The set splittability problem is the following: given a finite collection of finite sets, does there exist a single set that contains exactly half the elements from each set in the collection? (If a set has odd size, we allow the floor or ceiling.) It is natural to study the set splittability problem in the context of combinatorial discrepancy theory and its applications, since a collection is splittable if and only if it has discrepancy at most 1. We introduce a natural generalization of the splittability problem called the p-splittability problem, where we replace the fraction 1/2 in the definition with an arbitrary fraction p in (0, 1). We first show that the p-splittability problem is NP-complete. We then give several criteria for p-splittability, including a complete characterization of p-splittability for three or fewer sets (p arbitrary), and for four or fewer sets (p = 1/2 ). Finally, we prove the asymptotic prevalence of splittability over unsplittability in an appropriate sense.