The OED and other sources suggest that playoff is a construction from the late 19th century, while the following source suggests that it was originally used by Shakespeare in Henry IV.
What does that have to do with the word playoff, then? and most importantly Shakespeare? Well, the word playoff comes from Shakespeare himself, and, even more relevant to our league—it was used colloquially in terms of drinking. The expression to play it off or to play off, used in Henry IV, meant “to finish what you started,” specifically to drain or finish an alcoholic drink.
and the following extract from Word Detective appears to support such usage:
This “play-off” invoked a very old sense of “off” meaning “exhaust or finish completely” (as in our modern “finish off”). It wasn’t until 1932 that “play-off” came to mean (first in the US, of course) “a series of games, matches, or contests played to decide a championship, competition, etc.” (Oxford English Dictionary).
The points here are the “old sense of off meaning finished” and this long periond of time (from Shakespeare’s till the 19th century) during which the above usage apparently disappeared to reemerge later in expressions like play-off.
Was “playoff” really coined by Shakespeare with the meaning of “finish something”?
Are there other usage instances or phrasal verbs of “off” meaning finished before play-off reappeared in the 19 century?