Note that the formula from post #2 is calculating the following:
(# cells that say WINNER) / (# cells that are not blank)

If you wanted this:
(# cells that say WINNER) / (# cells that say WINNER, SCRATCH, or LOSER)
then you can use this:

=SUMPRODUCT(SUBTOTAL(3,OFFSET(A2:A251,ROW(A2:A251)-ROW(A2),0,1)),--(A2:A251="WINNER"))/SUMPRODUCT(SUBTOTAL(3,OFFSET(A2:A251,ROW(A2:A251)-ROW(A2),0,1)),(A2:A251="WINNER")+(A2:A251="SCRATCH")+(A2:A251="LOSER"))