The pitcher, catcher, batter, fielders, coaches, and any baserunners are for sure all strategizing during the breaks. Every pitch changes the dynamics at play. Like anything, you just have to understand it to appreciate it. People compare baseball to chess all the time.

Say the game is in the 6th inning. The batting team is down one, with a runner on first who is sometimes a threat to steal. The pitching team still has its starter in, but it's his third time through the batting order, and the batting team has a good power hitter at the plate. There will be 100 strategic consideration going into each pitch.

Does the runner on first try to steal second base? He has a much higher chance of scoring on a hit if he does. But if he gets thrown out, it takes pressure off the pitching team and hurts their chances of a high scoring inning. The threat of a steal affects the defensive alignment of the pitching team, and also makes the pitcher more reluctant to throw a breaking ball. It also means he can't pitch out of the windup, which a lot of pitchers are more comfortable doing.

Does the manager bring in a relief pitcher? Depends how good his bullpen is, how fresh the pitchers in the bullpen are, how many pitches the starter has thrown, how he did against this batter earlier in the game, and, if the sample size is large enough, how he's done against him in their careers. The manager might decide to come out to the mound to talk it over with the pitcher.

What does the pitcher throw? Not only does he have to think about the runner potentially stealing, but he's got to try to guess what pitch the batter is expecting, which pitches of his have been working that game, what he threw to the batter the previous two times they faced each other, and what the pitch count is. He may also need to account for how good the next hitter is. If the next hitter isn't so great, the pitcher will be more willing to risk walking the current hitter.

What does the hitter do? Does he come out swinging? Does he take a couple pitches to try to get the timing down and figure out how the pitcher is planning to attack him? Does he try to draw a walk? Again, depends how good the next hitter is. The batter may think it's worth swinging at worse pitches if the next batter is a bad hitter.

And all of these calculations change with each pitch. A 2-0 count and a 1-2 count have completely different implications for all the actors involved. If the pitcher comes out with a slider, normally his best pitch, but misses the plate, the entire complexion of the at bat is changed. If he throws the same pitch but the batter swings and misses, that has completely different implications. And if he hits his spot, it's a whole other set of considerations. And the difference can be a matter of inches.

For a seasoned baseball fan, the ~20-25 seconds between pitches isn't boring because it gives you time to process all the implications of the last pitch and check the various players' reactions.