INDIANAPOLIS -- Changes are coming this offseason for the Indianapolis Colts. They had to be, with the team finishing with its first losing record since 2011.

The Colts fired Chuck Pagano after six seasons on Sunday, giving general manager Chris Ballard his first chance to hire a head coach.

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Finding a new coach, particularly if all indications are that Andrew Luck (shoulder) will be ready for the 2018 season, shouldn’t be a problem for owner Jim Irsay and Ballard. But it isn't about finding just any coach. It's about finding one who shares a vision with Ballard, who has made it clear that he wants to build the roster through the draft and that it isn't all about Luck.

Who will lead the coaching search: Ballard or Irsay?

Do the Colts go with an offensive-minded coach to help Luck, who could be looking at his fourth offensive coordinator in seven years?

Do they go with a defensive coach to try to lead a unit that has consistently been one of the worst in the NFL in recent years while he hands the offense to the offensive coordinator?

Do they go with a coach who wants a big role in personnel decisions?

Those are some of the things the Colts will have to think about. With that in mind, here's a look at possible candidates:

Kansas City special-teams coach Dave Toub. Ballard and Toub worked together in Chicago and Kansas City between 2004 and 2016. Hiring Toub would mean the Colts need a strong offensive coordinator to pair with Luck because Toub has been a special-teams coach throughout his NFL career.

New England offensive coordinator Josh McDaniels. McDaniels is a big reason the Patriots have routinely had one of the league's best offenses. You have to believe McDaniels learned his lesson when it comes to being a head coach after going 11-17 with Denver in 2009-10. But you also have to wonder how much of McDaniels' success as a coordinator is because of Tom Brady, one of the NFL's all-time great quarterbacks.

Michigan coach Jim Harbaugh. He spent four seasons as coach of the San Francisco 49ers and led them to a Super Bowl appearance. Harbaugh knows Luck well after coaching him at Stanford, and familiarity with Luck would help if the quarterback is adjusting to another offensive coordinator. Harbaugh, who played four seasons at quarterback in Indianapolis, is also the type of flashy name who would draw Irsay's attention.

Jon Gruden. ESPN’s Adam Schefter reported last January that, with Pagano’s job status in limbo, Irsay reached out to the former Tampa Bay coach and current ESPN Monday Night Football analyst to gauge his interest in returning to coaching. Gruden would be the best offensive coach Luck has had arguably since Bruce Arians was offensive coordinator in 2012. But the Raiders are reportedly making a push to bring Gruden back to coaching.

Minnesota offensive coordinator Pat Shurmur. Shurmur was only 9-23 as coach of the Cleveland Browns in 2011-12. But you can’t dismiss the job he has done with Case Keenum as his quarterback, and without having rookie running back Dalvin Cook for most of the season in Minnesota. The Vikings have a top-10 offense.

Philadelphia offensive coordinator Frank Reich. The former Buffalo Bills quarterback has helped make the Eagles one of the NFL's top three offenses this season. What makes Philadelphia’s offense impressive is that its running game is second in the league and its passing game is eighth. The Colts will always be a pass-first offense, but it would help if they had more balance.

Editor's note: This story was originally published on Dec. 23 and has been updated with news of Pagano's firing.