  We study the distribution of attraction basins as a function of energy in
simple glasses. We find that it is always broad. Furthermore we identify two
types of glasses, both with an exponentially large number of metastable states.
In one type the largest attraction basin is exponentially small, whereas in the
other it is polynomially small in the system size N. If there exists a tuning
parameter that connects one regime with another, then these two phases are
separated by a critical point. We discuss implications for optimization
problems.
