When a query has a multi-column condition, consider creating multi-column statistics if you suspect that the optimizer is not producing the best plan for the query. You get multi-column statistics as a by-product of creating a multi-column index, so if there is already a multi-column index that supports the multi-column condition, there is no need to create statistics explicitly. Auto create statistics only creates single-column statistics, never multi-column statistics. So if you need multi-column statistics, create them manually, or create a multi-column index.
Consider a query that accesses the AdventureWorks.Person.Contact table, and contains the following condition:
FirstName = 'Catherine' AND LastName = 'Abel'
To make selectivity estimation more accurate for this query, create the following statistics object:
CREATE STATISTICS LastFirst ON Person.Contact(LastName,FirstName)
This statistics object will be useful for queries that contain predicates on LastName and FirstName, as well as LastName alone. In general, the selectivity of a predicate on any prefix of the set of columns in a multi-column statistics object can be estimated using that statistics object.
For a statistics object to fully support a multi-column condition, a prefix of the columns in the multi-column statistics object must contain the columns in the condition. For example, a multi-column statistics object on columns (a,b,c) only partially supports the condition a=1 AND c=1; the histogram will be used to estimate the selectivity for a=1, but the density information for c will not be used since b is missing from the condition. Multi-column statistics on (a,c) or (a,c,b) would support the condition a=1 AND c=1, and density information could be used to improve selectivity estimation.