People often predict the final medal count of the Olympics based on factors such as the number of events and the host country information. This paper will predict the final medal table data based on models like Markov and Logistic Regression. Based on the Markov model, the number of gold medals and the total number of medals are each represented by four states. A model is established according to these four states, and the state transition probability matrix is calculated. Then, the Monte Carlo algorithm is used to solve the model. The results show that the number of medals and gold medals of countries such as CHN and USA are in state 4, while those of countries such as ZAM and DOM are in state 1. Indicators such as Mean Squared Error (MSE) and Mean Absolute Error (MAE) are also used to measure the model's performance. The results show that the prediction model performs relatively well in predicting the total number of medals. A 95% confidence interval is also provided for all prediction results. Regarding the issue of taking into account countries that haven’t won any medals yet, by analyzing the dataset, three factors are counted: the number of participations NC, the number of participating events NL, and the average ranking A. Based on these, a logistic regression model is established to predict the countries that will win their first medal in the next Olympic Games. Finally, the specific countries predicted to win their first medal in the next Olympics are identified as BOL, ESA, LIE, MLT, MYA, and NCA. Moreover, a feasibility analysis of the established model is carried out. Metrics such as accuracy, precision, recall, and the F1 - score are calculated. The results indicate that the model performs well overall and is feasible. Regarding the impact of the “Great Coach” effect on a country’s Olympic performance, the Propensity Score Matching (PMS) method is selected. According to the model solution results, for national teams with the “Great Coach” effect, the difference in the winning situation under the influence of other winning-related factors is small. Therefore, it can be considered that the “Great Coach” effect has a significant impact on the winning situation of national teams. Regarding the problem that requires considering the competition events of a specific Olympic Games. The results show that the model can explain approximately 72.97% of the variation in the dependent variable, indicating that this quadratic fitting model has a certain feasibility.