Performance Metrics After Enabling Auto-Stats
If SET AUTO_CREATE_STATISTICS ON improved performance (anecdotally) for your end users, it likely means that queries with predicates on columns without statistics have gotten better execution plans, and thus shorter runtimes.  A "better" execution plan could result in one or more of these improvements:


Fewer logical / physical reads
Lower CPU usage
Shorter query runtimes / duration


I'm not sure what metrics you're capturing.  If you're able to get to the level of individual query execution time, you could find examples of the same queries before and after the change and confirm that they have reduced runtimes (or less CPU and reads, etc).

For example, if you're logging the contents of sys.dm_exec_query_stats to a table, you could find queries that have the same sql_handle but lower CPU, reads, etc after the setting was changed.



If you are logging execution plan XML, you might be able to look for the presence, and then absence, of warnings like this:



It shows up in the XML like this:

  &lt;Warnings&gt;
    &lt;ColumnsWithNoStatistics&gt;
      &lt;ColumnReference Database="[TestDB]" Schema="[dbo]" Table="[Hist]" Column="Num" /&gt;
    &lt;/ColumnsWithNoStatistics&gt;
  &lt;/Warnings&gt;




If you just have server level aggregated metrics to look at, you might still see overall reads or CPU has gone down, but it's probably a lot harder to see that for sure if it's watered down by other workloads and maintenance activities.