Sorry, but teams need to be analytically capable these days. If you can use numbers to your advantage you need to do it or you will put yourself at a huge disadvantage.
But here is a point that absolutely NOBODY is talking about. Rocco Baldelli is not a slave to analytics, he is a slave to his 'gut' despite what the common refrain is. I dare someone to provide a stat that says Manny Margot should ever pinch hit after he's gone it 0-fer-whatever. Baldelli refuses to use young left handed hitters against left handed pitchers even if the alternative is a poor option and it's certain it will only be one at bat. Baldelli pinch runs for minimally slower but better hitters at all points in the game. He uses Jhoan Duran in non-save situations when Duran has a 5.63 ERA in non-save situations. These moves are his prerogative, not analytics because an analytical evaluation would tell him NOT to make these moves, or at minimum, don't ALWAYS make these moves.
He is extremely predictable which all but proves he is managing with his 'gut' and not numbers because when factoring in all of the variables like pitcher, opponent, ballpark, inning, number of outs plus all all of the actual counting stats, there is no way that the same decision should be made Every Single Time when the factors are never the same. An analytically inclined manager would surprise you with his decisions due to obfuscated data, yet we are never surprised.