During the season, 13 is a good number to have when you have 2 league games and a scrimmage. I usually carry 12-14 depending on the time of the season. Right now I have 12, and I hope to add one player through the draft or TL. So I will start the season with 14 players. Once I get bumped from the cup, I will trim it down to 13, and then sell a player near the end of the season to get to 12 again.
That cycle seems to work good. One thing to consider is what to do when an injury hits. With 13 players, when a player goes down, you can still manage the minutes with 12. Personally, I find it hard to maintain good GS when there are only 11 players and 3 games.
Just my 2 cents.