In some televised sports, such as downhill skiing, individual competitors take turns for the best time on a course. After each competitor the announcers will give the current standing. So for example, the first person will always be announced as ranked 1 (though this will likely change), the second person will be announced as either 1 or 2, and so on.
By the end of the competition everyone's final rank will be the same or higher.
a) In an event with n competitors, what is the expected difference between the first announced and final rank of competitor that goes xth?
b) What is the expected average difference for all n competitors?
Note: the order of the competitors is random.