Thursday night, however, was a new one even for him.
With the first pick in the NHL All-Star Player Fantasy Draft, Team Chara captain Zdeno Chara made Datsyuk the first selection.
"Never in my life I was picked first," Datsyuk told NHL.com/ru, the NHL's Russian-language site. "Ever since I was a child playing pick-up games outdoors, I was picked closer to the end or dead last."
Datsyuk may have been a sixth-round (No. 171) pick in the 1998 Entry Draft, but no one ranks him near the bottom of anything now. Now in his 10th NHL season, Datsyuk has won three Selke trophies, four Lady Byng trophies and a pair of Stanley Cups. Currently tied for third in the League with 53 points, he's a major reason the Wings entered the All-Star break sitting atop the NHL standings.
2012 NHL ALL-STAR GAME
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"Thank you very much to my captains and teammates for the confidence in me," said Datsyuk. "Finally I know what guys feel and experience when they get picked that early."
Datsyuk might have been surprised to hear his name called first -- especially surrounded by some of the game's best players -- but Chara said he knew exactly who he wanted with his first pick.
"I think it's pretty obvious that he's an unbelievable player," Chara told reporters Thursday night. "I really admire the way he plays the game, the way he acts on and off the ice. It was my individual goal to get him first, and I was happy that I could have done it."
Datsyuk also will get the chance to skate on a team with countryman Evgeni Malkin, Team Chara's third selection.
"It was great news," he said. "Until this year I have participated in this game twice and never had a chance to play with a countryman on the team."
He did, however, say he would have liked to see another of his fellow Russians in Ottawa - Alex Ovechkin, who opted not to attend All-Star Weekend in the wake of his three-game suspension for a charging incident in a game last Sunday.
"Of course he is missed here," said Datsyuk, "but I think he will have many more of these All-Star experiences ahead of him."
At 33 and healthy again after injuries limited him to just 56 games last season, Datsyuk also should have many All-Star experiences ahead of him. However, he can see the advantage to taking a few days in the middle of the season to rest.
But when he thought about it, he knew he'd have too much fun to pass on the trip to Ottawa.
"From one side we are losing some rest, but from another it is a great source of motivation for me," he said. "It's great to be able to hang out with some guys that you are always playing against and to play with them on the same team. And most importantly it is great because of the fans that are here and the atmosphere that they create. I always enjoy the fans during those events."
One of those events is the 2012 Molson Canadian NHL All-Star Skills Competition, which will be held Saturday (7 p.m. ET, NBCSP, CBC). Which event would Datsyuk want to partake in?
"I don't see myself anywhere," he said. "I just want to observe my teammates at it and enjoy it."