## 3 Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & **VAR-1** & **VAR-2** & **VAR-3** & **VAR-4** & \multirow{2}{*}{**F**} & \multirow{2}{*}{**\(p\)**} \\  & **(n:306)** & **(n:306)** & **(n:420)** & **(n:380)** & & \\ \cline{2-6}  & **Mean \(\pm\) SD** & **Mean \(\pm\) SD** & **Mean \(\pm\) SD** & **Mean \(\pm\) SD** & & \\ \hline Goals & 2.68 \(\pm\) 16.7 & 2.86 \(\pm\) 1.63 & 2.71 \(\pm\) 1.77 & 2.81 \(\pm\) 1.63 & 0.879 & 0.452 \\ Fouls & 27.55 \(\pm\) 5.38  & 27.05 \(\pm\) 5.21  & 26.31 \(\pm\) 5.33  & 24.36 \(\pm\) 5.43 & 23.386 & \(<\)0.001 \\ Yellow Cards & 4.44 \(\pm\) 2.10 & 4.54 \(\pm\) 2.04 & 4.24 \(\pm\) 2.05 & 4.13 \(\pm\) 2.26 & 2.642 & 0.048 \\ Red Cards & 0.26 \(\pm\) 0.55 & 0.32 \(\pm\) 0.60 & 0.29 \(\pm\) 0.55 & 0.25 \(\pm\)0.53 & 1.192 & 0.312 \\ Offsides & 3.74 \(\pm\) 2.20 & 3.84 \(\pm\) 2.32 & 3.42 \(\pm\)2.08  & 3.89 \(\pm\) 2.17 & 3.39 & 0.009 \\ Penalties & 0.40 \(\pm\) 0.64 & 0.45 \(\pm\) 0.68 & 0.42 \(\pm\) 0.65 & 0.40 \(\pm\) 0.67 & 0.449 & 0.718 \\ \hline \hline \end{tabular} Note: VAR-1: the first season in which VAR was implemented; VAR-2: the second season in which VAR was implemented; VAR-3: the third season in which VAR was implemented; VAR-4: the fourth season in which VAR was implemented.  
\end{table} 
Table 4: Comparison of match performance indicators according to seasons after VAR implementation. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & **Estimate** & **SE** & \multirow{2}{*}{**exp (B)**} & \multicolumn{2}{c}{**95\% CI**} & \multirow{2}{*}{\(p\)**} \\ \cline{3-3} \cline{5-6}  & & & & **Lower** & & **Upper** \\ \hline Goals & \(-\)0.02 & 0.02 & 0.98 & 0.94 & 1.03 & 0.483 \\ Fouls & \(-\)0.19 & 0.01 & 0.82 & 0.81 & 0.84 & \(<\)0.001 \\ Yellow Cards & \(-\)0.06 & 0.02 & 0.94 & 0.91 & 0.98 & \(<\)0.001 \\ Red Cards & 0.01 & 0.07 & 1.01 & 0.87 & 1.16 & 0.943 \\ Offsides & \(-\)0.09 & 0.02 & 0.92 & 0.88 & 0.95 & \(<\)0.001 \\ Penalties & 0.25 & 0.07 & 1.29 & 1.13 & 1.46 & \(<\)0.001 \\ \hline \hline \end{tabular} Note: SE: standard error; 95% CI: 95% confidence interval.  
\end{table} 
Table 3: Generalized linear model for each variable. Figure 2: Density plot comparing seasonal match performance indicators before and after VAR implementation. While several performance indicators showed statistically significant differences before and after the implementation of VAR, the corresponding effect sizes, measured by [PERSON]'s \(d\), were mostly small, with the exception of fouls, which demonstrated a large effect. This discrepancy is not uncommon in studies with large datasets, where increased statistical power can yield low \(p\)-values even for modest differences. Small effect sizes indicate that although certain match performance indicators (such as penalties, offsides, and yellow cards) significantly changed from a statistical perspective, the practical magnitude of these changes per match is limited. To address this and gain a more nuanced interpretation, we supplemented our analysis with generalized linear models, which confirmed the relative weight of VAR's impact on each variable. Together, these statistical approaches provide a balanced understanding of the influence of VAR, both in terms of statistical reliability and practical significance.