# Achievement Prediction and Performance Assessment System for Nations in the Asian Games
## 2 Materials and Methods
### Back-Propagation DEA Algorithm
\begin{table}
\begin{tabular}{c c c} \hline \hline
**No.** & **Nation** & **Participating Years** \\ \hline
1 & Afghanistan & 51, 54, 58, 62, 66, 74, 82, 90, 94, 02, 06, 10, 14, 18, 23 \\
2 & Bahrain & 74, 78, 82, 86, 90, 94, 98, 02, 06, 10, 14, 18, 23 \\
3 & Bangladesh & 78, 82, 86, 90, 94, 98, 02, 06, 10, 14, 18, 23 \\
4 & Bhutan & 86, 90, 94, 98, 02, 06, 10, 14, 18, 23 \\
5 & Brunei & 90, 94, 98, 02, 06, 10, 14, 18, 23 \\
6 & Cambodia & 54, 58, 62, 70, 74, 94, 98, 02, 06, 10, 14, 18, 23 \\
7 & _China_ & 74, 78, 82, 86, 90, 94, 98, 02, 06, 10, 14, 18, 23 \\
8 & _Chinese Taipei_ & 54, 58, 66, 70, 90, 94, 98, 02, 06, 10, 14, 18, 23 \\
9 & _Hong Kong_ & 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 02, 06, 10, 14, 18, 23 \\
10 & _India_ & 51, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 02, 06, 10, 14, 18, 23 \\
11 & _Indonesia_ & 51, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 02, 06, 10, 14, 18, 23 \\
12 & _Iran_ & 51,58,66, 70, 74, 82, 86, 90, 94, 98, 02, 06, 10, 14, 18, 23 \\
13 & Iraq & 74, 78, 82, 86, 06, 10, 14, 18, 23 \\
14 & Israel & 54, 58, 66, 70, 74 \\
15 & _Japan_ & 51, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 02, 06, 10, 14, 18, 23 \\
16 & Jordan & 86, 94, 98, 02, 06, 10, 14, 18, 23 \\
17 & Kazakhstan & 94, 98, 02, 06, 10, 14, 18, 23 \\
18 & Korea & 18, 23 \\
19 & Kuwait & 74, 78, 82, 86, 90, 94, 98, 02, 06, 10, 14, 18, 23 \\
20 & Kyrgyzstan & 94, 98, 02, 06, 10, 14, 18, 23 \\
21 & Laos & 74, 82, 90, 94, 98, 02, 06, 10, 14, 18, 23 \\
22 & Lebanon & 78, 82, 86, 90, 94, 98, 02, 06, 10, 14, 18, 23 \\
23 & _Macau_ & 90, 94, 98, 02, 06, 10, 14, 18, 23 \\
24 & _Malaysia_ & 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 02, 06, 10, 14, 18, 23 \\
25 & Maldives & 82, 86, 90, 94, 98, 02, 06, 10, 14, 18, 23 \\
26 & _Mongolia_ & 74, 78, 8290, 94, 98, 02, 06, 10, 14, 18, 23 \\
27 & Myanmar & 51, 54, 58, 62, 66, 70, 74, 78, 8290, 94, 98, 02, 06, 10, 14, 18, 23 \\
28 & Nepal & 51,58,66, 70, 74, 78, 82, 86, 90, 94, 98, 02, 06, 10, 14, 18, 23 \\
29 & North Borneo & 54, 58, 62 \\
30 & North Korea & 74, 78, 82,90,98, 02, 06, 10, 14, 18, 23 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Asian Games participating nations from 1951 to 2023. ### Operational Definitions

1. Population: The number of people in a nation or region, indicating demographic strength. The larger the population is, the higher the proportion of talented individuals in various sports, leading to victory. Conversely, when two nations achieve the same number of medals, the one with a smaller population is likely more efficient [2]. 2. Gross domestic product (GDP): All economic activities within a nation, regardless of who owns the production assets. For instance, if a foreign company establishes a subsidiary in the United States and even repatriates profits to its parent company in another nation, those profits are still part of the United States GDP [3]. A higher GDP signifies more substantial national economic power, indicating that wealthier nations can provide better public sports facilities, and sports professionals are more likely to receive social support [2; 47]. 3. Athletes: Athletes representing various Asian nations participate in the Asian Games. 4. Zero-sum game (ZSG): [PERSON] et al. [2] proposed that the traditional ranking based on gold, silver, and bronze medals constitutes a lexicographic multicriteria approach, leading to the overvaluation of gold medals. This results in nations that have not won gold but have silver and bronze being significantly ranked lower, creating a situation in which the overall sporting prowess of a nation is not accurately represented. The original data envelopment analysis model allows decision units to choose the weights of various output categories freely [49]. In this study, assigning higher weights to silver or bronze medals than gold could distort the findings. To avoid this scenario, [PERSON] et al. [2] integrated output to create a single output to reduce bias and achieve a more accurate assessment, serving as the calculation model for the relative efficiency of the integrated output.