If the measure with the average allocation is off by a factor that is proportional to the "sparseness" of my facts, i.e. the ratio of days in a period and actual fact rows, then it can be corrected as follows:
adjusted average allocation =
(calculated average allocation) * (fact count)/(number of days in period)
I created two new hidden measures, one named [Fact Count] for the fact count (a measure using the AggregateFunction "Count") and a calculated measure named [Days In Period Count] for the number of days, using the expression
COUNT(Descendants([Date].[Calendar].CurrentMember,5),INCLUDEEMPTY)
with [Calendar] being the name of the hierarchy in my Date dimension.
Finally, I added a calculated measure that implements the corrective formula:
[Measures].[Allocative Head Count]/
(
[Measures].[Days In Period Count]/[Measures].[Fact Count]
)
and named it [Adjusted Average Allocation]. This I can now use in reports and it appears to somewhat approximate the average cost center allocation over longer periods.
The formular for [Days In Period Count] btw does not work for the row totals when filters are involved. I opened another question for this.