlated variables into a set of uncorrelated variables, referred to as principal components. PCA identified the most significant variables contributing to differences in performance and player roles, providing a clearer understanding of the underlying dimensions of performance [27; 39].  
Finally, k-means clustering was performed to identify current player roles based on statistical analysis. This method grouped players into clusters according to similarities in their performance data, optimizing the number of clusters. The analysis revealed emerging patterns and roles among players beyond traditional positions, enabling a more updated and accurate classification [40].  
Statistical analyses were conducted using Jamovi 2.5.3, an open-source statistical analysis platform. Jamovi was chosen for its user-friendly interface and robust capabilities for performing complex analyses efficiently. Results are shown as mean \(\pm\) standard deviation, and the statistical significance threshold was set at \(p\) < 0.05.