Always a voice of calm reason, the 40-year-old southpaw is something of an authority on catchers. He has worked with dozens of receivers over the years, all sizes, shapes, nationalities and attitudes.
Very few, he will tell you without qualification, have measured up to Jeff Mathis.
"My locker was next to Jeff's in Anaheim," Oliver, an Angels reliever for three seasons before joining the Rangers for a third stint, said on Wednesday at Surprise Stadium. "I got to know him well. I think he learned some things from me, and I learned some things from him. He's a smart guy, a take-control kind of catcher. He's a good athlete, and he called a good game, to me.
"I really enjoyed working with him, and I know the other pitchers felt the same way. He had a rough time last year, breaking his wrist [two weeks into the season], not playing the way he can. He carried us in the playoffs [in 2009] with his bat. If he can do that under that kind of pressure, it tells me he can hit if he just relaxes and plays the game. I'll take him, any time.
"I think it's going to click for him one of these years and he's going to take off from there. He could be an All-Star catcher. No doubt in my mind."
This, no doubt, will generate expressions of disbelief accompanied by howls of protest from the many Mathis detractors who point to his .199 career batting average in 333 games and insist he is a liability no matter how good he might be defensively.
Mathis, in his customary manner, is quietly going about his business this spring.
"I'm just trying to concentrate on what I'm doing and playing with a free mind, not letting anything bother me," he said. "It's the same attitude I've always taken to Spring Training. I'm here to try to win a job. Nothing is handed to you in this game.
"I feel good. The wrist is healed. I just have to stay healthy and perform the way I can."
His best friend, Mike Napoli, has moved to Texas, an American League West rival, to team up with Oliver and another former Angels reliever, Darren O'Day.
"I'm pulling for Jeff to have a good year, show everybody the kind of player he is," Napoli said. "I don't think anyone realizes how tough it was for him last year trying to come back from a fractured [right] wrist. That affects everything you do as a catcher and a hitter.
"When everything was good, and we were winning, everyone loved him. The guy gets hurt, and everyone gets all over him. I saw him this winter. We hit in the cage [at Mathis' Florida home], and he looked awesome. He was sitting back a little more on his back side. I think he's going to have a good year."
In terms of experience, Mathis seems the logical candidate to assume the No. 1 job with the Angels after basically sharing it with Napoli the past four seasons. But Bobby Wilson and Hank Conger also have designs on the position, and manager Mike Scioscia is holding judgment.
"He knows he has to bring more offense," Scioscia said. "On the defensive end, he's an important piece to give guys out there in our rotation. As far as what he's done on the defensive end, that's critical.
"If Bobby and Hank can match that defensive end, there's obviously more pressure on Jeff to match that offensive presence. He has more potential. I think he's better than a .200 hitter. He understands he has to move forward."
In the 2009 postseason referenced by Oliver, facing the Red Sox and the Yankees, Mathis was 8-for-15 (.538) with five doubles. His 11th inning walk-off double claimed Game 3 of the American League Championship Series against New York.
A .276 Minor League hitter in 681 games, he was hitting .324 and riding a 10-game hitting streak last April when he fractured the wrist trying to block a pitch in the dirt. He never regained his stroke when he came back two months later, finishing at .195.
"There are times during the season when he got hit and hit like he did [in the 2009 postseason]," Scioscia said. "He's capable of going on runs like in the playoffs."
Conger is a switch-hitter with power and discipline, and Wilson is a contact hitter with the ability to reach the seats on occasion. They will be pushing Mathis, a man they respect a great deal.
"We've learned a lot from watching Jeff and Nap," Wilson said. "We're all here trying to show what we can do and win jobs."
Scioscia is raising the bar for Mathis, who is hitting .333 through three spring games. That is clear in the boss' bottom-line statement: "The competition level for his position has risen."
In other words, Mathis needs to carry an October attitude -- competitive juices flowing, his focus sharp and narrow -- through March and into April and beyond.
Lyle Spencer is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.