The stamina is a factor, yes. Are your pitchers all tired? In the entry pool league, my pitchers (especially relievers) are all exhausted by Saturday, as the team has to play 6 days in a row. It’s not as bad in the Iron/Bronze leagues, but even so, if you have a lot of low-quality relievers with low stamina, fatigue will be an issue.
Also, the AI does a bad job of matching relievers to roles. You don’t want “red stamina” guys doing middle or long relief. They should be setup, closers, “openers,” or specialty (meaning left-handed specialists, brought in to pitch to lefties). I had to switch all mine around. “Blue stamina” guys should be starters, long relief, or middle relief. “Green stamina” can be in all roles, but if they start, I put pitch count limits on them.
One intriguing question is whether to use the new “opener/follower” roles. I’m trying it now, as an experiment – setting a low-stamina reliever to “opener” and a high-stamina one to “follower”. I don’t know how this affects the regular rotation. A related question: is lefty “specialist” still a thing? Does baseball now require relievers to pitch to 3 batters or something?
You can change how often the AI hooks your pitchers in both Team (also called “Global” or Overall") Strategy and Player Strategy. If you click on your team menu, you’ll see options for both.
In Team Strategy, you can set overall priorities for hooking pitchers, depending on the phase of the game. You can also decide how much to emphasize handedness matchups, how to handle intentional walks and pitch-arounds, etc. I don’t use Team Strategy as much in PT as I do in other modes. In regular OOTP, I can sim many games quickly and see how Team Strategy is affecting things more clearly. That’s harder in PT.
I do use Player Strategy in PT, though. In particular, for starters with mediocre Stamina, I set pitch-count limits: 80-90 pitches for a pitcher with stamina in the 60s, say. In addition, you’ll see options for when to hook a reliever, etc. For batters, you can adjust base-stealing frequency, bunting, pinch-hitting, benching, etc. The easiest way to get to these options is to select strategy from the “Actions” drop-down menu on the top-right of the player’s screen.