Why people often use an expected value notation to tell something about randomized or probabilistic algorithm?
What can expected value tell us about this algorithm? Does this algorithm have a low chance of error or what?
So far, I know that expected value can be used in order to show that particular algorithm belongs to ZPP (by definition), but I'm pretty sure that's not the main thing here.
Also, I know that it is possible to prove that QuickSort is $O(n \log n)$ in average case, using expected value notation, so I assume it can help us to find that the time complexity of some randomized/probabilistic algorithm, but only in average case?