SAN FRANCISCO — Jake Peavy was in the midst of a long explanation of why he has been better with the Giants than he was with the Red Sox. He stopped, squinted and started scanning the room of reporters, a new thought suddenly on the tip of one of the most talkative tongues in baseball.

“Y’all, our catcher is a special player,” Peavy said, changing directions. “Buster Posey is a unique individual and a unique player.”

Posey is in the sixth year of a career that very well could earn him a speech in Cooperstown one day, and it wouldn’t be a long one. Peavy’s answer, the one bisected by Posey praise, was 339 words, more than Posey might say during half an hour on a podium.

The 27-year-old catcher is as even-keeled when he’s hitting .450 for a month as he is during those rare slumps. Most questions about bumps and bruises are answered with a nod and a quick “It’s not too bad,” or “I should be all right.”

In quiet moments, with the cameras off, Posey can be as quick and droll as any player in the clubhouse. He responded to one reporter’s query this spring with a quote from Lindsay Lohan’s “Mean Girls.” Last week, he stopped while answering a question and pointed out to one of the assembled reporters that his fly was down.

Ask Posey about himself and he’s not likely to fill your notebook, but the men who trust him most are happy to fill the void. We asked all the Giants’ postseason pitchers for the one Posey trait that stands out above the rest. The consensus was to look away from the bat that won a batting title. Don’t focus on the arm that allowed Posey to pitch at Florida State and now controls big league running games.

To fully appreciate Posey’s talent, his pitchers say, you need to look into his eyes.

“There’s no panic in his eyes, regardless of the situation,” left-hander Javier Lopez said. “We all pick up on each other’s body language, and if you have a guy that’s a little nervous or tense, you’re going to inherit that tension. He’s able to separate that, and I think that’s what makes us click.”

That’s particularly important this time of the year. It’s no accident that the Giants pitching has hummed along from one World Series run through the next. They have changed aces — from Tim Lincecum to Matt Cain to Madison Bumgarner — and closers — Brian Wilson to Sergio Romo to Santiago Casilla — but Posey is an anchor in the season’s biggest moments.

With games hanging in the balance, he gives relievers of all stripes the same secure look and directness. Hunter Strickland learned that Sept. 1, a game that’s all but forgotten to everyone but the rookie right-hander. It was his major league debut, and when Strickland took the mound, Posey waved away the pressure in a matter of seconds.

“He just looked at me and said, ‘Let’s go, let’s do it,’ ” Strickland said.

That was that. The messages are short and precise and tend to hit the spot. Casilla takes the mound in the ninth ready to pump gas like a prototypical closer.

“He’ll tell me, ‘Casilla — you have to believe in what you’ve got, and you’ve got a good breaking ball,’ ” Casilla said, chuckling. “He always tells me to believe.”

The calmness — the trait cited most often by Posey’s pitchers — was there in the third inning of Game 1 of the World Series on Tuesday, when Bumgarner loaded the bases and Posey walked out for a 20-second chat and pat on the back. The inning was over a pitch later.

The trait is apparent during most of Jeremy Affeldt’s outings, when he’ll call Posey out to the mound to discuss a curveball the left-hander tends to bounce in front of the plate. Posey tells Affeldt the ball looks good coming out of his hand but gently reminds him that, sure, “maybe just try to stay on me a little bit longer” as you come to the plate. That’s the type of reinforcement Posey prefers.

“Everything is always positive,” right-hander Ryan Vogelsong said.

Vogelsong, 37, has been a professional since Posey was in middle school. Tim Hudson, 39, was making postseason starts when Posey was a skinny shortstop at Lee County High in tiny Leesburg, Georgia. But even the veterans benefit from Posey’s tranquillity.

“As a pitcher, you’ve got a tornado out there on the mound sometimes,” Hudson said. “A calm, even temperament from your catcher can really help you settle down. He’s just calm, man. Sometimes I feel like he’s yawning out there. The game is pretty easy to some people, you know?”

Posey does his best to simplify it for others. He’ll urge Bumgarner to climb the ladder with his fastball and will inch farther and farther away from a hitter to make sure Yusmeiro Petit keeps peppering the outside corner with his off-speed pitches. Petit said he doesn’t notice it from the mound, but Posey will see a hitter move his feet an inch or two to cheat on the darts Petit loves to throw on the outside, so the catcher will shift the whole plate over. When Petit first started throwing to Posey, he was baffled when the catcher would call for time in the split-second before he was about to start his delivery.

“It’s because he thinks the hitter maybe knows what’s coming,” Petit said. “He’ll see some move, and he’ll call time out and we’ll go through the signs again.”

Tim Lincecum calls this Posey’s “head game.”

“He’s always been like that — a student of the game,” Lincecum said. “As a pitcher, you always think about what a hitter is doing lately. But he cuts that into a more minute sequence for just that game. It’s not easy to do, but he’s got such a great eye and feel that he can read hitters and make adjustments mid-at-bat.”

Peavy fully comprehended Posey’s intelligence as he watched the Cardinals’ pitchers waffle through the NLCS without Yadier Molina, generally regarded as the best defensive catcher and game-caller in the majors.

“Buster runs the game and manages the game no less in my eyes than Yadier Molina,” Peavy said. “It blows me away that he’s the player he is offensively because of how much he is involved on the defensive side of the ball. I’ve never played with anybody that quite does it the way he does.”

Peavy compared Posey to former Red Sox teammate David Ross, a 37-year-old journeyman known for his game management. But while Ross is a career .233 hitter, a typical line for a defense-first catcher, Posey is batting .308 in six seasons. He was in the squat for nearly 1,000 innings this season but still finished fourth in the league with a .311 average and hit 22 homers with 89 RBIs. Posey is hitting .288 this postseason and has caught every inning.

“The dude is resilient,” said Romo. “He’s tough. He’s back there taking shots, foul tips, blocking balls, calling games, batting third, driving in runs, facing the other team’s best dudes — I don’t know how he does it.”

For Posey, it’s simply the job, one he loves and wants to continue even as others talk of moving him to a less demanding position. So, what exactly is the catching trait Posey is most proud of?

“I get really excited when it’s a close pitch and I keep it in the strike zone,” he said. “I think that’s something that’s maybe something small, but it can be a difference maker.”

Framing a pitch is an art that Posey gets better at by the year, one that boils down to stealing a strike for your pitcher. No wonder they appreciate him so much.

For more on the Giants, see Alex Pavlovic’s Giants Extra blog at blogs.mercurynews.com/Giants.