# The Effect of Situational Variables on Women's Rink Hockey Match Outcomes
## 3 Results
The odds ratios (ORs) indicated that several factors increased the chances of winning the match: playing at home (in comparison to playing away), having a high-level team (in contrast to a low-level team), facing a low-level opposing team (versus a high-level opponent), and either drawing or winning at halftime (compared to losing). Among these factors, match status at halftime had the most substantial impact on the match outcome (\(\chi^{2}_{LR}=342.3\), \(df=2\), \(p<0.001\)), followed by the opponent's level (\(\chi^{2}_{LR}=176.0\), \(df=2\), \(p<0.001\)), team level (\(\chi^{2}_{LR}=175.0\), \(df=2\), \(p<0.001\)), and match location (\(\chi^{2}_{LR}=9.5\), \(df=1\), \(p=0.002\)). \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & & & \multicolumn{3}{c}{**95\% CI for \(\beta\)**} & \multicolumn{3}{c}{**95\% CI for**} & \\  & & & & \multicolumn{3}{c}{**OR**} & & \\
**Predictors** & \(\mathbf{b}\) & \(\mathbf{LL}\) & \(\mathbf{UL}\) & \(\mathbf{OR}\) & \(\mathbf{LI}\) & \(\mathbf{LS}\) & \(\mathbf{P_{\text{Wald}}}\) & \(\mathbf{P_{\text{LR}}}\) \\ \hline Match location & & & & & & & & 0.002 \\ Away (base) & & & & & & & & & \\ Home & 0.445 & 0.161 & 0.729 & 1.560 & 1.174 & 2.072 & 0.002 & \\ Team level & & & & & & & & \(<\)0.001 \\ Relegation (base) & & & & & & & & & \\ Remained & 1.374 & 0.956 & 1.793 & 3.952 & 2.601 & 6.006 & \(<\)0.001 & \\ Champions & 2.808 & 2.341 & 3.275 & 16.572 & 10.388 & 26.437 & \(<\)0.001 & \\ Opponent’s level & & & & & & & & \(<\)0.001 \\ Champions (base) & & & & & & & & \\ Remained & 1.473 & 1.112 & 1.834 & 4.364 & 3.042 & 6.260 & \(<\)0.001 & \\ Relegation & 2.836 & 2.376 & 3.297 & 17.053 & 10.761 & 27.022 & \(<\)0.001 & \\ \hline \hline \end{tabular} Note. AUC = area under the ROC curve; AIC = [PERSON]’s information criterion; ROC = comparison of models with ROC curves (chi-squared test); Se = sensitivity for cut-off point 0.5; Sp = specificity for cut-off point 0.5; \(p_{\text{HL}}\) = significance of the Hosmer-Lemeshow test.  
\end{table} 
Table 4: Parameters of the selected model to predict the match outcome. \begin{table}
\begin{tabular}{l l c c c c c c} \hline \hline
**Model** & **Predictors** & **AIC** & **AUC** & **Se** & **Sp** & \(\mathbf{p_{\text{HL}}}\) & **ROC** \\ \hline
1 & [PERSON], TeaLev, OppLev, ScoFir, MatStaHal & 1238.7 & 0.9163 & 82.3\% & 86.0\% & 0.436 & base \\
2 & [PERSON], [PERSON], ScoFir, MatStaHal & 1245.5 & 0.9151 & 79.0\% & 88.0\% & 0.009 & \(-0.12\%\) \\  & & & & & & & & (\(p=0.337\)) \\
3 & [PERSON], [PERSON], [PERSON], MatStaHal & 1245.7 & 0.9143 & 78.9\% & 88.1\% & 0.145 & \(-0.20\%\) \\  & & & & & & & (\(p=0.116\)) \\
4 & [PERSON], OppLev, MatStaHal & 1253.2 & 0.9105 & 78.9\% & 88.1\% & 0.247 & \(-0.58\%\) \\  & & & & & & & (\(p=0.004\)) \\
5 & MatLoc, TeaLev, OppLev, ScoFir & 1371.1 & 0.8933 & 83.1\% & 80.2\% & 0.849 & \(-2.30\%\) \\ \hline \hline \end{tabular} Note. AUC = area under the ROC curve; AIC = Akaike’s information criterion; ROC = comparison of models with ROC curves (chi-squared test); Se = sensitivity for cut-off point 0.5; Sp = specificity for cut-off point 0.5; \(p_{\text{HL}}\) = significance of the Hosmer-Lemeshow test.  
\end{table} 
Table 3: Statistics and goodness-of-fit indices for the five models with the lowest AIC. The logistic regression equation below was constructed based on the \(b\) coefficients listed in Table 4:  
\[ \begin{split}\text{logit (MatOut = Won | MatLoc TeaLev OppLev MatStaHal)}=-4.991+0.445\times\text{MatLoc + 1.374 \times TeaLea2 + 2.808 \times TeaLev3 + 1.473 \times OppLev2 + 2.836 \times OppLev3 + 1.496 \times MatStaHal2 + 3.023 \times MatStaHal3}\end{split} \]  
Subsequently, the logistic function presented below was employed to predict the likelihood of winning the match in 18 common scenarios of the analyzed competition:  
\[\Pr(\text{MatOut}=\text{Won | MatLoc TeaLev OppLev MatStaHal})=\frac{1}{1+\text{e}^{-\text{logit}}}\]  
Table 5 displays the 18 predictions.