> the famous "Stooge Sort", which is basically quicksort with the pivot at 1/3 rather than 1/2. Naively, one might think it is faster than Quicksort, but of course it isn't.

The pivot in quicksort isn't located anywhere fixed. You can do quicksort by always choosing the pivot to be the first element in the (sub)list before you do the swapping. If it happens that the pivot you choose always belongs 1/3 of the way through the sorted sublist... that won't even affect the asymptotic running time; it will still be O(n log n).

Stoogesort is nothing like that. It's worse than quadratic.

In quicksort, though, once you've done your thing with the pivot, you break the list into two non-overlapping sublists. If it happened that the pivot broke the list into 1/3 and 2/3, you'd then recur with one sublist of length n and one of length 2n.

Stoogesort has a different recursion pattern: you recur on the first 2/3, then you recur on the second 2/3, then you recur on the first 2/3 again.

The processing step isn't similar to quicksort either - in quicksort, you get a sublist, choose an arbitrary pivot, and then process the list such that every element of the list is correctly positioned relative to the pivot, which takes O(n) time. In stoogesort, you process the list by swapping the beginning with the end if those two elements are out of order, which takes O(1) time.