Studying the performance and efficiency of countries participating in the Olympic Games is a topic of interest in the area of economics and operations research. Commonly, efficiency in this area has been analyzed using outputs like number of medals, the number of medals weighted by category, and the number of diplomas, while the most common inputs are gross domestic product (GDP) and population. This paper contributes to the literature by analyzing the countries’ efficiencies in the Rio 2016 Summer Olympics with stochastic frontier models. Moreover, this study aims to fill three research gaps in the literature. On the one hand, given that the athletes’ qualification for the Games is a great achievement itself for many countries, the analysis uses the number of participants as the output. On the other hand, the analysis weights the number of medals in relation to the number of participants in each competition (i.e., two in tennis doubles, 14 in handball). Finally, this paper develops a measure to calculate the inefficiency of countries with zero medals, since traditional frontier methods do not consider them.