The Hockey Hall of Fame formally welcomed five new inductees Monday night — players Chris Chelios, Brendan Shanahan, Scott Niedermayer, and Geraldine Heaney, and coach Fred Shero in the “builder” category.

With the Class of 2013 now official, we can start looking ahead to 2014 and beyond. So here are a dozen names eligible for next year’s vote, and my best guess at their chances.

Dominik Hasek

Eligible since: New in 2014

The case for: Hasek was the undisputed best goalie in hockey for a long stretch in the late ’90s, and he belongs in the discussion as the greatest of all time. He won six Vezina Trophies as the league’s best goaltender and is the only goalie in NHL history to win multiple MVPs. He has the highest career save percentage in history. He single-handedly won the gold medal for the Czech Republic in 1998. I could keep going, but it would be overkill.

The case against: He didn’t become a full-time starter until his late twenties, so his career totals in counting stats like wins are less impressive than you might expect. His style could be called “unorthodox” if you were being polite, or “completely insane” if you weren’t. He played professionally until he was 46, making you feel bad about never using your treadmill.

Odds he gets in next year: 97 percent, only because there’s still a 3 percent chance he launches another comeback before then.

Odds he gets in eventually: 100 percent

Bottom line: He’s a lock. Have fun deciphering his induction speech.

Eric Lindros

Eligible since: 2010

The case for: For a time, Lindros was the most feared player in hockey. He won the Hart Trophy in 1995, and there was a time when winning even one Hart all but guaranteed induction — of eligible winners since 1924, only two aren’t in the Hall of Fame. He also played in six All-Star games. Despite playing his entire career in the dead puck era, Lindros’s 1.14 career points per game lands him in the top 20, and every eligible player ahead of him is in the Hall except for Kent Nilsson (who played in the high-flying ’80s).

The case against: His career was derailed by injuries, he played at least 75 games in a season only once, and he was out of hockey by 34. That means his overall career totals aren’t especially impressive. He (and his family) had a reputation for being incredibly difficult to deal with dating back to his days in junior, which probably shouldn’t matter but does.

Odds he gets in next year: 20 percent

Odds he gets in eventually: 50 percent

Bottom line: Lindros might be the most interesting case out there. His career was cut short by injuries, but you could say the same for Pavel Bure and Cam Neely, and they made it in. We understand concussions much better than we did a decade ago, so the knock against Lindros for being soft or “playing with his head down” has faded. At his peak, there was nobody better. He’d have my vote, but so far the committee hasn’t felt the same.

Peter Forsberg

Eligible since: New in 2014

The case for: He was a three-time first-team All-Star, two-time Cup champion, and won the Calder, Art Ross, and Hart. He was also an excellent two-way player, and his 0.9 career assists per game ranks him behind only Wayne Gretzky, Mario Lemieux, Bobby Orr, and Sidney Crosby.

The case against: He couldn’t stay healthy. Despite multiple comebacks, he played just 708 career games, so his overall numbers aren’t impressive.

Odds he gets in next year: 70 percent

Odds he gets in eventually: 90 percent

Bottom line: Forsberg’s case for induction is eerily similar to Lindros’s, especially when you consider they began their careers by being traded for each other. Yet Forsberg seems like a much safer bet to make it in, probably in his first year of eligibility. That’s partly because of his two-way game, partly because of his two rings, and partly because he made it through his career without making anyone hate him. My prediction is that he makes it in next year, which clears a path for Lindros in 2015.

Pat Burns

Eligible since: 2010

The case for: He’s the only three-time winner of the Jack Adams Award as the NHL’s best coach, and he did it with three different teams. He won the Stanley Cup with the Devils, and he’s a member of the 500-wins club.

The case against: Nobody’s really sure, but there must be one since he’s been passed over four times. The Hall of Fame is funny about coaches — Shero was eligible forever but didn’t make it until last year, and Mike Keenan’s 672 wins don’t even seem to get him into the discussion. And coaches are grouped into the “builder” category, which is limited to just one or two honorees per year. Still, the all-time leader in Jack Adams awards being passed over four years in a row? Indefensible.

Odds he gets in next year: 50 percent

Odds he gets in eventually: 75 percent

Bottom line: Burns, who died in 2010, has to get in eventually. But his repeated snubs have become an annual story, and when you’re dealing with an induction committee that can be downright stubborn, that might not be helping him.

Mike Modano

Eligible since: New in 2014

The case for: Modano recorded 561 goals and 1,374 points over a 21-year career. He ranks 23rd all-time in points, and every eligible player ahead of him is already in. Seven-time All-Star. Won a Stanley Cup. Is the greatest player in Minnesota/Dallas franchise history, and arguably the greatest American forward of all time.

The case against: Was very good for a long time, but you could argue he was rarely elite. He never had 100 points or won a major award, and he was only a postseason All-Star once. Had trouble with a stretcher.

Odds he gets in next year: 75 percent

Odds he gets in eventually: 90 percent

Bottom line: Modano won’t be a slam dunk, but his point total (and, if we’re being honest, his passport) should be enough to get him in, probably on the first ballot.

Chris Osgood

Eligible since: New in 2014

The case for: He’s a three-time Cup champion and one of just 10 members of the NHL’s 400-wins club.

The case against: Was never really considered an elite goalie (he played in just two All-Star games, never won a Vezina, and only had a top-five save percentage once). The knock against Osgood has always been that he was a good-but-not-great goalie who was lucky enough to play most of his career behind excellent Red Wing teams.

Odds he gets in next year: 10 percent

Odds he gets in eventually: 30 percent

Bottom line: Osgood’s case basically comes down to how you feel about wins and championships. If you believe they’re a good way to judge a goaltender, he’s pretty much a lock. If you believe they’re basically team-based accomplishments that goalies shouldn’t get extra credit for, he’s nowhere close. Keep an eye on this one; it has a chance to turn into the NHL’s version of the Jack Morris debate.

Mark Recchi

Eligible since: New in 2014

The case for: Recchi was one of the most prolific scorers of the 1990s, and that — combined with his freakish longevity — allowed him to pile up the counting stats. His 1,533 career points rank him 12th all time. Not only is everyone ahead of him already in, but they were all slam dunks, so you could argue that Recchi should be too.

The case against: Even in his prime, he was rarely if ever described as a future Hall of Famer the way so many star players are. He never won an award or was named a first-team All-Star, though he did play in seven All-Star games and finished in the top five in scoring three times.

Odds he gets in next year: 50 percent

Odds he gets in eventually: 80 percent

Bottom line: I’m not sure Recchi ever “felt” like a Hall of Famer, but his numbers are just too good for him not to make it eventually. The question will be whether the committee makes him wait a few years.

Curtis Joseph

Eligible since: 2012

The case for: Joseph is the fourth-winningest goalie in NHL history. He led the league in goalie point shares three times and was second twice; that’s not a stat a lot of people put much stock in, but it does point to him being one of the league’s best goalies for much of his career.

The case against: Despite a knack for single-handedly stealing playoff series, he never won a Stanley Cup. He also never won the Vezina, though he was a finalist twice. His win totals were largely a result of longevity, and he also ranks second all time in career losses. He’s already been passed over twice, so clearly the current committee isn’t sold.

Odds he gets in next year: 5 percent

Odds he gets in eventually: 25 percent

Bottom line: Joseph is basically Osgood with more wins and a slightly higher peak, but no Cups. It’s possible that Osgood getting in could lead voters to take another look at Joseph someday.

Dave Andreychuk

Eligible since: 2009

The case for: Andreychuk scored 640 goals, making him the only eligible member of the 600-goal club who’s not already in. He underwent a fascinating late-career transformation from one-dimensional goal scorer to defensive specialist. He captained the Stanley Cup–winning Lightning in 2004 and hilariously hugged Gary Bettman.

The case against: For reasons I’ve never fully understood, Andreychuk’s candidacy has never seemed to receive much support. That’s partly because he’s another one of those “good for a long time but never great” guys, and probably also because of the way he bounced from team to team so much in the second half of his career.

Odds he gets in next year: 5 percent

Odds he gets in eventually: 20 percent

Bottom line: The almost total lack of buzz around Andreychuk’s candidacy would seem to indicate he has no chance, but it’s not unheard of for a player to be passed over year after year before suddenly getting the call. Mark Howe recently went in after a 13-year wait, and it’s possible that Andreychuk could follow a similar route.

Rob Blake

Eligible since: 2013

The case for: Blake was one of the most consistent defenseman of his generation. He was a seven-time All-Star and won the Norris in 1998.

The case against: Blake did everything well, but didn’t have that one trademark that defensemen often need to get in. He didn’t quite hit like Scott Stevens, or skate like Paul Coffey, or shoot like Al MacInnis. His 777 career points ranks in the top 20 for defensemen, but behind guys like Doug Wilson and Gary Suter who didn’t make the cut.

Odds he gets in next year: 20 percent

Odds he gets in eventually: 40 percent

Bottom line: Blake’s a tough call, and you could really see it going either way. He’s a long shot in any year with a lot of top candidates, but could sneak in as part of a thinner class.

Phil Housley

Eligible since: 2006

The case for: Housley ranks fourth all time in scoring among defensemen, trailing only Ray Bourque, Coffey, and MacInnis, who are all in. He put up some excellent offensive years, including an eye-popping 97-point season in 1992-93. He was also one of the best American players of the 1980s.

The case against: His offensive numbers often came at the expense of any particular attention to defense. In fact, it wasn’t unusual to hear him referred to as a fourth forward, which was not meant as a compliment. He was a career minus-53, and though plus/minus is a generally useless stat, that still stands out badly when you look at the numbers that most Hall of Fame defensemen put up.

Odds he gets in next year: 5 percent

Odds he gets in eventually: 20 percent

Bottom line: Housley’s been eligible for a long time and hasn’t got the call yet, which would ordinarily be a bad sign. Any buzz around his candidacy seems to have died down, so it would be a surprise to see him get in at this point.

Jeremy Roenick

Eligible since: 2012

The case for: His career numbers are good enough to get him into the discussion, with 513 goals and 1,216 points. He was one of the most popular players of his generation and was named to nine All-Star games. He was also one of the most entertaining personalities the league has ever seen, which won’t hurt his chances. He made heads bleed.

The case against: While his career stats are good, they’re far from sure-thing numbers. He never won a major award. He also never won a Cup, which is a bit of a sore spot.

Odds he gets in next year: 10 percent

Odds he gets in eventually: 40 percent

Bottom line: Roenick is a borderline candidate who probably won’t get the call in a stacked year like 2014, but I like his chances down the road.