Unknown, but possibly a use of pat (a light tap), in the sense of hitting the mark.
"off-pat." YourDictionary, n.d. Web. 20 September 2018. <http://www.yourdictionary.com/off-pat>.
off-pat. (n.d.). Retrieved September 20th, 2018, from http://www.yourdictionary.com/off-pat
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