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: