They have some very good pieces in place. On offense, the Patriots have quarterback Tom Brady, dynamic tight ends in Rob Gronkowski and Aaron Hernandez, an emerging 1-2 punch at running back in Stevan Ridley and Shane Vereen, a franchise left tackle (Nate Solder) and guard (Logan Mankins), and a center in Ryan Wendell who is coming off a terrific season.

On defense, Vince Wilfork, Jerod Mayo, Chandler Jones, Dont’a Hightower, Rob Ninkovich, and Devin McCourty are core players, most of whom are expected to remain with the team for some time.

Many teams would love to have that group of bedrock players — it’s a very good group.

But as NFL free agency starts Tuesday at 4 p.m., the stark reality is that when you step back and look at the roster as a whole, the Patriots have a lot of holes to fill if they are to improve on last season, get back to the Super Bowl, and win the franchise’s first title since the 2004 season.

This is not a case of the Patriots being one or two players away from a Super Bowl title, so it would be an upset if the Patriots get in early at the luxury level like they did in 2007 with linebacker Adalius Thomas. The Patriots have significant voids on the depth chart to fill — 14 by my subjective count — so it likely will be more prudent for them to cast a wide free agent net.

Because of poor drafts in 2008 and ’09, specifically, and some misses with free agency/trades, New England is missing a class of players that should have added to its core and made the team formidable across the board.

The good news is that if there was any offseason to be looking for the right pieces for the Patriots, this might be it. While the Patriots prepared well for the flat salary cap era thanks to the sage advice of owner Robert Kraft, many other teams did not. There is more mid-level to good talent available this year in free agency than in recent years, especially in the secondary and at receiver — where the Patriots need the most help. Same goes for the draft, where receiver, safety, cornerback, offensive tackle, and defensive line are deep positions.

So the Patriots have $25 million in cap space and five draft picks for now (both can be added to) to fill out a championship roster. It will be challenging, but certainly is doable.

Two notes before we begin. While the Patriots can gain more cap space with a few moves (not picking up Brandon Lloyd’s option, releasing Daniel Fells, winning an injury grievance against Jonathan Fanene), the amount of cap space a team has is not what a team will spend in free agency.

If the Patriots are planning on extending the contract of any player before free agency next year (McCourty, Ninkovich, and Wendell would be the prime targets), that would come off this year’s cap. A draft class will take up at least $4 million of the cap. Money needs to be saved for emergency in-season moves, and you need some to pay off incentives that could be reached. The past two seasons (even with Brady’s restructure last year at this time that gained the team $7.2 million in cap space), the Patriots ended each year with an average of $6.15 million in cap surplus that was carried over from one year to the next. I expect the Patriots to cut that number in half this year, but it’s a good starting point for how much a team will hold back against the cap.

So, basically all totaled, lop $8-10 million off the $25 million and that’s what the Patriots have to spend right now pending further moves.

The second factor is that player evaluations are in the eye of the beholder. One player might be more talented than another, but the Patriots might prefer the latter. And it’s not just because of a cheaper price tag. Some teams go about only collecting talent in the offseason. The Patriots are in the business of building a championship team. There is a difference, and that’s an understated reason for their sustained success. The Patriots might not have the most talented players across the board, but collectively they are an elite unit.

Now, onto the Patriots’ needs: