I think there's a real, substantive difference between the very, very best, and everyone else. I think amongst the everyone else, it doesn't really matter very much. This is in terms of overall team performance.
What it does do is change the chemistry in the locker room. The actual effect this has on performance is really hard to quantify, though.
This is such a useless answer, but I think it's completely true:
I'm sure that some captains play a greater role than other captains. Some captains are the best player on the team. Some captains exhibit great leadership and are 'heart-and-soul' players. Some are both. Some are neither.
It really depends. But I think as long as you do have solid leadership in your dressing room (regardless of who it comes from; whether that person wears the C or not) and as long as you have solid talent, you've got a good team.
I think that disregarding the formality (ie. Who wears the C) underestimates group dynamics a little bit. Whoever wears the C, whatever the reason for such an assignment, is expected to take the leadership role. If he is good in his role, he can coexist with other leaders in the room, perhaps even relying on them and factually assigning the leadership duties to them. But the others cannot effectively take leadership role without the support of the formal captain.
I love the all the stories here about playing Junior hockey, etc., and then having a definitive opinion on the uselessness of captains at the pro level. Here's the difference between the pros and just about any other level of hockey...the coach's involvement with locker room matters.
Coach's are heavily involved in the player's welfare at just about every non-professional level. They largely provide the leadership, structure, rules, etc. that a team needs to live by in order to be successful. At the pro level, the coaches are a lot more hands off. They're in charge of preparing their team for the next game, they help with roster development, they choose the lineup, etc. But they're not hanging out in the locker room all day, some of them aren't even running practices, and they're largely invisible to the players away from the rink. For all those matters, they depend on the leadership that Captains provide to keep the room together, deal with locker room issues internally, and generally set the tone for the group both at the rink and when they travel.
For those of us that played hockey at even a decent level, our experiences have largely been that the Head Coach is "the guy" that provides the majority of the leadership on a team. But professional coaches don't micromanage their teams like amateur coaches do...they rely on their leadership for some of those things.
Sounds like you have never played a sport outside of a youth or adult recreational league.
Captains are important. Sometimes words are not enough to explain it to someone that has not experienced it first hand.
Not every captain fulfills his/her responsibilities. There are good captains and bad captains. Some captains receive their captaincy for the wrong reasons. See Ovechkin.
A captain is someone who should be looked upon to lead by example. Someone that commands others attention and respect. They don't necessarily have to be the best player, despite the fact that it seems to be a common occurrence in the NHL.
Nonetheless, captains play a important role in all team sports.
But the C on your jersey wont change this... if youre leader and the team looks to you to lead then it doesnt matter if you have a C on your jersey or not.
My opinion of a player isnt going to change because he was named captain. Im not suddenly like 'oh wow I guess maybe I should listen to him now that hes been named captain'.
Leaders matter for sure but the 'Captain' doesnt matter at all. A team would be just as good with no official captain.
As being a leader of the team, who's willing to do what's best for them and be willing to carry the load, so much. The C or A on the jersey is simply the cherry on the top, or a sign of how skilled you are. (The case with many of the teams...)
Captains that lead by example, like Shane Doan, can be a pretty big motivator to a team IMO. On the Isles, I'm a big Mark Streit fan and I think he got a lot of flak this season for having to shake the rust off of missing a season, but I honestly believe the C belongs to Tavares who absolutely busts his ass every shift.