The efficiency of participated countries and the fairness of medal ranking list in Olympic Games have always been controversial. So far, there is still no such a ranking method recognized
universally to solve this issue.
On account of this, we consider the evaluation on efficiency of participated countries from the view of economy and convert it into an input-output problem that discusses which country has
greatest amount of output at a certain input level. Our research samples come from London Olympic Games which covers 87 different countries (altogether 73 countries after deleting countries with
default data). By taking GDP, population and the ratio of public finance expenditure to GDP as input variables, weighted number of gold, silver and bronze medal as output variables, we apply
Three-stage Data Envelopment Analysis (DEA) method which removes the influence of environmental variables (such as the degree of economic openness, research expenditure rate on sports and geographical
factor) on input variables to study the efficiency of participated countries in 2012 London Olympic Games.
Our results show that: 1) America, China, France and Germany are the top four countries with effective participating efficiency greater than 1. It is almost consistent with their performance in
London Olympic Games. 2）Although Russia ranks 3rd in the medal ranking list, its participating efficiency is lower than France, Germany and Italy. 3) After applying SFA, the efficiency of participated
countries has changed differently. Among them, the efficiency of 43 countries increases, 29 decreases. 4) All of these participated countries in research samples have increasing returns to scale
except America and China. The research shows Three-stage DEA are proved to be a reasonable method in solving the fairness of ranking problem.
The results could be used for evaluation of participated countries' performance and for continuous research purpose. Countries with lower efficiency could increase its sports expenditure for
further efficiency improvement.