How do I derive an expected total for a subset of items based on the expected overall total?
You can derive expected totals for subsets of items by taking fractions of the expected total of all T items IF each subscale has the same expected value and each subscale is weighted equally in computing the total scale score. Expressed more formally
If each of T items has the same weight, W and expected score, E(S) then it follows fot 1 <= t <= T:
E(total of all T items) = TW E(S) and E(total of a subset of t items) = [TW/t] E(S) = E(total of all T items)/t
For example if t=2 then do obtain the expected total for half the items you just need to half the total for all T items.