Your formula on unconcatenated string does not seem to work correctly.

Worked ok for me, I suggest you try it again. You can change
(B$3:B$13="A")/(C$3:C$13="C") to MMULT((B$3:B$13="A")/(C$3:C$13="C"),1)
to make it a normal formula with out array-entry.

formula solutions are about 20 times slower than my VBA code.

Formula solutions are always preferred in the worksheet functions group,
many people don't want the hassle of enabling macros and the files are easier
to distribute. If you want to do these sort of operations efficiently and
much faster try
downloading cygwin and write a one line awk command.