But two of his players whom he seemed to talk about the most in those situations this season were second baseman Maicer Izturis and shortstop Erick Aybar.
He praised the duo all season for their ability to hit in those pressure-filled situations and various stats on the season proved his assertions correct -- for example, Izturis batted .311 with runners in scoring position and two outs and Aybar batted .318 in the same situation.
So, it was no surprise when the two delivered the two biggest hits in the Angels' crucial 4-1 win over the Red Sox to take a commanding 2-0 lead in the American League Division Series on Friday.
It was Izturis who delivered the go-ahead single in the seventh inning before Aybar gave the Angels two important insurance runs later in the frame with a triple that knocked right-hander Josh Beckett out of the game. And of course, both hits came with two outs in the inning.
"I think a lot of it has to do with maturity," hitting coach Mickey Hatcher said about the duo's success in those tense situations. "I think those guys really believe they can play. Being a young guy on a championship-caliber team is tough. It's not about developing anymore, you have to play winning baseball."
But it was really the entire middle-infield trio of Aybar, Izturis and fellow second baseman Howard Kendrick that came through for Angels in their seventh-inning rally.
Izturis, who platoons with Kendrick at second, got the start, but Kendrick played a huge role when he pinch-ran for Vladimir Guerrero after the slugger drew a walk against Beckett.
Kendrick was able to steal second base to set up what proved to be the game-winning single for Izturis on a line drive back up the middle just past the glove of Beckett.
"Fortunately, Izzy got the big two-out hit for us," Scioscia said. "Howie got a good jump and was able to get to second. And you know, Izzy got the big hit that made it all work."
For Izturis, the key was to try to hit the ball back up the middle after flying out to left in his first at-bat and striking out in his next appearance against Beckett. He said he was trying to pull the ball earlier in the game, but his strategy certainly worked this time around.
"In that situation in the playoffs, that was one of the biggest hits of my career," Izturis said.
It was just another example of Izturis getting a huge hit for the Angels, as the switch-hitter is a career .263 hitter with the bases empty and a .327 hitter with runners in scoring position.
"I look at video for those situations because pitchers sometimes change the way they pitch," Izturis said. "I just try to follow what I learn from watching video."
Izturis then took it upon himself to steal second base with catcher Mike Napoli at the plate to further put pressure on Beckett, who threw 28 pitches in the inning.
"Everybody knew I was going to steal, but they didn't know what pitch," Izturis said with a smile. "I picked the right one to steal on."
Izturis, though, would've eventually reached second anyway, as Napoli was hit by a pitch to set the stage for Aybar, who earlier singled off Beckett in his first at-bat of the game.
This time, Aybar got Beckett again, as the right-hander left a 2-1 fastball over the plate and Aybar connected for a triple over the head of center fielder Jacoby Ellsbury for the decisive blow against the Red Sox.
"I saw a fastball right down the middle, and fortunately I was able to connect," Aybar said.
Beckett, who allowed four runs on five hits over 6 2/3 innings to get pegged with the loss, was none too pleased with the pitch he threw Aybar.
So with the two big hits by Aybar and Izturis, as well as a superb effort by right-hander Jered Weaver, the Angels are now just one win away from advancing to the American League Championship Series for the first time since 2005.
And Izturis made it clear that the team's strategy won't change heading into Game 3 at Fenway Park on Sunday.
"It's a short series," Izturis said. "We've played there before, and we know that we're going to continue playing aggressive just like we've been playing so far."