In fact, five of them have been suspended by the former chief NHL disciplinarian this season alone.
"We kind of did joke about it," said forward James van Riemsdyk with a laugh. "He owes a couple of guys some money here."
After watching their season fall apart, the Leafs announced Friday that Shanahan is joining the team as president and alternate governor.
Shanahan, who had been working as the head of the NHL's Department of Player Safety, will oversee all team operations for the Leafs and will begin work immediately.
Toronto players say they having a huge amount of respect for Shanahan, who is a member of the Hall of Fame after a playing career that included more than 1,500 games, three Stanley Cups and an Olympic gold medal.
"His resume speaks for himself," said van Riemsdyk. "He's a Hall of Fame player, won championships so I'm sure he knows what it takes on that respective. We'll meet him I'm sure in the coming weeks or whatever and I'm sure he'll do a good job."
"He has a good hockey resume and it's always good to have people like that associated with you."
The Leafs wrap up the regular season Saturday night against the Ottawa Senators and are excited that action has already been taken after what can only be called a disastrous season.
Toronto will miss the playoffs after an eight-game losing streak saw them go from second in the Eastern Conference's Atlantic Division to out of contention, and they were never able to claw their way back in to the top eight.
Heading into Saturday's game the Leafs sit 12th in the conference, and the hope is Shanahan will bring a winning culture to the underachieving club.
"It's nice and a refreshing feel," said Nazem Kadri. "It gives you an opportunity to evaluate the season and overlook what we've done.
"He's definitely an experienced person that's going to bring a lot of depth to the organization."
While Kadri looks forward to having someone of Shanahan's pedigree join the organization, he also realizes it could result in a number of changes.
"I guess you could look at it that way," said Kadri. "Like I was saying before he's a very experienced person, 20 years in the league, a few Stanley Cups so he's definitely the ideal person you want in your organization."
Shanahan's arrival could impact Randy Carlyle, who has come under fire of late, but the Leafs head coach said he's not about to worry about things out of his control.
"I'm trying to live my life as a hockey coach and do the things that you do," said Carlyle. "Come to work and try to be positive and put an honest day's work for an honest day's pay. Our job doesn't change dramatically. Obviously when the situation is the one we're in it makes it more difficult, but you still have to come to work and you have to live."
That's not to say that Carlyle doesn't expect changes to take place.
"Obviously (Shanahan) with his appointment and his hiring in the upper tier of management obviously has a new voice, a new say and he determines is the right way to go so that's why they hired him," said Carlyle.
Carlyle has a past with Shanahan as the two played together for Canada and were roommates at the 1989 world championship.
"I was more the veteran presence and he was the younger guy at that time," recalled Carlyle with a laugh. "I only had to show him once how to fold the clothes properly and make sure I had the remote."
Carlyle couldn't help but point out how small the hockey community can be.
"It's a crazy game how things come around isn't it," said Carlyle.
While the players aren't overly familiar with the role Shanahan will play, they believe he was hired in an effort to make the franchise stronger and will likely have a strong presence.
"I played with him in Jersey and he was a great teammate," said forward David Clarkson. "He played the game hard. Having him come in will be something great. I've just found out and don't have too many details."
Notes: The Leafs are expected to call up a forward for Saturday's game…G Craig Anderson will get the start for the Senators Saturday. C Mika Zibanejad will not play in the Senators final two games as he will continue to undergo further tests for an undisclosed condition. Jean-Gabriel Pageau is expected to take his place in the lineup. Ottawa C Kyle Turris and D Marc Methot have confirmed that they will represent Canada at the upcoming World Hockey Championships in Belarus. LW Clarke MacArthur also received an invitation from Hockey Canada, but will need to clear up green card issues before making a decision.