No, not for players -- that's a tired old assumption that should be discarded with the leftovers sitting in your fridge since the Brewers were still mathematically alive.
I'm talking managers.
Take Buck Showalter.
In his first postseason, which was with the Yankees in 1995, he suddenly lost faith in his closer, John Wetteland, after he'd faced four batters in Game 4 of the ALDS against the Mariners. All had reached base, topped off by Edgar Martinez's grand slam. In Game 5, he let a fatigued David Cone walk in the tying run in the eighth inning on his 147th pitch of game. He didn't yet trust a rookie reliever named Mariano Rivera, even though he'd pitched well in the series and kept the game tied in the eighth. So he brought in Game 3 starter Jack McDowell, who couldn't hold the lead the Yankees had taken in the top of the 11th. (Really, this article is just an excuse to link to this video. And just because: Here's the grand slam.)
Then, while managing the Diamondbacks in 1999, Randy Johnson took a 4-4 tie into the ninth inning. Yes, it's Randy Johnson. But he'd faced 32 batters. Showalter let him face four more. Three got on, and then Edgardo Alfonzo hit a grand slam off a reliever named Bobby Chouinard.
Showalter learned: Trust your bullpen. We saw quick hooks in the Orioles' series against the Tigers. Yes, some of that is a function of not having a Cone or Johnson to overextend, plus a deep bullpen you can rely upon, but I believe Showalter has learned not to let your starter go too deep. He's also showed the willingness to stick with the hot hand. He used Andrew Miller twice against the Tigers to get five outs and once in the sixth inning (earlier than he had used him all season).
Bruce Bochy managed the Padres to four playoff appearances before the Giants hired him. He's learned that you can't manage the playoffs like you do the regular season, whether it's putting Tim Lincecum in the bullpen like he did in 2012 or pulling a starter with a 3-1 lead in the third inning like he did with Barry Zito that same year. I was actually a little surprised he let Ryan Vogelsong start the sixth inning against the Nationals in Game 4 the other night, but he did pull him with two outs and nobody on to bring on Javier Lopez to face Adam LaRoche.
Mike Matheny is now in his third postseason, but for the most part still seems to take a regular-season approach to managing his starters. He lost Game 5 of the World Series last year when the Red Sox scored twice off Adam Wainwright in the seventh to win 3-1 and then had a surprisingly slow hook with Michael Wacha in Game 6 (he allowed six runs). He got five good innings out of Shelby Miller in Game 4 against the Dodgers and then had a bit of a slow hook in the sixth inning. The Cardinals got three outs that inning -- two on a double play and the third when Andre Ethier got caught off third; that inning easily could have exploded in their faces, in part because Miller was left in too long.
Ned Yost? Yost certainly has a plan: Get a lead and then hand the ball in the seventh inning or later to Kelvin Herrera, Wade Davis and Greg Holland. The problem with him is if that plan doesn't unfold exactly like that, what does he do? His bullpen is deeper than those three with the emergence of Brandon Finnegan, the solid Jason Frasor and even starter Danny Duffy. He doesn't have to rely on his starters to go six or seven innings every game. It will be interesting in particular to see if he rides James Shields, who has scuffled in his two postseason starts. Yost has the bullpen depth to go to it early, especially if he's willing to extend his best relievers for more than three outs like Showalter did with Miller.
All this gets back to what I wrote Wednesday about when to remove a starter. All four of these teams have good bullpens. All four managers should be using them as much as possible. On paper, we should have two low-scoring series. The key innings may very well be those precarious sixth and seventh innings when the starter is getting tired and it's too early for your closer. How these four managers handle those innings will play play a key role.
Oh, and if you're facing a lose-and-go-home game and it's tied in the seventh inning, I recommend not using your 10th-best pitcher.