Say you have a tournament with N people. You can easily generate a schedule using whatever algorithm you'd like, and there you have one possible schedule.
Now by changing the order of players, you will change the order in which they play each other.
(Take your chart with players 1,2,3,4 with a set schedule. Setting Alice = 1, Bob = 2, Carl = 3, Dave = 4 will produce a different play order than if you set Alice = 4, Bob = 3, Carl = 2, Dave = 1).
There are N! ways of creating this permutation.
Your schedule also has N-1 rounds of play, which you can also change the order. This creates another (N-1)! ways of rearranging your tournament.
I don't know if I've thought of everything, but a lower bound for the number of possible tournament arrangements you could run is N!(N-1)!
If you have an odd number of contestants then N should be the number of contestants +1 since the schedule will use a ghost player.
I'm curious as to why you wanted this information, I can't think of any useful application of this.
