# Achievement Prediction and Performance Assessment System for Nations in the Asian Games
## 2 Materials and Methods
### Back-Propagation DEA Algorithm
We approved the competitive fluctuations in the efficiency prediction of Asian nations' mega-sports events, in which small- and medium-sized datasets are performing only as receiving and adopting regulatory bodies. The limitation of the study is that the conceptual framework and analysis considered a suitable quantification condition where other factors such as GDP, population, team size (athletes), medal weights calculation (ZSG), efficiency, and medals won are supportive. However, qualitative data and indicators were not considered in this study. Future research suggestions include investigating techniques that can improve the performance of artificial neural networks as proposed in retraining neural networks or deep learning frameworks applied to dynamically changing conditions. Following the previous studies, we aim to establish a linkage between the DEA method and artificial neural networks, and we propose an alternative way that combines DEA with ANN algorithms to predict the DEA efficiency of new DMUs to an Asian Games performance assessment system. A substantial body of literature validates the ideal outcomes of using DEA for performance assessment in mega-sports events. However, this study is the first publication to integrate DEA and ANNs, offering possibilities and research directions for the theoretical development of DEA-ANN models in the performance management of mega-sports events. We present an advanced performance assessment system for sports science by combining ANNs with performance analysis. This system addresses advancedperformance management issues and provides a positive point of reference for the decision-making process to improve national efficiency in the context of nations participating in mega-sports events. Conceptualization, W.-B.L., C.-C.-Y. and H.-T.P. ; methodology, W.-B.L. ; software, W.-B.L. and C.-C.-Y. ; data curation, W.-B.L. and C.-C.-Y. ; writing--original draft preparation, W.-B.L. and C.-C.-Y. ; writing--review and editing, C.-C.-Y. and H.-T.P. All authors have read and agreed to the published version of the manuscript. This research was funded by the Ministry of Science and Technology of Taiwan, grant number MOST 111-2410-H-119-003; NSTC 112-2410-H-119-005-MY2. Not applicable. The raw data supporting the conclusions of this article can be made available by the authors without undue reservation. The authors declare no conflicts of interest. ## References

* [PERSON] et al. (2002) [PERSON]; [PERSON]; [PERSON]; [PERSON] Measuring the performance of nations at the Summer Olympics using data envelopment analysis. _J. Oper. Res. Soc._**2002**, _53_, 501-511. [CrossRef]
* [PERSON] et al. (2003) [PERSON]; [PERSON]; [PERSON]; [PERSON]. Olympic ranking based on a zero sum gains DEA model. _Eur. J. Oper. Res._**2003**, _148_, 312-322. [CrossRef]
* [PERSON] and [PERSON] (2000) [PERSON]; [PERSON] Towards fair ranking of Olympics achievements: The case of Sydney 2000. _Comput. Oper. Res._**2006**, _33_, 2057-2082. [CrossRef]
* [PERSON] (2007) [PERSON] A study of Chinese Taipei's performance evaluation since its return to the Asian Games. _Sports Exerc. Res._**2007**, \(9\), 29-40. [CrossRef]
* [PERSON] et al. (2008) [PERSON]; [PERSON]; [PERSON]; [PERSON] Models for measuring and benchmarking Olympics achievements. _Omega_**2008**, _36_, 933-940. [CrossRef]
* [PERSON] (2009) [PERSON] Supplier selection: A hybrid model using DEA, decision tree and neural network. _Expert Syst. Appl._**2009**, _36_, 9105-9112. [CrossRef]
* [PERSON] et al. (2009) [PERSON]; [PERSON]; [PERSON]; [PERSON] Measuring the performance of nations at the Olympic Games using DEA models with different preferences. _J. Oper. Res. Soc._**2009**, _60_, 983-990. [CrossRef]
* [PERSON] et al. (2010) [PERSON]; [PERSON]; [PERSON] Measuring the performance of nations at Beijing Summer Olympics using integer-valued DEA model. _J. Sports Econ._**2010**, _11_, 549-566. [CrossRef]
* [PERSON] et al. (2012) [PERSON]; [PERSON]; [PERSON] A DEA model with a non discriminatory variablefor olympic evaluation. _Pesqui.