Bears free-agent signees weren’t scared off by 3-13 season

For quarterback Mike Glennon, deciding to sign with the Bears was a gut feeling he had for some time. It was where he could be a starter.

‘‘My wife can attest to that,’’ he said.

Receiver Markus Wheaton said the young team the Bears are building intrigued him. Tight end Dion Sims said he wanted a fresh start. And safety Quintin Demps thought it was important to feel wanted, especially at 31 years old.

The Bears’ free-agent signees — the four players who were introduced Friday at Halas Hall, at least — joined the team for different reasons. Or so they said.

New Bears WR Markus Wheaton. (AP)

The money always matters. Sims, for instance, got $10 million guaranteed. But none expressed any apprehension about joining a team that went 3-13 last season and is in the middle of an obvious rebuilding effort.

In fact, Wheaton (Steelers), Sims (Dolphins) and Demps (Texans) left behind teams that reached the playoffs last season.

‘‘You can’t really just base your decision off what happened last year,’’ Demps said. ‘‘Because every year you either get better or you get worse. For me, it was just more so feeling wanted and wanting to be a part of something where we have the potential to get better every week. I’m looking forward to it.’’

Wheaton shared that mindset.

‘‘I feel like in this league you can be one piece away from winning the Super Bowl, from 13-3 or 3-13,’’ he said. ‘‘That’s just my opinion. To say that it’s a bad team, I don’t think that it’s true. I think [the Bears] have a lot of good pieces. It’s just about filling the holes.’’

And some holes still exist. Just ask general manager Ryan Pace.

‘‘There’s need at different positions,’’ Pace said. ‘‘I don’t want to reveal all that right here and right now. That’s why [free agency] is still ongoing. That’s why we’re still talking about other positions at different levels of free agency and trades, and then we’re talking about the draft.’’

On paper, though, Pace can mark off some boxes.

A new quarterback? Check.

An experienced safety with playmaking skills? Check.

A tight end who excels as a blocker? Check.

A speedy receiver? Check.

An experienced cornerback? Check.

The Bears agreed to terms with veteran cornerback Prince Amukamara on a one-year, $7 million deal before Glennon and the others were introduced.

The Bears have swung and whiffed in free agency in recent years. That includes under Pace, too. Safety Antrel Rolle didn’t work out well in 2015, and receiver Eddie Royal continually struggled with injuries.

Pace indicated steep prices halted the Bears’ pursuit of top free-agent cornerbacks A.J. Bouye, Stephon Gilmore and Logan Ryan.

‘‘It’s important to be disciplined during these time periods,’’ Pace said. ‘‘We come to price parameters and where we think they are, and sometimes it exceeds those. That’s OK, but sometimes it can grossly exceed those, and you’ve just got to be mindful when you’re doing that.’’

As a result, Pace was left to discuss players who will move into Halas Hall as starters but don’t exactly move the needle — at least for now.

There’s nothing wrong with that. Lavish spending rarely equates to success for teams that need so much. The draft is and should be Pace’s focus.

‘‘We want to be responsible during this [free-agency] process and disciplined during this process,’’ Pace said. ‘‘I feel like we’ve done that and we’ve improved our team. I’m excited about the additions.’’