``The Elo rating system is a method for calculating the relative skill levels of players in two-player games such as chess'' (Wikipedia). This system is widely used to rank sport teams, online games, journals for instance. The Elo model studied is a Markov chain. When the players are numerous and interact a lot we derive a new continuous model: a kinetic equation with a mean field velocity. The asymptotic behavior of the ratings for large time, which is an important issue for the validity of the rating system, is studied. The idealistic case when all players are compared yields an exponential rate to the true rating independently of the initial rating. The realistic and complex case with only local interactions has several equilibria. The convergence holds to an equilibrium depending on the intial ratings but with no rate. What does it mean for this rating system? Some consequences and some open problems will be given.