Wolf spent the first eight of his 16 big league seasons with the organization, making the All-Star team in 2003. He went 69-60 with a 4.21 earned run average. Beyond that, he had a charisma that inspired the Wolf Pack, the first and best of the fans groups that popped up in the 700 level during the final seasons of Veterans Stadium.
• Phillies' alumni
It was only appropriate, then, that he returned last August to sign a ceremonial one-day contract that allowed him to retire as a Phillie.
"It's funny," the 40-year-old said. "While I was playing and near the end of my career, I thought that was something I would never do. But the more I talked about it, I thought it would be really cool. It was the place where I played the longest, arguably had the most success.
"And the way the fans treated me there was something I knew I'd never forget. Obviously, Philadelphia has a reputation for being tough on some people, for being tough critics. But the one thing I'll remember is that I was always treated really fairly there by the fans."
When he became a free agent after the 2006 season, Wolf chose to sign with the Dodgers, just missing out on the the Phils' streak of five straight division titles that began the following year. He went on to pitch for the Padres, Astros, Dodgers again, Brewers, Orioles, Marlins and Tigers. When he retired following the '15 season, he had 133 big league wins.
"At that point, I looked at baseball like a sweat-drenched jersey that I had squeezed every bit of moisture out of as I possibly could. So I knew I could look back and realize that I had played as long and as hard as I possibly could," he said.
He now lives in the Los Angeles area. After getting married in February 2016, he's focused on spending time with his wife, Lindsey, and savoring the freedom that comes with not having a life dictated by the baseball schedule. He plays poker. He learned to snowboard.
"I'm enjoying my time off," he said. "It's just been a little over a year since I retired, and I'm still enjoying that time off. Just kind of catching up on life. Not that I felt like I was giving anything up, but enjoying things."
At some point, he may decide to try to get back into baseball. Or he could go in an entirely different direction.
"I'm just going day by day. I think about possible things that I'm interested in getting into. But, the kind of person I am, I just want to be very passionate about whatever I dive into -- whether that's the in the baseball world or somewhere else. That's kind of my main thing. I want to be able to dedicate whatever I need to do things right," he said.
"I have a couple friends in film who have been trying to push me -- not in front of the camera -- to go that route. It's not something that you just jump into and you're successful. But something along those lines would be pretty cool to learn."
His brother, Jim, is a Major League umpire. That's definitely not an option.
"When I first experienced umpiring, I was 12 years old. I was umpiring 8-year-olds and I quit after two weeks, because I couldn't stand the parents yelling at me," Randy said with a laugh. "I couldn't imagine being an umpire. I don't know how he does it."
The decade that's passed since Wolf threw his last pitch for the Phillies has provided perspective. Back in the day, he publicly disagreed with manager Larry Bowa and pitching coach Joe Kerrigan from time to time. Like most pitchers, he wasn't a fan of the cozy dimensions of Citizens Bank Park.
"Reflection is always good. And reflecting on my time there, I realized that I did enjoy and value the time there," he said.
And then the memories come tumbling out.
His Major League debut on June 11, 1999, at the Vet when he held the Blue Jays to one run in 5 2/3 innings and got the win. Kevin Millwood's no-hitter against Giants, also at the Vet, on April 27, 2003. The arrival of Jim Thome in '03. Billy Wagner being acquired from the Astros ... and the good-natured booing he received when his fastball didn't hit triple digits on the radar gun. Teammates like Mike Lieberthal, Doug Glanville, Rheal Cormier and Thome.
The Wolf Pack, of course.
"Especially at the Vet, when the attendance wasn't as high and you could hear them cheering during the game," he recalled. "I always knew whether I was having a good or a bad game by the number of people who were up with the Wolf Pack. There were always the Wolf Pack guys. And then, if I was having a good game, more people would congregate there. But if I was having a bad game, it would stay pretty isolated."
And that time the construction guys recognized him on the streets of Philadelphia, even though he hadn't pitched for the Phillies in years.
"That was pretty funny," he said. "My time with the Phillies was just a cool experience, on and off the field."