Playing in a Dodgers franchise, it's really easy to carry 11 pitchers instead of 12, especially when one gets hurt. Depending on the situation, and who it was that gets hurt. I took 12 pitchers into the start of the season and 13 position players. Adrian Gonzalez got hurt, which was a big blow for one month so I actually had to call up Barnes to act in a backup catcher roll, put Ellis behind the plate exclusively, Grandal at first to fill in for Gonzalez, and then when fatigue set in when I had 20 games in a row without an off day, I had to put Turner at first base, give Grandal and Ellis some days off here and there, put Culberson in at 3rd, or Kike, throw Barnes behind the plate etc. it got tough sometimes and it was very frustrating as well because Ellis went 11 straight games without a hit but there was nothing I could do guys needed days off to avoid any further injuries or silly mistakes that led to errors (which there were a lot of). Now Utley just got hurt a few games after Gonzalez came back and he's gonna be out 2-3 weeks so I actually had to call up Crawford for an extra outfielder because I needed to put Kendrick at 2B instead of LF, so I had Kike, Thompson, and Crawford as my backup guys on the bench. The Dodgers have so many guys that can play so many places, especially the infielders so it makes roster management a lot easier than most other teams. They don't play all the positions at a gold glove level and have had some game costing errors but it has gotten me through tough times more than not.
Now if a pitcher were to go down, let's say while a fielder was also hurt, depending on who got hurt in the bullpen, I might stay with the 11 in the bullpen and bring up an extra batter and really focus on using the double switch to get as many innings out of my bullpen guys as possible and thus, have enough fielders for the situation. There's nothing worse than going extra innings and having to use bullpen guys in key hitting spots because you've ran out of position players. You can always try to save a long reliever for late tie game situations if you feel it's going to go extras and make sure to use that double switch.
If I was in the American League, I would never go below 12 pitchers simply because 13 position players is enough in almost every situation because there is no need to pinch hit unless a guy is extremely struggling or an injury. I would maybe even go 13 pitchers and 12 batters if my rotation was struggling and I was looking for a go-to reliever for some key middle innings.
Thank you to the OSFM guys for making it possible to pull up real-life ballplayers in the minors when guys are getting hurt at the big league level!!!