Modeling of the Randomness in the Process of E-sports Competitions Based on Neural Stochastic Differential Equations
DOI:
https://doi.org/10.67541/jdf2601Keywords:
Neural Stochastic Differential Equations; Modeling of E-sports Competitions; Stochastic Process; Uncertainty Quantification; Multimodal Temporal PredictionAbstract
The process of e-sports competitions exhibits complex dynamic characteristics such as strong nonlinearity, multi-time-scale coupling, and heterogeneous random fluctuations. Traditional deterministic models or constant noise assumption-based stochastic models are difficult to accurately depict their evolution patterns. This paper proposes a stochastic modeling method for the e-sports competition process based on neural stochastic differential equations. By parameterizing the drift function and diffusion function using neural networks, it learns the state-dependent deterministic trends and adaptive random perturbation intensities from the data end-to-end. A controllable stochastic regulation mechanism and a multi-level time-scale modeling structure are designed to address the significant differences in randomness at different competition stages and the coupling modeling of micro-operations and macro strategies. By integrating temporal event encoding, graph neural network relationship extraction, and numerical statistical features, a multimodal state representation is constructed. Experiments are conducted on a large-scale dataset containing 12,478 professional competitions. The results show that the model in this paper reduces the mean square error (2.37×10⁻³) and the average absolute error (1.03×10⁻²) by 46.0% and 32.2% respectively compared to Transformer, and the actual coverage rate of the 95% confidence interval of the prediction distribution reaches 93.7%. The average error in predicting key event times is 28 seconds, verifying the effectiveness and superiority of neural stochastic differential equations for stochastic modeling of e-sports competition processes.
References
[1] Duan, P., Wang, X., Zhang, A. Y., & Ji, B. (2023). Development environment of China’s e-sports industry. In Electronic sports industry in China: An overview (pp. 47-74). Singapore: Springer Nature Singapore. https://doi.org/10.1007/978-981-19-9288-9_3
[2] Cheng, B., & Bayasgalan, Z. (2024). RESEARCH ON THE DEVELOPMENT PROSPECT OF CONTEMPORARY E-SPORTS EDUCATION. In ICERI2024 Proceedings (pp. 1270-1277). IATED. https://doi.org/10.21125/iceri.2024.0391
[3] Liu, F., She, Q., Qiu, J., & Wei, Z. (2024). Theoretical logic and strategy of digital economy driving the high-quality development of China's regional E-sports industry. Journal of Management and Social Development (4), 11-15. https://doi.org/10.62517/jmsd.202412402
[4] Pfoff, J. C., & Lee, N. (2024). Super Smash Bros. Ultimate and E-sports. In Encyclopedia of Computer Graphics and Games (pp. 1783-1785). Cham: Springer International Publishing.
https://doi.org/10.1007/978-3-031-23161-2_472
[5] Vasiliev, A. A., & Pechatnova, J. V. (2023). Regulatory models in e-sports. Legal Issues in the digital Age, (4), 4-22. https://doi.org/10.17323/2713-2749.2023.4.4.22
[6] Bahrololloomi, F., Klonowski, F., Sauer, S., Horst, R., & Dörner, R. (2023). E-sports player performance metrics for predicting the outcome of league of legends matches considering player roles. SN Computer Science, 4(3), 238. https://doi.org/10.1007/s42979-022-01660-6
[7] Lu, Y., Chen, H., & Yan, H. (2022). E‐Sports Competition Analysis Based on Intelligent Analysis System. Computational Intelligence and Neuroscience, 2022(1), 4855550. https://doi.org/10.1155/2022/4855550
[8] Gerken, J., Zhang, H., Garnica Caparrós, M., Gardeweg, L., Memmert, D., & Wunderlich, F. (2026). The issue of sparse networks in sports competitions: can Elo ratings efficiently compare football teams that never play a match?. Journal of the Operational Research Society, 1-16.
https://doi.org/10.1080/01605682.2025.2612140
[9] Jalovaara, P. (2024). Win probability estimation for strategic decision-making in esports. https://urn.fi/URN:NBN:fi:aalto-202411217333
[10] Dai, M., Duan, J., Hu, J., Wen, J., & Wang, X. (2022). Variational inference of the drift function for stochastic differential equations driven by Lévy processes. Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(6). https://doi.org/10.48550/arXiv.2103.15080
[11] Schurz, H. (2024). A brief review on stability investigations of numerical methods for systems of stochastic differential equations. Networks & Heterogeneous Media, 19(1). https://doi.org/10.3934/nhm.2024016
[12] Yang, C. F. (2025). Uncertainty-Aware QoS Forecasting with BR-LSTM for Esports Networks. Information, 16(12), 1016. https://doi.org/10.3390/info16121016
[13] Liu, G., Luo, Y., Schulte, O., & Poupart, P. (2022). Uncertainty-aware reinforcement learning for risk-sensitive player evaluation in sports game. Advances in Neural Information Processing Systems, 35, 20218-20231. https://doi.org/10.52202/068431-1470
[14] Zhou, J., Petrosian, O., & Gao, H. (2024). Enhancing ecological uncertainty predictions in pollution control games through dynamic Bayesian updating. Scientific Reports, 14(1), 12594. https://doi.org/10.1038/s41598-024-63234-1
[15] Sufian, M. A., Varadarajan, J., Hanumanthu, M., Katneni, L., Jamil, A., Lal, V., & Boomer, J. (2024, June). Optimizing E-Sports Revenue: A Novel Data Driven Approach to Predicting Merchandise Sales Through Data Analytics and Machine Learning. In Science and Information Conference (pp. 522-567). Cham: Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-62269-4_35
[16] Wardaszko, M., & Kriz, W. C. (2025, July). Modelling In-Game Events in Game Scenarios: A Comprehensive Framework. In International Simulation and Gaming Association Conference (pp. 63-78). Cham: Springer Nature Switzerland. https://doi.org/10.1007/978-3-032-20129-4_5
[17] Ötting, M., & Karlis, D. (2023). Football tracking data: a copula-based hidden Markov model for classification of tactics in football. Annals of Operations Research, 325(1), 167-183. https://doi.org/10.1007/s10479-022-04660-0
[18] Kim, J., & Chatterjea, R. (2026). Stochastic Differential Equation Treatment of OPS in Baseball.
[19] Chulajata, K., Wu, S., Scalzo, F., & Cha, E. S. (2024). Predicting outcomes in video games with long short term memory networks. arXiv preprint arXiv:2402.15923. https://doi.org/10.48550/arXiv.2402.15923
[20] Xu, H., Lin, B., & Liu, L. (2025). Sports event data analysis and win rate prediction model using self-attention mechanism and Transformer. Journal of Computational Methods in Sciences and Engineering, 14727978251348637. https://doi.org/10.1177/14727978251348637
[21] Kovačević, M. A., Pešović, M. D., Petrović, Z. Z., & Pucanović, Z. S. (2024). Predictive analytics of in-game transactions: tokenized player history and self-attention techniques. IEEE Access, 12, 149263-149271. https://doi.org/10.1109/access.2024.3477624
[22] Montrucchio, M., Barbierato, E., & Gatti, A. (2026). Uncertainty-Aware Machine Learning for NBA Forecasting in Digital Betting Markets. Information, 17(1), 56. https://doi.org/10.3390/info17010056
[23] Liu, J., Zou, C., & Chintagunta, P. K. (2026). Bayesian learning and skill accumulation in video game play. Quantitative Marketing and Economics, 24(1), 5. https://doi.org/10.1007/s11129-026-09309-x
[24] Dong, S., Xi, G., & Li, B. (2026). Intelligent Games for UAV Systems: A Survey of Game-Theoretic and AI-Enabled Methods. Journal of Artificial Intelligence and Technology. https://doi.org/10.37965/jait.2026.1237
[25] Aslanimoghanloo, M., ElGazzar, A., & van Gerven, M. (2025). Generative Modeling of Clinical Time Series via Latent Stochastic Differential Equations. arXiv preprint arXiv:2511.16427. https://doi.org/10.1016/j.jbi.2026.105043
[26] Di Persio, L., Alruqimi, M., & Garbelli, M. (2024). Stochastic approaches to energy markets: from stochastic differential equations to mean field games and neural network modeling. Energies, 17(23), 6106. https://doi.org/10.3390/en17236106
[27] Oh, Y., Kam, S., Lee, J., Lim, D. Y., Kim, S., & Bui, A. (2025). Comprehensive review of neural differential equations for time series analysis. arXiv preprint arXiv:2502.09885. https://doi.org/10.24963/ijcai.2025/1179
[28] Eggen, S., Espe, T. J., Grude, K., Risstad, M., & Sandberg, R. (2026). Financial time series uncertainty: A review of probabilistic AI applications. Journal of Economic Surveys, 40(2), 915-953. https://doi.org/10.1111/joes.70018
[29] Jiang, S., Zhang, L., Xu, H., Huang, J., He, Q., Zhou, X., ... & Jiang, J. (2024, October). GameTrail: Probabilistic Lifecycle Process Model for Deep Game Understanding. In Proceedings of the 33rd ACM International Conference on Information and Knowledge Management (pp. 994-1003). https://doi.org/10.1145/3627673.3679736
[30] Vardakis, M., Margetis, G., Chatzakis, I., Apostolakis, K. C., & Stephanidis, C. (2026). Prediction of MOBA game events based on In-Game Data. Entertainment Computing, 101091. https://doi.org/10.1016/j.entcom.2026.101091
[31] Ghasemifard, A. (2025). Milstein scheme for the numerical solution of first-order uncertain stochastic differential equations in stock price simulation. Caspian Journal of Mathematical Sciences, 14(2), 433. https://doi.org/10.22080/cjms.2025.29406.1763
[32] Zhang, Q. (2026). Research on Multimodal Prediction Model of Sports Event Ticket Revenue Based on Transformer. International Scientific Technical and Economic Research, 4(2), 124-147. https://doi.org/10.71451/ISTAER2618
[33] Zhou, H. (2026). Research on the Fusion Model of DeepFM and XGBoost for Digital Consumer Behavior Prediction. International Scientific Technical and Economic Research, 4(2), 98-123. https://doi.org/10.71451/ISTAER2617
[34] Qin, Y. (2026). Research on Long Sequence Learning Behavior Modeling Based on Transformer-XL. International Scientific Technical and Economic Research, 4(2), 1-20. https://doi.org/10.71451/ISTAER2613
[35] Xu, H. (2026). A Deep Reinforcement Learning Signal Control Algorithm for Traffic Carbon Emission Optimization. International Scientific Technical and Economic Research, 4(1), 200–221. https://doi.org/10.71451/ISTAER2610
[36] Chen, G. (2026). Research on algorithm improvement of ARIMA-LSTM hybrid model in time series prediction of inflation rate. International Scientific Technical and Economic Research, 4(1), 90-122. https://doi.org/10.71451/ISTAER2605
[37] Ding, Y., & Chen, G. (2026). Joint Prediction Model of Reservoir Parameters Based on Multimodal Transformer Graph Neural Operator Physical Constraint Network. International Scientific Technical and Economic Research, 4(1), 70-89. https://doi.org/10.71451/ISTAER2604
[38] Zeng, X. (2026). Cross-Border Trade Fraud Detection via Integrated Heterogeneous Graph Neural Network and XGBoost. International Scientific Technical and Economic Research, 4(1),47-69. https://doi.org/10.71451/ISTAER2603
[39] Wang, W., Shen, S., & Wang, Y. (2026). Forecasting Short-Term Export Volumes with Hybrid Models Integrating SARIMA with Attention-Based LSTM. International Scientific Technical and Economic Research, 4(1),1-22. https://doi.org/10.71451/ISTAER2601
Published
Issue
Section
License
Copyright (c) 2026 Shuai Ma (Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.
