It can be hard to determine the philosophies of major league teams by looking at how those teams play, because every intelligent manager will tell you that the way he manages is largely dictated by the players he has available. The Rays bullpen has thrown more innings than any other bullpen in the American League, and while Kevin Cash and the Rays front office might have already thought that bullpens were generally underused, I doubt they'd be leading the pack if they had the Best Rotation in Baseball (TM) featuring Alex Cobb (RIP), Drew Smyly (RIP), Chris Archer, Jake Odorizzi (RIP), and Matt Moore (about to be resurrected?).
Similarly, how much a team bunts and how much they run is greatly affected by how fast their players are and how good they are at hitting. Major league teams play to their strengths.
But minor league wins don't matter in the same way, so I would imagine that if a front office wants their players to be good at something, they ask their minor league affiliates to practice that skill in minor league games. MLB Farm, the minor-league affiliate of Baseball Savant, has a pretty neat tool that allows you to compare tendencies of entire minor league systems. Let's take a look at a few.
One would expect American League teams to bunt less often than their National League brethren (because their pitchers won't be hitting), but the message is still clear. The Rays do not care about the sacrifice bunt. They do not ask their players to do it at the major league level, and they are having their players in the minors try it less than any other system but Baltimore.
But small ball doesn't just mean bunting. Here are stolen bases across the minor leagues:
And here are caught stealings:
Ah, but they don't want to simply "wait around for the three-run homer," as detractors of the power game like to say about teams with a modern understanding of run values. The Tampa Bay Rays think that stealing bases is important. Their players have stolen the thrid-most bases and been caught the third-most times, combining to be the second-most steal-happy organization in baseball behind only Colorado.
The organizational charts are a fun tool, and I urge y'all to head on over, and play with them for yourselves. Nothing else I saw was quite as clear as this, though. The Rays think that giving an out away to move the runner over is stupid. But they think that taking risks on the base paths in order to gain the extra base is smart.