I really don’t see the connection between the execution time (the first sentence) and the size of loss being well defined (the second sentence). The purpose of using “indeed” is also unclear. I understand both sentences, but I cannot understand the meaning of the whole paragraph.That said, average-case analysis for expected running time will prove very important with respect to randomized algorithms, which use random numbers to make decisions within the algorithm. If you make n independent $1 redblack bets on roulette in the casino, your expected loss is indeed well defined at $(2n/38), because American roulette wheels have eighteen red, eighteen black, and two green slots 0 and 00 where every bet loses.
Unless the algorithm is used to estimate the loss, directly or indirectly. Which, as it starts looking like, it indeed is.