Is a CFI's 1st-time pass-rate based on the student or the instructor's first attempt? This question doesn't apply to anything I have done personally, and beyond word-of-mouth, I have no references about this happening.
Some people claim that if an instructor endorses a student and they fail an FAA check ride and then a different instructor endorses the same student for the re-take and then the student passes the re-take, that the instructor who endorsed the re-take may count this on his or her record as a first-time pass since the student passed on the first attempt for that instructor's endorsement.
The intended benefit of recording this would be utilizing it for CFI renewals and gold-seal CFI applications.
Is this a practice that is considered to be acceptable to the FAA?
I believe that your pass rate is based upon your number of students who passed on their first attempt after endorsement vs the number of students you endorsed for the checkride.  I don’t believe the FAA makes any other distinctions here, at least not for §61.197 requirements for the renewal of a flight instructor certificate nor for 89001, Section 13, Issuance of a Gold Seal Fight Instructor Certificate.