Stats profiles are stored in your preferences, so they are part of your backup if you opt to include preferences in your backup.
In versions before 3.3, the preferences file was backed up (if opted), but upon restore it wasn't placed back into the correct location. So basically everything else was restored except preferences. In version 3.3, this was fixed, so if you included preferences in your backup, a restore should restore preferences (it was also fixed in patches to version 3.1 and 3.2).