A popular rating system to measure player strength by pairwise comparison is the Elo's system. This system is widely used to rank players in chess, go and online games. Assuming the independence of the outcomes, it is a Markov chain. The convergence of Elo ratings is studied when the update after each round-robin tournament is a contraction. An important case is the linear updating. The contractive assumption is discussed and compared to the non contractive usual Elo.