Sidgwick holds that ethics tends to divide into two different types, one focused on Happiness, and another focused on Perfection or Excellence, and he argues that being a determinist wouldn't seem to affect questions of Happiness. He then goes on to argue that the same is true of Excellence:
...if Excellence is in itself admirable and desirable, it surely remains equally so whether any individual's approximation to it is entirely determined by inherited nature and external influences or not:--except so far as the notion of Excellence includes that of Free Will. Now Free Will is obviously not included in our common ideal of physical and intellectual perfection: and it seems to me also not to be included in the common notions of the excellences of character which we call virtues: the manifestations of courage, temperance, and justice do not become less admirable because we can trace their antecedents in a happy balance of inherited dispositions developed by a careful education.
It is not at all obvious, however, that merit (or desert) is not part of our ordinary conceptions of intellectual perfection and moral excellence. Sidgwick accepts that determinism is inconsistent with "the ordinary notion of merit", although he holds that determinists can have other notions of merit (or similar notions) that can do similar work. So the question is whether our common notions of intellectual perfection and moral excellence are completely detachable from our common notions of merit. Sidgwick argues in a footnote:
But I do not see that Perfection becomes less an End to be aimed at, because we cease to regard its attainment as meritorious. The inapplicability of the notion of 'merit' to Divine action has never been felt to detract from the Perfection of the Divine Nature.
But the reason that the perfection of the Divine Nature doesn't involve merit is that God is not the kind of thing that merits any kind of goodness; God has it all by nature already. Human beings are not in any way like this, however; we are the kind of thing that do not have intellectual and moral goodness by nature and so we must achieve excellence in these things. That we can have a conception of excellence that does not require achievement does not establish that our conception of human excellence does not require it, and it is obviously the latter alone that is relevant to ethics. We often clearly recognize a distinction between having intellectual excellence by nature (native intelligence) and intellectual excellence by achievement (hard work, careful self-cultivation, etc. related to intellectual life). So the only question is whether the excellence of intellectual achievement itself involves the notion of merit. And that is certainly the most natural way to read the distinction. Thus our common notions of intellectual excellence appear to involve the common notion of merit, and thus are not detachable from the question of free will (assuming Sidgwick is right about everything else).
This becomes even more obvious with moral excellence than with intellectual excellence. The claim that the manifestations of the virtues do not become less admirable because of determinism is again a shifting to a different topic. The questions are whether the virtues themselves require some kind of free choice, and, more specifically, whether merit belongs to the notions of these virtues. We already know that 'manifestations' of virtues, i.e., actions, can be done by people who do not have the virtues, and that this is quite common. For instance, people who are trying to get the virtues, get them by doing the actions associated with the virtue. We can see that such action is admirable; but the question is not about the action without the virtue but about the having of the virtue itself. Another case, and an interesting contrast, is hypocrisy, since hypocrites are careful to have the same same 'manifestations' of virtues in order to cover up the fact that they don't have the virtue; and we can see that this is not admirable, whereas the same actions would certainly be admirable if done by someone who actually had the virtue or weren't using it as a way to deceive people into thinking that they had it. What makes the difference? One reading, a very natural one, is that virtues themselves are not merely admirable, but are admirable because they have been merited; and the actions of virtues are admirable, even without the virtues, when they are part of the work of meriting that goes into beginning to have the virtues.
And the admiration is an interesting aspect, too. When we say that something is admirable, we may mean either that it is admired, or that it is such as to merit admiration. These are not the same thing, and the latter is what is most commonly meant when talking about the admirableness of virtues and virtuous actions. If determinism, as Sidgwick thinks, messes with our notion of merit, then it messes with our notion of virtue.
Henry Sidgwick, The Methods of Ethics, Seventh Edition, Hackett (Indianapolis, IN: 1981), p 68 & 68n-69n.