Clock optimal solver

As there're only 18 possible moves in WCA notation (instead of all 30 moves of the clock puzzle), we can easily solve the clock by brute-force search + Gaussian Elimination.
The average solution length of the optimal solver is about 10.8 moves, which is 2 moves less than randomly generated moves (14 * (1 - 1/12) = 12.83). 
Why are we filtering out some in advance, but not all? It seems to me that we should do all or nothing.