The story
Alternately -istical (“adjective suffix”) + -ly (“adverb suffix”) or -istic (“adjective suffix”) + -ally (“adverb suffix”). In either case, ultimately -ist + -ic + -al + -ly.
Etymology from Wiktionary, CC BY-SA 4.0.
-istically
Today it means: Used to form adverbs describing action in the manner of the root adjective; use is identical irrespective of whether the root adjective ends with -istic or -istical. Full definition →