That wasn't the case late during his time with the Toronto Maple Leafs, when coach Randy Carlyle used him in a reduced role. After the Leafs bought out the final four years of his contract, he signed with the Washington Capitals, who figured to make him a more prominent part of their offence.
Grabovski is playing down the lineup on what could be called the Capitals' second or third line, but he's much more comfortable now.
"It's different," Grabovski said. "It's just trust of the people. They trust me like I can play."
Grabovski doesn't think that trust was there from Carlyle last season, so he considered the buyout a positive move for his career. Things aren't all perfect with the Capitals, but he's tied for third on the team in scoring and enjoying the fresh start going into Saturday night -- his first game against his former team at Air Canada Centre.
The 29-year-old is motivated to play in the place he calls his "hometown," but this entire season is a proving ground for Grabovski with the Capitals and the Leafs without him. Toronto is 13-8-1 and in third place in the Atlantic Division despite injuries to centres Tyler Bozak and Dave Bolland and the suspensions of winger David Clarkson and centre Nazem Kadri.
Meanwhile, Grabovski has found a groove on a line with Jason Chimera and Joel Ward and fit in comfortably within the Capitals' system, where he has fewer checking responsibilities and more offensive freedom.
"I don't think we produce like checking hockey here," Grabovski said in an interview with The Canadian Press this week at the team's practice facility near Washington. "It's more offensive smart hockey than we play in Toronto, completely different style of the hockey."
Grabovski has seven goals and 11 assists going into the Capitals' game Friday night against the Montreal Canadiens. He had nine goals and seven assists during last year's lockout-shortened 48-game season with the Leafs.
His ice time isn't substantially different, either -- just under 16 minutes a game -- but coach Adam Oates has put Grabovski into spots where he feels more comfortable.
"He just give me (a chance to) do on the ice what I do all my life, what I like to do," Grabovski said. "That's the best way I can play and enjoy the hockey."
And the Capitals enjoy having him around, on and off the ice. Oates is trying to mould Grabovski into more of the pass-first centre he prefers, but along the way he has been satisfied with Grabovski's willingness to learn.
"I really love how conscientious he is about his game," Oates said. "He likes video, he wants video, he wants to learn, he wants to watch his shifts, he wants to see where he made mistakes. I've talked to him about what I think in terms of he's got to change a little bit. Do I like the player? Yeah, I really do."
Grabovski likes the weather and living in the Washington area. And of course he likes playing hockey with more of an offensive focus.
Grabovski has bounced around the lineup a bit over the first quarter of the season. He had a hat trick on opening night at the Chicago Blackhawks, which included the only two power-play goals he scored for the Capitals before being moved off the top unit in favour of Marcus Johansson.
He's still getting power-play minutes, similar to the time he got last season for the Leafs.
"I still learn," Grabovski said of his role on the power play. "I learn new things about the team. But I just enjoy to stay and play here."
Oates doesn't know exactly why things went awry for Grabovski in Toronto, and before that in Montreal. What he knows is what he has seen in his growth alongside Chimera and Ward.
"He's played in two very stressful organizations, and I don't know what their rules are, but I've given him ours," Oates said. "It's funny how he's having success doing simple little things, just waiting for his opportunities. He's got two guys to play with that he's got to create (for) them. To score goals in this league it takes all three guys now, generally, and I think he's using them better and trusting them and they're getting to know him better."
Given what Oates wants in a centre, Grabovski has some adjusting to do. He's much different than the man he was theoretically replacing in the Capitals line, Mike Ribeiro, who was a point-a-game player last season before signing with the Phoenix Coyotes.
Oates has spent time working with Grabovski to get him more accustomed to the all-around job of manning the middle of the ice.
"Not that centremen don't score goals, of course they do. But they've got to play in their own end," he said. "They've got to spend a lot in their own end, so that makes it difficult to go down the other end and score. They've got too much responsibilities in their own end."
Grabovski knows all about the defensive end of the ice after playing for Carlyle. He made some disparaging comments about his former coach after being bought out but also understands Carlyle and his staff helped him become a better defensive player by preaching discipline.
Busy with his new life in Washington, Grabovski hasn't paid close attention to the injuries at centre that have forced Toronto to make plenty of changes. He didn't give any thought to the idea that the Leafs could've used him while they were experimenting with James van Riemsdyk at centre and acquiring Peter Holland.
"I don't think these injuries change the style of Toronto game," he said. "I know the players who scored before, they score right now."
Grabovski's scoring, too. His line has been the Capitals' most successful one of late, so much so that Oates joked it was the top unit on a team that has Alex Ovechkin and Nicklas Backstrom.
"Right now they are playing like a top line," Ovechkin said. "To be honest with you, Chimmer, Wardo, they score big goals for us, they make a play."
Ward said Grabovski has "embraced the enthusiasm of the green line" and has been a major part of that trio's success.
"He's a good skater, he's got a good shot, he's got a good hockey IQ," Ward said. "He's very offensive-minded, obviously, so it makes things a lot easier to play with when he's creating that momentum up the ice and with his abilities he creates a lot on his own."
Off the ice, Ward described Grabovski as pretty quiet. But Ovechkin likes how Grabovski has fit in to the Capitals' locker-room.
"He's not that kind of guy who's going to come here and scream and make jokes around," Ovechkin said. "He's kind of more focusing guy. It's a good part of him."