There's some logic to detect if the data is already sorted or reverse sorted, but I think that's only triggered at the very beginning and not at every recursion level. If the data is almost sorted it seems to become a little bit faster. Take a look at the appendix of the paper where there are timings for various distributions.
There's also some logic to handle the case where there are a lot of equal elements which also results in faster performance than the completely random case.
There's also some logic to handle the case where there are a lot of equal elements which also results in faster performance than the completely random case.