Evolution is all about processes that almost never happen. Every birth in every lineage is a potential speciation event, but speciation almost never happens, not once in a million births. Mutation in DNA almost never happens -- not once in a trillion copyings -- but evolution depends on it. Take the set of infrequent accidents -- things that almost never happen -- and sort them into the happy accidents, the neutral accidents, and the fatal accidents; amplify the effects of the happy accidents -- which happens automatically when you have replication and competition -- and you get evolution.