## 9 Conclusions  
This study developed a hybrid machine learning framework to predict Olympic medal performance for the 2028 Games, incorporating the impacts of host and coaching effects. The key findings are summarized as follows:  
1. Classifying global countries into four categories based on Olympic participation and medal outcomes, with an analysis of their 2028 medal trends. To simplify the analysis of 234 countries, we categorized them based on shared characteristics using the K-means clustering method. The algorithm divided the nations into four distinct clusters (\(\alpha_{1}\), \(\alpha_{2}\), \(\alpha_{3}\), \(\alpha_{4}\)). The first three clusters (\(\alpha_{1}\), \(\alpha_{2}\), \(\alpha_{3}\)) contain countries with Olympic medal achievements, while the fourth cluster (\(\alpha_{4}\)) consists of nations without any medalss. 2. Integrating factor analysis, time series, and four machine learning methods into the MPXG model to predict individual country medal outcomes. From each of the medal-winning clusters, we selected 2-3 representative nations for detailed examination, using the United States as a primary example for comparative analysis. Through dimensionality reduction analysis, ten original variables were consolidated into three principal components: competition scale factor (F1), medal distribution trend factor (F2), and the gender-athletic performance composite factor (F3). The ARIMA forecasting model yielded 2028 coefficient estimates of 0.9539, 0.7999, and 0.2937 for these factors, respectively. A comparative evaluation of four predictive algorithms (random forest, back propagation neural network, XGBoost, and Support Vector Machine) revealed XGBoost's superior predictive accuracy with minimal error margins. This methodological framework establishes a robust foundation for nation-specific medal outcome projections. Based on predictive modeling, the United States is projected to secure 57 gold medals, with an estimated total medal count reaching 135 in the 2028 Olympic Games. The analysis of the overall performance trends among \(\alpha_{1}\) group nations reveals relatively stable competitive levels. The \(\alpha_{2}\) group demonstrates a clear upward trajectory in athletic performance. Meanwhile, competitive outcomes for \(\alpha_{3}\) group nations primarily depend on two key factors: athletes' competitive condition and the inclusion of their specialty events in the Olympic program. 3. Employing a FCNN to predict the probability of non-medal-winning countries winning their first medal in the next competition. For non-medal-winning nations, we developed a three-layer fully connected neural network architecture that attained 85.5% prediction accuracy during validation. Within the \(\alpha_{4}\) cluster, probabilistic modeling indicates distinct medal prospects for the 2028 Olympics: the United Arab Republic (UAR) shows a 77.47% likelihood of podium achievement, while Mali (MLI) demonstrates a 58.47% probability. Furthermore, four additional nations in this group exhibit success probabilities surpassing the 30% threshold. 4. Quantifying the host effect value for the past eight Olympic Games. We developed a weighted scoring system (gold = 13, silver = 12, bronze = 10 points) and a quantitative host advantage model. Analysis shows that host nations achieve 74% higher weighted scores than non-host years, based on 30 years of data. 5. Developing a Bayesian linear regression-based coach effect scoring system to evaluate the extent to which coaches enhance the overall strength of athletes in a discipline. We introduce the Athletic Winning Potential (AWP) metric to quantify the impact of elite coaching. The Coaching Effectiveness (C.E.) index is stratified into three distinct tiers (1.0, 0.5, 0.25), determined by the coach's current professional status (active/retired) and their specialization scope (single event/multi-event).