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NHL coaching staffs think about matchups on the ice from shift to shift, game to game, practice to practice. Those matchups tend to be focused on which line of three forwards is facing which line from the opponent. It further includes attempting to get the best defenders on ice to combat the foe's top scorers.
But there is a whole different sort of matchup when young hockey players pick up a stick. Do you shoot right or left? Then, later, as players develop and progress, if you play on the wings or defense, to play the right or left position?

"You just pick up a stick and whatever hand you are, you are," said right-handed, left-shooting center Matt Duchene to Denver Post reporter Mike Chambers in 2015 when the Nashville forward was then playing for the Colorado Avalanche. "Most right-handed throwers are left-handed shots because you steer the stick with your top hand. "
Uh, yes but no, or maybe? Right-shooting Avs center Nathan MacKinnon, the paused NHL's fifth-leading scorer, has a dominant right hand. His dominant hand is the lower hand on the stick: "Right away, it just felt right, shooting right," MacKinnon said.

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Ryan O'Reilly, the 2019 Stanley Cup Final most valuable player, says he "did what was naturally comfortable. He throws a ball right-handed but plays hockey and golf as a lefty. He admits to being influenced by his lefty hockey shooter older brother, Cal, while they both idolized Wayne Gretzky, the NHL's all-time leading scorer and fellow left-handed shot. Cal O'Reilly has played 145 NHL games and 719 American Hockey League games during his 14-season career.
For his part, Gretzky plays golf right-handed-mostly because he first attempted the sport with right-handed clubs-and throws a baseball right-handed. Alex Ovechkin, the NHL star chasing Gretzky's all-time goals record, shoots his deadly floating, dipping, speeding shot right-handed and throws a baseball left-handed.
Some left-right stats: Roughly 60 to 70 percent of NHL players are left-handed shooters, depending on the season. Six of the NHL's top 10 current scorers are lefty shots, but three of the top five goals leaders shoot right-handed. Duchene, for one, says right-handed shooters have a goal-scoring advantage because most NHL goalies handle their sticks right-handed. Players agree the non-stick, catch-glove hand usually provides a bit more room to shoot to empty space.
At the NHL level, the left-right matchup extends to positions played. There are prolific scorers such Tampa Bay's Nikita Kucherov and Chicago's Patrick Kane, both left-handed shooters who play right wing. Yet, Boston's right-handed shot David Pastrnak, the league's leading goal scorer and third overall in scoring, plays on the right wing or what hockey observers call his "natural side."

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Kane played and starred as a left wing in juniors but his surefire Hockey Hall of Fame NHL career has featured his goal-scoring and playmaking skills skating up at right wing. He's been versatile enough to play some left wing on a line with two other future Hall of Famers, Jonathan Toews at center and the retired Marian Hossa at right wing. Hossa and Kane typically played on separate lines; both are left-handed shooters.
One reason Kane lights the right-side lane is he has a signature move entering the offensive zone in which is goes toward the goal line fairly deep then curls to his stickhand side for a player trailing the rush. As a left wing, the same move would require a backhand shot from Kane.
On the other hand-ok, pun intended-some wings and their coaches prefer players to to play their natural side - right shooters on the right, left shooters on the left - because they can carry the puck along the boards and away from defenders. Other wings and their coaches argue to lefties have a better shooting angle on the right side and vice versa for righties. Alex Ovechkin scores lots of his 706 NHL goals from the left-side faceoff circle, nicknamed his "office" because he scores power play goals on "one-timer" shots synchronized to shoot the puck as soon as the pass arrives.
The final right-left matchup and ensuing debate is whether NHL coaches and general managers prefer their defensive pairings to have a left-hander on the natural left side and same for righty on the right side. On average, about 60 percent of the league's defensemen are left-handers.

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"We prefer to have guys on their strong sides as defensemen," Penguins coach Mike Sullivan said earlier this to Seth Rorabaugh of the Pittsburgh Tribune-Review. "It helps going back for pucks. You're always on your forehand. You have the ability to change the point of attack on your forehand, make that (defense-to-defense) pass. It puts guys in more advantageous positions."
Sullivan's boss and Pittsburgh GM Jim Rutherford concurs that "you see the [positive] difference in our team" when the top three defensive pairs each have a right and a left-hander.
Barry Trotz, the New York Islanders coach, says he and his coaching colleagues have to look for special players who can handle the off-handed side on defense. When you get the statistically more probable lefty and lefty defensive pairing, Trotz says the lefty on right side "loses about a third of the ice offensively" and that passing between the defensive partners requires "the ability to contort" by off-handed defender.
As a result, NHL GMs are typically looking to balance out their right- and left-handers on defense, through drafts, trades and locking up top-performing right-handed defensemen. Rorabaugh of the Pittsburgh Tribune-Review did some digging to find 11 of the league's most highly paid defensemen are right-handed, including San Jose's Erik Karlsson ($11.5 million salary cap hit), Los Angeles' Drew Doughty ($11 million) and New Jersey's P.K. Subban at the 1-2-3 spots.