Ah I see.
Well, then it goes back to Rosco's concern.
I might win against Dan (or many other very skillful players, but Dan has the shortest name) if I'm super lucky that day during our first game, but without the luck in streak, I probably will lose. Then in my 2nd game with Dan, he can easily beat me with his skills, regardless of the starting player.
So I might just lose badly in all of the 2nd legs in each pairing, as opposed to more loss when not being the first/second player.