To scientifically estimate medal allocations at the 2028 Los Angeles Olympic Games, this study develops a set of quantitative models, including multiple linear regression, ARIMA time-series analysis, and logistic regression. These models are applied to examine national medal totals, longitudinal medal trends, probabilities of winning a first Olympic medal, and the influence of event composition on medal performance. The analysis is based on historical Olympic data spanning 1984 to 2024. The findings reveal strong linear associations between medal outcomes and key explanatory factors, consistent and reliable forecasting performance from the ARIMA model, and a maximum first-medal probability of 62.5% for Azerbaijan. Additionally, the results demonstrate a positive relationship between the number of contested events and overall medal counts, providing empirical support for strategic planning and resource allocation by National Olympic Committees.