I've noticed using BackupLoupe that stuff under ~/Library/Saved Application State/ pops up in my Time Machine backups. I can't find that much about this folder online, but one site describes it as "where the information regarding files that should be re-opened on startup is stored." This doesn't sound to me like it needs to be covered by Time Machine backups. Is there a good reason why this folder needs to be backed up?
The folder is small, but if it changes frequently then its footprint in Time Machine could be large.
Best Answer
There's no reason to backup this directory.
The contents changes so frequently that any backup is outdated by the time the backup's finished. This is no exaggeration; simply the act of making a backup will change the contents of this folder.
If you're relying on an unsaved document being there next time you open an app based on Restore, you're doing something wrong. Providing you save documents, the data in that folder will be saved to the appropriate location in the file anyway.
The saved application state stores a bunch of useless information anyway. When you're restoring a full Time Machine backup, the lack of cached data makes any app restore a strenuous task and the saved application state won't help.
Also, for what it's worth, this directory used to be (and still is on most installations) part of the standard exclusions list for Time Machine backups.