Many things need to go right for a team to 'succeed.' What's more "success" is hard to define in a game in which there is only one winner. Does success mean winning the Cup? does it mean making it into the playoffs? It's more black-and-white than that. If the Wild are going to find success, though, there are a few things that will need to happen regardless of what that success is.
1) Competent Goaltending
Last season Devan Dubnyk was a superhero for the Wild, and they needed him to be. According to War on Ice, even after a month of Dubnyk's Vezina-level goaltending, the Wild's 5v5 Save Percentage was a second-worst 90.7. It's been said before, but the bad run of form for Wild goalies last year was nearly historic in just how bad it really was.
The Wild don't need that iron-man level goaltending this year though. Not yet, at least. All they need from Dubnyk and Kuemper is NHL-average, middle-of-the-road goaltending. Given that, this is a playoff team at worst. Once the postseason begins, goalies decide the result. Last year, Crawford stoned the Wild into a 4-game submission. He did the same one year earlier, despite the Wild being the better team by a fair margin in most other statistical categories. For that matter, the Wild nearly lost in the first round due to Semyon Varlamov being a Vezina- and Jack Adams-level goaltender.
2) The Kids are Alright
The Wild is a team built with aging veterans and up-and-coming kids. They have only one forward in their "prime" age range (Justin Fontaine) and he is getting towards the end of it. They have only two defensemen in their "prime" (Ryan Suter and Nate Prosser) and one of those is Prosser, who's 'prime' is worse than a base-line for most other d-men on the team.
The veterans are known quantities. Koivu will provide a lot of assists and a few goals, Parise will score right around 30 goals, Pominville will be a little below him, etc. Vanek is perhaps the biggest question mark of all the veterans, but he will probably not be winning any awards for point-getting or goal-scoring. Ryan Suter, by the way, would be my other question mark. I'm considering starting the #DriveForFive with Suter- will he reach 5 goals this season? He only got 2 last year... so that would be a 150% increase in production.
Nino Niederreiter, Charlie Coyle, Jason Zucker, and Mikael Granlund are the biggest unknown threats on the Wild. Though they've been around for a few years now, none are in their prime quite yet, and given better situations and better handling by Mr. Yeo, it's not hard to see two of the four becoming 30+ goal scorers in the near future. Erik Haula is another candidate for growth- after wowing people two seasons ago, he had a terrible season last year, and could well rebound and have a solid year. He may never be the top-line speedster he looked in those playoffs, but he could well be a good penalty killing depth-scorer.
Then there's the defensive corps. Jared Spurgeon is arguably the best defender the Wild have, and he is merely 25. Marco Scandella is the same age, and still has room to improve his play. Christian Folin is only 24. Jonas Brodin is 22, and Dumba is 21. The Wild's defensive corps could still be working on their bachelor's degrees, with a few graduate students mixed in! They are the most exciting blue line corps in the league, and still have room for growth.
In short, the Wild have an older core of players, but their young players are very young and we should still see growth out of them. That bodes very well for the future of these players.
3) The Leader of the Pack
The Wild's kids need to improve. Despite some good play last season, if the Wild are going to progress, they need to. The veterans, too, need to lead. I don't mean they need to go out and score a million points (though that would help). Nor do I mean they need to act like certain other "leaders" in the league. Yes, improved production from Pominville is likely, and it would be great if Vanek could knock in more than 21 goals. Koivu, too, could improve on his numbers from last season and it would be great.
More important than that, though, is leadership in behavior. The Wild will lose this season; it's going to happen (even though Parise is on pace for 164 goals and the Wild are on pace to be undefeated). More importantly, the Wild are going to suffer some dirty hits, teams are going to get physical, and referees will not always (or even usually) call things that are in the grey area between "legal" and "against the rules."
It is in times like that that the Wild's leaders need to lead. Rather than get drawn into trying to out-muscle a team like the Anaheim Ducks, the Wild simply need to stick to their game. When the Wild play fast, possession-based hockey they are one of the best teams in the league. When they try to muscle other teams around, they aren't.
I don't mean to say the Wild can't or shouldn't play physically- Charlie Coyle, Marco Scandella, and numerous other Wild players have proven that they can play physically. But it would be hard to argue that the "bruiser style" hockey is the Wild's forte.
A lot of things will need to go right for the Wild to get further in the postseason than they did last year, but it is absolutely possible. If the Wild are going to prove themselves to be the team we think they are, they will need competent goaltending, improvement from their young players, and leadership from their veteran's to do so.