 In the worst case, the number of comparisons merge sort makes is given by the sorting numbers.These numbers are equal to or slightly smaller than ("n" ⌈lg "n"⌉ − 2⌈lg "n"⌉ + 1), which is between ("n" lg "n" − "n" + 1) and ("n" lg "n" + "n" + O(lg "n")).For large "n" and a randomly ordered input list, merge sort's expected (average) number of comparisons approaches "α"·"n" fewer than the worst case where formula_1

In the "worst" case, merge sort does about 39% fewer comparisons than quicksort does in the "average" case.