Probability of Finding A Lower Minimum

Question

I have a system f($\vec x$) periodically bounded by {$\vec a$} and I would prefer to find the absolute minimum. Suppose I drop n balls that always roll to the bottom of a local minimum, and from them, I gather data of f($\vec x$) along with the paths $\vec x$(t) they have taken. I take the lowest value of these minima, M$_i$, which is my proposed absolute minimum. How do I quantify the probability that I will find a comparable or lower minimum if I were to drop more balls into the system (e.g. $M_{i+1}< M_i+0.1|M_i|)$?