## 2 Methods
### Data Analysis Process  
The statistical significance level for data processing and analysis was set to 0.05, and the IBM SPSS 24.0 ver. was used. First, descriptive statistics of data were carried out. Each game record's mean and standard deviation (SD) was calculated for descriptive statistics. To verify differences in game records depending on winning and losing groups in the PIH games, the Mann-Whitney U test, a non-parametric statistical technique, was performed. This was applied because the game records of some study variables did not meet the basic assumptions of parametric statistics.  
Second, a decision tree analysis was applied to explore game records affecting winning and losing. A classification and regression tree (CART) was applied for the algorithm to apply the decision tree analysis. CART is a decision tree method that determines and classifies the relationship between dependent and independent variables. The CART algorithm is practical if the dependent variables act as category data. The result of CART is a classification tree or a regression tree, depending on the type of independent variable [19]. If the explanation and prediction power is the highest in the relationship between dependent and independent (prediction) variables, the decision tree is classified as optimal separation and child nodes are selected if estimated errors are the lowest. The CART algorithm shows the highest utilization in the decision tree analysis. Figure 1 is the process structure of the CART algorithm.  
For the precise application method of the CART algorithm, this study tried to produce optimal separation standards by setting improvement levels and decreasing variance to 0.001. For a simple model of decision-making, a three-step depth of the tree, five-step parent node, and three-step child node were applied.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Subject** & **Event** & & **Teams** \\ \hline Ostrava 2021 & & USA & CAN \\ World Para Ice Hockey & 20 & RUS & KOR \\ World Championships & & NOR & ITA \\  & & CZE & SVK \\ \hline Ostersund 2021 & & CHN & FIN \\ World Para Ice Hockey & 15 & GER & JPN \\ Championships & & POL & SWE \\ \hline Berlin 2021 & & GER & ITA \\ World Para Ice Hockey & 15 & JPN & NOR \\ Paralympic Winter Games & & SVK & SWE \\ Qualification Tournament & & & \\ \hline Beijing 2022 & & USA & CAN \\ Paralympic & 16 & KOR & CZE \\ Winter Games & & ITA & CHN \\  & & SVK & RUS \\ \hline \hline \end{tabular}
\end{table}
Table 1: Research subjects and variables.  
The standard error, risk estimate, and classification accuracy index were calculated to ascertain the adequacy of the decision model. To rank the main game factors classifying a winning group and a losing group, the normalized importance (NI) index was calculated. The NI index indicates the relative importance of variables affecting the relationship between target and prediction variables among the total input variables in the decision tree analysis. The prediction variable chiefly affecting outcomes was set to 100, and the NI index indicates relative influence compared with the standard [19].  
In applying the decision tree analysis, this study selected three clear goals. First, winning and losing prize-determining factors were explored, except the total goals generated in each game. Second, the winning and losing factors were explored by removing total goals and goals in each period. Third, an analysis was performed by excluding total goals, period goals, and shot goals. These are the known variables directly affecting a game's winning and losing. Therefore, those variables were excluded from prediction variables to draw detailed results in analyzing game factors that influence winning and losing in PIH games. Finally, records connected to direct winning and losing by step were excluded, and this study tried to explore winning and losing, along with prize-winning determinants based on game detail variables as Table 2.