  We study here the Bak and Sneppen model, a prototype model for the study of
Self-Organized Criticality. In this model several species interact and undergo
extinction with a power law distribution of activity bursts. Species are
defined through their ``fitness' whose distribution in the system is uniform
above a certain universal threshold. Run time statistics is introduced for the
analysis of the dynamics in order to explain the peculiar properties of the
model. This approach based on conditional probability theory, takes into
account the correlations due to memory effects. In this way, we may compute
analytically the value of the fitness threshold with the desired precision.
This represents a substantial improvement with respect to the traditional mean
field approach.
