Hi Amy,

The counting appears suited to using a Pivot Table with:
Owner in Row,
Year, Type, #Days in Column; and
count of Date in Data.
You then set the criteria for the Columns of the PivotTable to extract the count.
AutoSort|Autoshow of the top three can be shown in the Advanced Field setting for the Owner.

Please note the descriptions I use are for excel 2003 and from memory they may vary slightly with later versions of excel.

HTH.