For probabilistic algorithms, we can look at the worst-case-w.h.p runtime: that is, a randomized quicksort, although technically still having an "absolute" worst case of O(n^2), actually is considered to have a worst case of O(nlog(n)), with probability 1 - 1 / (n^c) when bounded by Chernoff, as shown here: https://web.cs.hacettepe.edu.tr/~ozkahya/classes/bbm402/Lect...
