Alan Beban wrote...
....
I didn't claim any advantage for those formulas; simply that they were

an alternative. . . .

As in '=1+1+1+1+1+1+1' is an alternative way of representing 7?

Some alternatives are bad ideas. Sadly, some people are incapable of
grasping that simple fact.

. . . I started working on them in an effort to provide
something that might be useful after that little snippet of silliness
that you proffered as a solution(!) for the case of an unsorted list
of
names in your first posting in this thread. (By the way, some might
be
wondering about the acknowledgment of your mistakes that you are wont
to
claim you always step up to.) Since I had done the work, I posted the
result.

Reread my preceding message to which you responded. Especially, notice
the phrase, "Fixing the A3 and Y4 formulas." I'll be more explicit,

FIXING *MY* PREVIOUS A3 and Y4 FORMULAS, AND THE FORMULAS IN MY FIRST
RESPONSE DIDN'T WORK AT ALL.

Happy?

The differences in performance of the several approaches,
notwithstanding your esoteric analysis, are probably trivial for many
(most?) users in many (most?) circumstances.
....

In which case there are considerable advantages to the single
formula/result approach, namely,

A3:
=IF(ISERROR(MATCH(B3,B$1:B2,0)),MAX(A$1:A2)+1,
INDEX(A$1:A2,MATCH(B3,B$1:B2,0)))

As for esoteric, it explains a lot that you're apparently indifferent
between O(N) and O(N^2) approaches to solving problems.