In the 22 years I've been a Braves fan, I've seen us fall in the playoffs with just about every sort of team. We've lost with rotations stuffed with aces and shaky bullpens. We've lost with decent rotations and outstanding bullpens. We've lost with outstanding rotations and outstanding bullpens. We've lost with outstanding pitching staffs and poor offenses. We've lost with fair pitching staffs and outstanding offenses. We've lost with offenses that hit the ball out of the park and with offenses that drew lots of walks and offenses that struck out a ton and offenses that made a ton of contact and offenses that scored lots of runs and offenses that scuffled. We've lost with great defenses and average defenses and mediocre defenses and poor defenses.
We've had great, 100+ win teams fall in the LDS (2002, 2003). We've had extraordinary, amazing teams fall in the LCS (1993, 1998). We've lost with a newly minted Hall of Fame manager. We've lost with teams assembled by a future Hall of Fame executive.
The lesson here is simple: the only thing you can do to improve your chances in October is to improve your team overall, and even then you're just making a marginal change in your odds. Since there are rarely mediocre teams in the playoffs (that .500 Padres team a few years ago notwithstanding), a postseason series is usually a battle between two reasonably good teams. And when two reasonably good teams play five games, picking the one that's going to win three games is largely just a matter of guess work.
There's no magic October Formula(TM). You want top-notch, shutdown aces? Been there, done that, witnessed the heartbreak. My namesake headed our rotation for a decade and is a couple months away from being the least controversial Hall of Famer in recent memory. One title from him. And he was backed by what was arguably the greatest rotation in the history of the game.
You want David Price? Sure, we all do. He's a great pitcher. And since he became a starter, Tampa has never advanced beyond the LDS.
In fact, let's go big and give up the farm for Clayton Kershaw. He'll guarantee a deep postseason run. Except since becoming a starter for LA, the Dodgers are 2-2 in his postseason series and he has a 1-3 record and a 4.23 ERA.
Put simply, there's nothing you can do in the off-season that will significantly affect your odds of winning a postseason series, save improving your team to the point where you can reasonably expect to make a postseason series. If you're already in that position, then you, as a general manager, just have to accept that what happens in October is out of your hands, unless you're capable of assembling a true, 1998 Yankees-esque juggernaut.