In another post I got an Offset answer, but what I ultimately want to do and
can't seem to get to is:

On Sheet YTD, look up Cell A10 (Smith) in the range "Budget", (Smith is
found in cell A13 in the range), then calculate this offset for the Row A13
in the range "Budget"

=SUM(OFFSET(A13,0,0,1,A1-4))

And change the row number based on the look up.
TIA!