  We review and refine the concept of a mean-field theory for the study of
sandpile models, which are of central importance in the study of self-organized
criticality. By considering the simple one-dimensional random walker with an
absorbing and reflecting boundary we are able to construct a complete
mean-field picture which we can solve in detail for different types of driving.
Using this theory, we are able to clarify the effect of finite driving rate on
sandpile models, as well as the observed sensitivity of certain universal
quantities on the driving.
