# Leveraging the Chain on Goals Model in Football: Applications for Attack and Defensive Play
## 3 Results  
Considering the definitions of the variables presented in Tables 1 and 2 illustrates the distribution of values that were calculated for all variables mentioned along the entire season, including mean, standard deviation, and percentile distribution, for both leagues. In the overall dimension only, defensive performance (measured as the average number of goals conceded per match) and GSAA showed statistically significant differences between the two leagues (\(p\) = 0.03 and d\(=-0.57\); \(p\) \(<\) 0.001 and d \(=-1.26\), respectively). Table 3 presents the reference values for the four practical concepts in each league. Significant differences were observed only in off-ball movement (\(p<0.001\) and d = 1.31) and team's positioning (\(p<0.001\) and d = \(-1.34\)) when comparing the two leagues. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline  & **LigaF** & **LaLiga** & \(p\)**Value** & \multicolumn{3}{c}{**LigaF**} & \multicolumn{3}{c}{**LaLiga**} \\ \cline{2-9}
**Variable** & **Mean \(\pm\) SD** & **Mean \(\pm\) SD** & \multicolumn{3}{c}{**Weakness Index (20 th)**} & \multicolumn{1}{c}{**Strength Index (80 th)**} & \multicolumn{1}{c}{**Weakness Index (30 th)**} & \multicolumn{1}{c}{**Strength Index (70 th)**} \\ \hline Performance & 1.41 \(\pm\) 0.68 & 1.36 \(\pm\) 0.54 & 0.63 & 0.94 & 2.02 & 1.05 & 1.56 \\ Offensive & 1.58 \(\pm\) 0.95 & 1.32 \(\pm\) 0.48 & 0.58 & 1.05 & 2.02 & 1.00 & 1.53 \\ performance & \(-\)1.57 \(\pm\) 0.55 & \(-\)1.32 \(\pm\) 0.33 & _0.03_ & \(-\)1.93 & \(-\)0.97 & \(-\)1.45 & \(-\)1.17 \\ GSAA & \(-\)0.19 \(\pm\) 0.19 & 0.00 \(\pm\) 0.11 & \(<\)0.001 & \(-\)0.36 & 0.04 & \(-\)0.08 & 0.06 \\ PV & 1.25 \(\pm\) 0.67 & 1.34 \(\pm\) 0.28 & 0.39 & 0.84 & 1.52 & 1.14 & 1.50 \\ xG & 1.39 \(\pm\) 0.74 & 1.30 \(\pm\) 0.31 & 0.83 & 0.95 & 1.69 & 1.12 & 1.37 \\ xGOT & 1.35 \(\pm\) 0.67 & 1.32 \(\pm\) 0.34 & 0.85 & 0.95 & 1.74 & 1.12 & 1.50 \\ PVA & \(-\)1.25 \(\pm\) 0.33 & \(-\)1.34 \(\pm\) 0.18 & 0.50 & \(-\)1.55 & \(-\)1.03 & \(-\)1.42 & \(-\)1.24 \\ xGA & \(-\)1.39 \(\pm\) 0.40 & \(-\)1.30 \(\pm\) 0.21 & 0.27 & \(-\)1.64 & \(-\)0.97 & \(-\)1.434 & \(-\)1.14 \\ xGOTA & \(-\)1.38 \(\pm\) 0.42 & \(-\)1.32 \(\pm\) 0.25 & 0.30 & \(-\)1.60 & \(-\)0.93 & \(-\)1.41 & \(-\)1.14 \\ \hline \hline \end{tabular} Abbreviations: GSAA, goals saved above average; PV, possession value; xG, expected goals; xGOT, expected goals on target; SD, standard deviation.  
\end{table} 
Table 2: The values for the variables of the overall dimension and chain in goals model metrics in each league. \(p\) value for between-groups statistical significance (Independent Student’s \(t\)-test) are reported. For LigaF, the correlation coefficients between off-the-ball movement and player's offensive quality were r = \(-\)0.1207 and R2 = 0.0146 and between team's positioning and player's defensive quality were r = \(-\)0.1074 and R2 = 0.0115. For LaLiga, the correlation coefficients between off-the-ball movement and player's offensive quality were r = \(-\)0.1324 and R2 = 0.0175 and between team positioning and player's defensive quality were r = \(-\)0.0280 and R2 = 0.008. In all cases, the level of correlation was trivial. This implied that the practical concepts of each phase of the game could be considered independent of one another, ensuring that the weakness or strength of one phase did not influence the others. Figures 1 and 2 establish the relationship of off-ball movement and player's offensive quality and team's positioning and player's defensive quality for all teams in the women's and men's leagues, respectively. From these figures, the strengths and weaknesses of each team can be identified, whether in the defensive or attack phase, at any given point in time or at the conclusion of the season, as demonstrated in this study. In the defensive evaluation figures, the x-coordinate represents the team's positioning, while the y-coordinate represents the player's defensive quality.