"You'll be hoping for a bit more from the new player, I suppose." Why the future continuous?

Hope is a concept related to expectations and desires for the future, so most expressions of hope are about the future whenever present or future tense is used. The statements "I hope for a bit more from the new player", "I am hoping for a bit more from the new player", "I will hope for a bit more from the new player" and "I'll be hoping for a bit more from the new player" technically have slightly different meanings, but in practice it is hard to imagine a situation where only some of them would be true. In this situation the choice of which statement to use is more a matter of style than of correctness.

In this construction, the purpose of the progressive is to ensure that the question is not understood as a request; it 'softens' it, as it were.

Discussion

Here is a relevant section of CGEL (pp. 171-172):

Will + progressive

[22]  i  When we get there, they'll probably still be having lunch.       [aspectual meaning]
         ii  Will you be going to the shops this afternoon?                                [special meaning]
        iii  When the meeting ends we'll be flying to Bonn.                                       [ambiguous]

In [i] we simply have the ordinary use of the progressive to express progressive aspectuality: the lunch will be still in progress at the time of our arrival. This is not how we interpret [ii], however. The meaning can best be seen by comparing it with the nonprogressive counterpart, Will you go to the shops this afternoon? The salient interpretation of the latter is as a request to you to go to the shops, and the role of the progressive in [ii] is to avoid such an interpretation. The progressive indicates that the matter has already been settled rather than being subject to decision now. Compare, similarly, We won't buy any more (interpretable as a refusal, made here and now) vs We won't be buying any more (following prior decision), or Will he help us? ("Is he willing?", decision still to be made) vs Will he be helping us? ("Has it been decided that he will?").

The distinctness between the two meanings is seen clearly in the ambiguity of [22iii]. On the progressive aspectuality reading, we will already be flying to Bonn when the meeting ends; on the 'already decided future' interpretation, the when adjunct says when we will leave. The first is imperfective, with reference to a mid-interval; the second is perfective, just as in the non-progressive we'll fly, which, however, suggests that the decision is being made now. This use is particularly common with will, but it is also found with, for example, the idiom be going, as in Are you going to be helping them again this year? (where the non-progressive might again be construed as a request).