Player by player is the only way to evaluate this imo.
Gallant Says Schmidt And Theodore Play Best On Right Side; Where's That Leave Coghlan And Whitecloud? - SinBin.vegas
(setting myself up for the Gallant was fired so what does he know, though Theodore still plays the right iirc)
Whatever exception there might be just confirm the rule.
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But seriously though, my impression is that I’ve seen so many players really regress when they are put on the wrong side.
I saw Jonas Brodin play for Minny the other night. People had been hyping him before the deadline. I mean, he was really really solid. This guy was used as an example of someone that could play on the wrong side. It almost destroyed him. He was a wreck for many years. Look what happened to Gostisberre after his rookie year. Will he be able to rescue his career after getting moved to the wrong side? Sergachev should be entering his prime. Everyone, him included, said that he was — better — on the wrong side. He can’t play there and is back on the left.
There are of course pros and cons. But in a few areas it puts the defender in a really tough situation, and teams take advantage of that. Dump the puck in on the D playing the wrong side and hammers him when he has to turn up ice with the back against the ice. There will also be more ugly mistakes that gets to the confidence when you try to stop pucks along the board with the back hand.
This is an issue in the NHL due to how fast the game is. It’s not an issue to the same extent in college and juniors or Europe.