Going back a little ways (and by the way, hit tool? Ty Cobb is in the conversation too, despite the different era), not every team has a capital-C Captain, but every team, every great team anyways, has a leader, occasionally two leaders, that the rest of the team defers to and/or takes their cues from. Sometimes for better and sometimes for worse. It's not always the best player on the team, but they're usually pretty easily identified if you watch enough of their games. Let's look at the last few championships for a minute, to illustrate what I mean:
Royals and Giants.
The Royals took and take their cues from Alex Gordon, no question about it. He's not the best player on their team, but he is the most important. Without Gordon, the Royals identity doesn't work--he's the guy that holds it all together, and makes all the other pieces, some of whom are better or more skilled players than him, mesh together. The Giants leader was Sandoval, and a little bit Bumgarner, though I wouldn't be surprised if Lincecum was still the leader of the staff.
Sox and Cards
The Cards leader is of course Yadi. Nuff said. The Sox are a little more complicated though, and almost have a dual-leadership. Pedroia is the heart and soul of the team, but David Ortiz is, I mean, he's Papi. Everyone looks up to him, and how could you not with what he's done in the Postseason? But even he defers to Pedroia. There were a few other guys on the team with leadership qualities, Napoli and Victorino come to mind, but the key when it comes to a team like that year's Sox, is that there isn't a fight or debate who the leader is--it was (and still is) Pedroia, and that was never in question, one of the reasons this team was able to play and function as successfully as they did. An interesting note that the leaders of the last two teams to win the Series are on the same team now.
Going back a little farther, to the Sox of 2004. Their leaders were probably their 6th or 7th best player, Jason Varitek. Millar got the press for his "we're idiots" thing, but Tek was the leader of that team, no doubt about it. This is a good example though of a team that had lots of players with leadership qualities and potential (Pedro, Derek Lowe, Bill Mueller, Tek, Trot Nixon, Kevin Millar, Ortiz, Manny (yikes), Mike Timlin), but instead of there being confusion over who was in charge, they ended taking on the best parts of all those players personalities, and taking their cues from Tek. An example of a team like this, with lots of potential leaders on it, would be last years Dodgers (Adrian Gonzalez, Hanley Ramirez, Kershaw, Beckett, Juan Uribe, Matt Kemp, Zack Greinke, Puig). The difference though, is that while the Red Sox all took their cues from Tek (who did end up getting the capital-C Captain patch eventually, but that doesn't always mean anything), and he had the ability to rein in any of them when needed but knew when to let them go, the Dodgers didn't have anyone like that. They ended up taking the negative bits from guys like Kemp and Hanley, because there was no one to rein those guys in and keep them on course. Remember Kemp yelling at Puig in the dugout? That's where a captain comes into things, and settles things in way that it doesn't end up lasting and turning into resentment. The Red Sox had, if I'm remembering right, Manny and Youkilis go at it in the dugout, and you know who settled things between them? That's right, Tek. Who settled things between Puig and Kemp? No one. Gonzalez tried to, but the problem is, neither guy felt like they had to respect him, because in the back of their heads both those guys are thinking "No, I'M the leader, not him." And that comes down to respect. This kind of thing doesn't always sink you as a team, of course, but it does handicap you and it really hurts you in the playoffs, when it's more important than ever that everyone is on the same page.
So my point is, yes leadership matters--part of why the Dodgers haven't had the kind of success they expect in the last two or three years is because they had no leader, or the wrong one. It isn't tangible in that you can't qualify it with numbers, and not every good team has the right leader (the Dodgers last year), while not every team with a good leader plays well (the Sox last year), but it is a real and an important thing. It translates to other sports as well. Far be it from me to defend Jeter, I can't stand the guy and he was highly overrated most of his career, but give him credit where credit is due, he was the leader on most if not all five of those championship teams. Which explains why their defense was never great ;)