The design of large scale DNA microarrays is a challenging problem. So far, probe selection algorithms must trade the ability to cope with large scale problems for a loss of accuracy in the estimation of probe quality. We present an approach based on jumps in matching statistics that combines the best of both worlds. This article consists of two parts. The first part is theoretical. We introduce the notion of jumps in matching statistics between two strings and derive their properties. We estimate the frequency of jumps for random strings in a non-uniform Bernoulli model and present a new heuristic argument to find the center of the length distribution of the longest substring that two random strings have in common. The results are generalized to near-perfect matches with a small number of mismatches. In the second part, we use the concept of jumps to improve the accuracy of the longest common factor approach for probe selection by moving from a string-based to an energy-based specificity measure, while only slightly more than doubling the selection time.