Research question: Several studies report modelling relating countries’ medal shares at the Olympics to population and per capita income (host status and political system are typically included as controls). This paper uses a similar model but disaggregates to the level of the individual sport to ask questions such as whether some sports have a less steep relationship with income levels than others and whether hosting effects are more pronounced in some sports than others. Research methods: Employing a random effects tobit model, data on medal shares are modelled across 15 sports at six editions of the Games (1992–2012). Marginal effects, calculated for the case of cycling, illustrate how far many poor countries are from reasonable expectation of achieving medals. Results and findings: Income is influential on outcomes in all sports, its effects most pronounced in sports with substantial requirements for specific capital equipment; the distribution of medals is less unequal in sports practised in multi-sports venues. Gains from hosting vary in magnitude, performance tending to be elevated most in sports with outcomes strongly influenced by judges. Implications: For poorer countries, the paper identifies a small group of sports on which it would be most realistic to focus resources. For Games organisers, who must decide which sports to include, it provides information relevant to the goal of spreading success more evenly across countries. For example, proposals to exclude wrestling are shown to have been potentially harmful to medal prospects of poorer countries.