With the Sochi Winter Olympics now well underway, I was reminded of the empirical literature that has attempted to model the number of medals that different countries win.
Back in 2006, one of our students, Glen Roberts, wrote an excellent paper, titled "Accounting for Achievement in Athens: A Count Data Analysis of National Olympic Performance", on this topic. Glen's work was based on a term project that he undertook for my ECON 546, "Themes in Econometrics" course. This is an elective course for M.A. students, and it emphasises the thematic content of econometric methods - MLE, IV/GMM, Bayesian inference, etc.
Glen found that the empirical analyses of Olympic medal wins largely ignored the "count data" aspect of the problem. You can find plenty of references in Glen's paper. He then set about rectifying this situation, as the abstract to his paper describes:
"We model summer Olympic medal counts using count data analysis. The advantage of this methodology is its explicit recognition of the discrete non-negative form of the dependent variable; i.e. the total number of medals won by a nation in a summer Olympiad. Using data from the most recent 2004 Summer Games in Athens, Poisson and negative binomial count data regression models are constructed. The chosen model is negative binomial and attaches statistical significance to Gross Domestic Product (GDP) per capita, the age dependency ratio, and a relatively cold winter climate. In contrast to previous studies, population, health expenditure per capita, and the effect of being a host or neighbour nation are all insignificant in explaining medal counts. We also find no 'cricket effect' or 'rugby effect' "
I haven't kept up with the literature on this topic since Glen undertook his study. However, I imagine that there are still opportunities for some further interesting econometric analysis of Olympic medal counts.