In order to predict the distribution of medals at the 2028 Olympic Games in Los Angeles scientifically, this study constructs models like multiple linear regression and ARIMA logistic regression for analyzing the issues of the quantity of national medals in the Olympic medal table and its trend change, the possibility of the country’s first medal, and the effect of the selection of Olympic sports on the number of medals. Firstly, the paper establishes a prediction model for the quantity of medals in the Olympic Games based on multiple linear regression, and obtains a high linear correlation between data characteristics and the number of medals. Secondly, in order to predict the medal development trend of each country in the 2028 Olympic Games, this paper adopts the ARIMA model for prediction, obtaining the medal trend of each country in the 2028 Olympic Games, and verifying that the ARIMA model is smooth and effective. Finally, for the countries that have not yet won medals, the relevant characteristics of the countries that have not yet won medals are collected, and the 10 countries with the highest probability of winning medals for the first time are obtained, among which Azerbaijan has the highest probability of 62.5%. The present study found that the quantity of events is positively correlated with the quantity of medals, which provides a reliable basis for the resource allocation of the National Olympic Committee. The model is both explanatory and flexible, thus providing a novel perspective on the prediction of Olympic medals and the strategic planning of national sports.