A Study on the Factors Affecting the Number of Olympic Medals Based on a Multivariate Negative Binomial Model

This paper focuses on a systematic study of the factors influencing the number of medals won by countries at the 2028 Olympics. By constructing a multivariable negative binomial mixed-effects model and combining it with hierarchical regression analysis, the study delves into the mechanisms through which multidimensional factors influence medal counts. The research introduces interaction variables between countries and sports, quantitatively revealing each country's core strengths in specific sports. Additionally, it finds that negative regression coefficients for certain sports can indicate a country's weaker areas in sports. When examining the ‘great coach’ factor, specific cases confirm that coaches have differing impacts on various events, with more significant returns on investment in events with multiple medals. Additionally, the study quantifies the influence of socio-economic and geographical factors, clarifying that sports culture and historical background have the greatest impact, while population size has a relatively minor influence. This research provides a multi-dimensional theoretical basis for understanding the distribution mechanism of Olympic medals and formulating sports development strategies.