In this work we have addressed the problem of understending which features of a game influence the convergence of a learning algorithm. Taking recent literature as a starting point we focused on the relation between the empirical convergence frequency for a given game and its best reply structure. We tried to broaden this framework and obtain more precise predictions by including quasi best replies. In order to do so, we developed an analogy between the execution of a game by two players and a diffusive process on a fully connected weighted graph. We looked at the stationary distribution of such a process and tried to see if it could be used to calibrate the strenght (e.g to infere the relative size) of each attractor.The aforementioned analogy was based on a logit one parameter (β) transformation that mapped the payoff matrix in a stochastic one.