How can I delete an iOS app and preserve its data? I have a 16 GB iPhone and there are a few sizable (~1 GB) games that I have not played lately, but I would like to preserve my progress in case I play them again at some future time.

These games do not store progress in iCloud or some other network service; they appear to save only to the device.  If I delete them from the device, either from the springboard or with iTunes, their data is lost; it does not appear to be preserved in the iTunes backup.

What can I do to preserve data but free space on my device?
Make sure you are on iOS 11, then got to Settings>General>iPad Storage Tap the app,then tap Offload App